Temperature and pressure limits of guanosine monophosphate self-assemblies

Guanosine monophosphate, among the nucleotides, has the unique property to self-associate and form nanoscale cylinders consisting of hydrogen-bonded G-quartet disks, which are stacked on top of one another. Such self-assemblies describe not only the basic structural motif of G-quadruplexes formed by, e.g., telomeric DNA sequences, but are also interesting targets for supramolecular chemistry and nanotechnology. The G-quartet stacks serve as an excellent model to understand the fundamentals of their molecular self-association and to unveil their application spectrum. However, the thermodynamic stability of such self-assemblies over an extended temperature and pressure range is largely unexplored. Here, we report a combined FTIR and NMR study on the temperature and pressure stability of G-quartet stacks formed by disodium guanosine 5′-monophosphate (Na25′-GMP). We found that under abyssal conditions, where temperatures as low as 5 °C and pressures up to 1 kbar are reached, the self-association of Na25′-GMP is most favoured. Beyond those conditions, the G-quartet stacks dissociate laterally into monomer stacks without significantly changing the longitudinal dimension. Among the tested alkali cations, K+ is the most efficient one to elevate the temperature as well as the pressure limits of GMP self-assembly.


Results and Discussions
Concentration-dependent self-assembly. In the planar G-quartets, hydrogen bonds are formed between N1-H and N2-H as H-donors and O6 and N7 as H-acceptors, whereas dimer formation is based on hydrogen bonds between N1 and O6 (Fig. 1a). Hence, significant shifts and absorbance changes of infrared (IR) bands in the region of 1700-1500 cm −1 characteristic of the guanine base can be observed upon 5′-GMP self-assembly 52 . Figure 1b displays concentration-dependent Fourier-transform infrared (FTIR) spectra of Na 2 5′-GMP at pH 8. The band at  v max = 1657 cm −1 has been assigned to the C6=O6 stretch vibration of guanine. Upon 5′-GMP self-association, the carbonyl band is blue shifted to  v max = 1673 cm −1 and becomes sharper. Simultaneously, the ring vibrations of guanine including C=C and C=N stretch vibration are also affected by base pairing and stacking of 5′-GMP, i.e., an intensity increase of the bands at  v max = 1592 cm −1 and 1537 cm −1 as well as an intensity decrease of the bands at  v max = 1582 cm −1 and 1568 cm −1 . Further, we followed the self-assembly of Na 2 5′-GMP via dynamic light scattering (DLS) and obtained qualitative information about the size distribution of 5′-GMP aggregates (Fig. 1c). The cylinder diameter of monomeric and tetrameric 5′-GMP aggregates are approximately 1 and 2.6 nm, respectively 32 . The length of the cylinder is defined by (n − 1) × 0.34 nm, where n is the number of quartets in the stack. At a concentration of 0.12 M and pH 8, our FTIR and DLS data indicate that Na 2 5′-GMP does not form stacks of dimers or quartets, but non-hydrogen-bonded aggregates, thus very likely monomeric stacks are present only. These findings are in agreement with literature data 32 . Starting from 0.24 M, initial formation of larger hydrogen-bonded 5′-GMP assembled species can be observed. They coexist with the monomeric stacks and their presence increases with the concentration of Na 2 5′-GMP ( Fig. 1a and c). To further characterize those assemblies, we applied 1 H nuclear magnetic resonance (NMR) spectroscopy. Upon self-association of 5′-GMP, ring-current and electrostatic effects induce upfield and downfield shifts of the H8 signal 30 . The four peaks of the H8 region located between 7.1 and 8.6 ppm of the 1 H NMR spectrum have been assigned to monomeric, dimeric and tetrameric species of 5′-GMP (Fig. 1d) 34,53 . The "outer" peaks at 8.5 and 7.2 ppm (H α and H δ ) with equal intensities are attributed to tetrameric 5′-GMP with either a C2′-endo or a C3′-endo sugar pucker conformation. The H γ peak at 7.9 ppm indicates monomeric 5′-GMP, whereas the H β peak at 8.2 ppm corresponds to dimeric 5′-GMP. By integrating the H8 signals, we could quantify the population distribution for the self-assembly of Na 2 5′-GMP (Fig. 1e). At a concentration of 0.48 M, more than 50% of the 5′-GMP molecules participate in forming G-quartet stacks. Only about 22% of the nucleotides are in the short-lived dimeric state 34 . Previous NMR diffusion experiments have revealed that the number of stacks increases with the nucleotide concentration 32 . Thereby, Wong et al. found the mechanism of stacking to be the same for monomers and G-quartets 32 . Hence, the channel cation in G-quartet stacks might be less needed for stacking, but rather to neutralize the electrostatic repulsion of the O6 atoms of the G-quartets. Furthermore, we found the concentration dependence of the Na 2 5′-GMP self-assembly to be affected by temperature (Suppl. Fig. S1), in good agreement with literature data 32 . While initial hydrogen-bonded self-assembly is observable at 0.24 M Na 2 5′-GMP and 282 K, the critical concentration is increased to 0.48 M at 296 K, indicating high entropic costs for the self-association.
Thermal Stability of 5′-GMP self-assemblies. Previous NMR diffusion experiments have demonstrated that the stacking behaviour of G-quartets and thus the length of the stacks are not modulated by temperature in the range between 278 and 298 K 32 . To yield information about the thermal stability of the hydrogen bonds formed in dimers and G-quartets of 5′-GMP, we performed temperature-dependent FTIR measurements for 0.48 M Na 2 5′-GMP at pH 8 (Fig. 2). IR spectra of both the carbonyl band and the ring vibrations change markedly with increasing temperature, indicating dissociation of the dimers and G-quartets (Fig. 2a). Upon temperature increase, the carbonyl band shifts from 1673 to 1657 cm −1 and broadens. In the case of the ring vibrations, the band intensities at 1592 and 1537 cm −1 decrease at elevated temperatures, whereas the bands at 1582 and 1568 cm −1 show increased intensities and slight red shifts. To better describe the "melting" behaviour, we plotted the band intensities at 1673, 1592, 1568 and 1537 cm −1 as a function of temperature (Fig. 2b). The "melting" curves follow the same course, indicating that any of those bands can be used to follow the self-association of 5′-GMP. Assuming an apparent thermodynamic equilibrium between all the hydrogen-bonded and the monomer stacks, a global Boltzmann fit of the IR data was performed. We obtained a melting temperature of T m = 281 ± 2 K and a standard-state van't Hoff enthalpy change of ∆H vH 0 = 124 ± 8 kJ mol −1 for the dissociation reaction of Na 2 5′-GMP. In this thermodynamic model, the contribution of 5′-GMP monomers not participating in the self-association reaction, are not considered in the initial plateau values. Using 1 H NMR, we obtained comparable trends by analyzing the temperature-dependent population distribution of the monomer, dimer and G-quartet species (Fig. 2c). Although ab initio calculations have assigned the Watson-Crick faced guanine dimer (GG3 2 ) to be the most stable homo base pair 54 , it is less thermally stable compared to the cation-templated G-quartet. Furthermore, our temperature-dependent DLS measurements suggest that temperatures up to 348 K induce only the dissociation of hydrogen bonds and do not affect the stacking behaviour (Suppl. Fig. S2). The hydrodynamic size of the monomer stacks is hardly changed by the temperature. Taken together, our data reveal that the stacking interaction involved in 5′-GMP self-assembly can withstand a wide range of temperatures, whereas the base pairs are only stable at low temperatures. In an entropy-centered view, the favourable stacking interactions at high temperature can be explained by the hydrophobic effect and thus an entropy gain due to water release, whereas the G-quartet formation is accompanied by conformational entropy loss and thus becomes unfavourable with increasing temperature.
Effect of pressure on 5′-GMP self-assembly. Pressure acts on molecular systems through changes in specific volume that are due to changes in hydration and packing efficiency 55 . According to Le Châtelier's principle, conformations occupying smaller volumes and processes for which the transition state has a smaller volume than the ground state are favoured under high pressure conditions 56 . In the case of proteins, pressure favours conformations that minimize solvent-excluded void volume and causes water filling of hydrophobic cavities/ voids. Furthermore, pressure leads to greater hydration of polar/charged amino acids, resulting in attenuation of ionic interactions 56 . Therefore, pressure is particularly sensitive to changes in hydration as the density of hydration water around charged residues is higher than that of bulk water 57 . Interestingly, conformations and configurations of DNA duplexes have been demonstrated to be relatively unaffected by pressure perturbation [58][59][60][61] , whereas an intramolecular, antiparallel DNA G-quadruplex structure has been reported to be more pressure-sensitive 62 . To study the pressure effect on the self-assembly of 5′-GMP, we first applied pressure-dependent FTIR measurements at various temperatures (Fig. 3). Upon pressurization, a blue shift of the IR bands is observable and can be explained by the pressure-induced compression of the bond lengths (Figs 3a and S3) 63 . Due to this intrinsic elastic pressure effect on the vibrational frequency, we decided to consider the IR band at ~1537 cm −1 for further analysis and plotted the absorbance intensity of the band maximum as a function of pressure (Fig. 3b). Again, we obtained an intensity decrease suggesting pressure-induced dissociation of the hydrogen-bonded species. However, the pressure-induced disassembly is less pronounced compared to the thermal-induced dissociation. At 278 K, dissociation could not be completed upon pressurization up to 1200 MPa. When the thermal disassembly is nearly complete at 308 K, no further pressure-induced assembly or disassembly of G-quartets is observable. Complementary high pressure 1 H NMR measurements confirm that pressure populates the monomeric state (Figs 4 and S4). Upon pressurization up to 240 MPa, the tetrameric fraction is reduced from 56% to 26%, whereas the dimeric fraction diminishes from 22% to 11%, indicating that the G-quartets and the rather thermally unstable dimers feature similar pressure stabilities (Fig. 4b). The standard-state free energy change for the disassembly process of 5′-GMP, ∆G D 0 , was calculated from the mole fractions of monomeric and hydrogen-bonded species and plotted as a function of pressure (Fig. 4c). The pressure-dependence of ∆G D describes the standard molar volume change for the disassembly process of 5′-GMP, ∆V D 0 . We obtained ∆V D 0 = −18 mL mol −1 at 278 K. The corresponding transition pressure value, p m , is 164 MPa (at ∆G p ( ) D 0 m = 0). ∆V D 0 increases, whereas p m decreases with elevated temperature (Suppl. Fig. S4). To address the question whether the length of the stacks and thus the stacking interaction is affected by pressure, we performed pressure-dependent small-angle X-ray scattering (SAXS) and diffusion-ordered NMR spectroscopy (DOSY). Owing to the high polydispersity within the system, as stacks of monomers, dimers and G-quartets are present in equilibrium, the SAXS data are interpreted in a qualitative manner, only. The overall high intensities of the scattering profile indicate the existence of large species (Fig. 5a). Upon pressurization, a slight decrease of the scattering intensity can be observed at 280 K, whereas the scattering profile at 308 K is marginally changed with pressure, suggesting that the longitudinal dimension of the monomer stacks is hardly affected by pressure. Complementary 1 H DOSY NMR experiments yielded the molecular translational diffusion coefficients, D t , of stacks formed by 5′-GMP monomers and G-quartets as a function of pressure (Fig. 5b). The D t values reveal that the stacking interaction and thus the longitudinal dimension of the G-quartet stacks are pressure-resistant up to about 240 MPa, independent of temperature. In contrast, at low temperature the number of stacks for 5′-GMP monomers is even increased with pressure, indicating dense packing of such assemblies.
Overall, our results show that pressure increases base stacking and induces lateral dissociation of dimer and G-quartet stacks of 5′-GMP into monomer stacks (Fig. 5c). In general, high pressure studies on DNA duplexes have revealed that pressure decreases the extent of charge neutralization by cations, reduces the Watson-Crick hydrogen-bond distance and favours base stacking, but leads to a very small net effect on the stability and conformation 58,59,64 . The attenuation of electrostatic interactions is explained by greater hydration of the cations and the phosphate groups under high-pressure conditions (electrostrictive effect). Consequently, the electrostatic repulsion between adjacent, negatively charged phosphates is also decreased, favouring stacking of neighbouring bases 64,65 . Stacking of aromatic compounds has been shown to be accompanied by a negative volume change and is thus favoured at elevated pressures 66 . In case of the 5′-GMP self-assembly, the observed pressure resistance of the longitudinal dimension and thus the stacking interaction can be explained by the same mechanism. In the liquid-crystalline phase, where the 5′-GMP quartet stacks are hexagonally arranged, the stacking distance has been shown to be decreased upon compression 67 . Further, an acidic shift of the water pH upon pressurization would lead to partial protonation of the doubly charged phosphate groups, thus reducing the electrostatic repulsion between adjacent guanine bases 68 . In contrast, the typical pressure-induced strengthening of hydrogen bonds does not lead to a stabilization of the G-quartet structure, but rather a dissociation at elevated pressures. This finding suggests a volume increase upon G-quartet formation, which is unfavourable under high pressure conditions. The distance between the diagonal O6 atoms in the G-quartet is approximately 5 Å and the eight inwardly pointing guanine O6 atoms of two adjacent G-quartets span a volume of 40 Å 3 38 . The Na + ion has a diameter of 1.9 Å and a volume of 3.6 Å 3 . As the central channel formed by G-quartet stacks is only occupied by dehydrated cations and very few water molecules (diameter d = 2.75 Å) 69 , it is reasonable to assume that a significant number of water-inaccessible voids is present in the G-quartet stacks. Those voids will disappear upon dissociation of the G-quartet structure. Further volume reduction can be obtained from rehydration of the Na + ions and the nucleobases after release from the channel, as the density of the hydration water is higher compared to that of bulk water 57,70,71 . Elimination of void volume, though of much lesser extent, in the dimer stacks upon pressure-induced formation of monomer stacks explains their pressure sensitivity as well.
Effect of alkali salt on the thermal and pressure stability of 5′-GMP self-assemblies. In a very elegant approach, using NMR titration experiments Wong and Wu have shown that the channel Na + ions bound to the G-quartet stacks are replaced by K + and Rb + ions in a competitive equilibrium, whereas the Na + ions bound to the peripheral phosphates remain unaffected 38 . This allows us to explore the thermal and pressure stability of 5′-GMP quartet stacks when the channel Na + ions are gradually replaced by K + and Rb + , respectively. Hence, we added increasing amounts of additional MCl to 0.48 M Na 2 5′-GMP. First, we performed temperature-dependent FTIR experiments and studied the thermal stability of the hydrogen-bonded 5′-GMP self-assemblies in the presence of the alkali salts, MCl = NaCl, KCl and RbCl (Suppl. Fig. S5). The IR bands assigned for guanine are not affected by the alkali salts, indicating that additional structures are not formed. The "melting" curves reveal that all three alkali salts are able to increase the thermal stability of the hydrogen-bonded 5′-GMP self-assemblies (Fig. 6a). While the melting temperature, T m , in the presence of additional NaCl is only slightly increased, additional KCl causes a concentration-dependent stabilization of G-quartets against temperature, indicating gradual replacement of the channel Na + by K + (Fig. 6b). In contrast, the addition of RbCl induces a moderate stabilization, which seems to be concentration-independent. RbCl could be tested only up to 0.2 M due to precipitation of 5′-GMP at higher concentrations of RbCl. The stabilization effect of these alkali cations follows the affinity order K + > Rb + > Na + found for the channel site 38 , confirming the hypothesis that the channel cation determines the thermal stability of the G-quartet structure 38 . To examine the effect of the alkali salts on the  (Figs 6 and S6). We found KCl to be most effective against pressure-induced dissociation of G-quartets. At 240 MPa and 278 K, the population distribution is 40% G-quartets, 16% dimers, and 44% monomers (Fig. 6c). This is consistent with our complementary FTIR results revealing a stabilization trend of K + > Rb + > Na + (Fig. 6d). This stabilization sequence against pressure can be explained by the concept of optimal packing. The K + ion has a diameter of 2.66 Å and occupies consequently a larger volume of the channel cavity leading to reduced voids. Furthermore, owing to its low charge density and slightly hydrophobic nature 72 , K + is very likely less densely hydrated and thus the volume reduction upon rehydration would be less compared to Na + . Both contributions result in a reduced ∆V D 0 and an improved pressure resistance. In the case of Rb + , the same argumentation should be valid, causing even more increased pressure stability. However, it is very likely that the channel Na + ions are not completely replaced by Rb + , as the constant for the competition equilibrium has been found to be 1.8 38 . Thus, the observed stabilizing effect is achieved by both cations, Na + and Rb + , in the channel cavity.

Conclusions
In summary, we have presented to our knowledge the first comprehensive thermodynamic study on the molecular self-assembly of 5′-GMP. Using a combination of scattering and spectroscopic methods, we have studied the stability of supramolecular self-assemblies of 5′-GMP and the stabilization effect of alkali salts over a wide range of temperatures and pressures. We found that under abyssal conditions, where temperatures as low as 5 °C and pressures up to 1 kbar are reached, the G-quartet structure of Na 2 5′-GMP is stable. Beyond those conditions, the G-quartet stacks dissociate laterally into monomer stacks without changing the longitudinal dimension. Hydration, stacking interactions and packing defects play important roles in determining the stability of such supramolecular structures. In the presence of the alkali cations K + and Rb + , which bind and replace the Na + cation from the channel cavity of the G-quartet stacks, the temperature and pressure stability of the 5′-GMP quartets is significantly increased. As the G-quartets serve as building blocks of G-quadruplexes, our results provide also insights into how different forces determining the folding of G-quadruplexes are modulated by temperature and pressure. Especially, the pressure effect on the G-quartets can be extrapolated to their oligomeric analogues and help to explain the pressure sensitivity of G-quadruplexes in general 62,71 .

Methods
Sample preparation. Disodium guanosine 5′-monophosphate salt hydrate (Na 2 5′-GMP, >99% purity) from yeast was purchased from Sigma-Aldrich. Stock solutions of GMP (35 wt%) and the alkali salts (1 M) were prepared in doubly distilled water or D 2 O and filtered (0.2 µm PVDF membrane). 5′-GMP samples were dissolved overnight to ensure homogeneity. The concentration of the stock solution was determined from UV-absorption measurements at a wavelength of 260 nm (20,000-fold dilution, ε 260 = 10674 [M cm −1 ) and adjusted to the appropriate concentration 31 . For FTIR measurements, stock solutions of Na 2 5′-GMP in D 2 O are lyophilized twice before filtration in order to remove H 2 O from the crystal water. For NMR measurements, Na 2 5′-GMP was dis- Temperature-and pressure-dependent FTIR spectroscopy. Temperature-dependent FTIR measurements were performed using a Nicolet 5700 (Thermo Fisher Scientific, USA) equipped with a liquid-nitrogen-cooled MCT detector (HgCdTe) in the wavenumber range of 4000-1100 cm −1 and in the temperature range of 1-70 °C. The sample was placed between two CaF 2 windows separated by a mylar spacer (thickness, 50 µm) and assembled in a temperature cell which is connected to an external water bath. The temperature was measured with a digital thermometer placed in the sample cell (accuracy: ±0.5 °C). The sample was equilibrated for 5 min at each temperature before spectra were collected. Pressure-dependent FTIR spectra were collected using a Nicolet 6700 (Thermo Fisher Scientific, USA) equipped with a liquid-nitrogen-cooled MCT detector (HgCdTe) in the wavenumber range of 4000-650 cm −1 . Pressure up to 1200 MPa was applied using a P-series diamond anvil cell (DAC) with type IIa diamonds (High Pressure Diamond Optics Inc., Tucson, USA). A 20 µm thick gasket of CrNi steel with a 0.3 mm drilling was placed between the two diamonds holding 2.5 µL of the sample. The temperature of the DAC was controlled by an external water bath and the internal temperature was measured with a digital thermometer. BaSO 4 was used as an internal pressure gauge. The stretching vibration of SO 4 2− (~983 cm −1 ) is pressure-dependent 73 . For each temperature or pressure, 128 scans were collected with a spectral resolution of 2 cm −1 and averaged. Data analysis was carried out using the GRAMS software (Thermo Electron). After buffer subtraction and baseline correction in the range of 1710-1630 cm −1 (band for the C=O stretch vibration) and 1610-1518 cm −1 (band for the C=N ring vibration), those bands were area normalized and smoothed. All measurements were performed at least in duplicate.
Assuming an apparent thermodynamic equilibrium between hydrogen-bonded and monomer assemblies, a Boltzmann function was fitted to the temperature-dependent band intensities at 1673, 1592, 1568 and 1537 cm −1 using where I 1 and I 2 are the plateau values of the IR band intensities of the monomeric and hydrogen-bonded state, respectively. T m is the melting temperature and ∆H vH 0 the standard van't Hoff enthalpy for the dissociation reaction.
High pressure Synchrotron SAXS. Pressure-dependent SAXS measurements were performed at the ESRF beamline ID 02 (Grenoble, France) in a home-built high pressure cell with diamond windows 74 . The sample volume was 10 µl. The energy used was 16 keV and the sample to detector distance was 2.4 m. The samples were exposed to the beam for 0.25 s for each measurement. No radiation damages were detected within the total exposure time of a complete pressure series. Data were collected in 50 MPa steps. The scattering data were background corrected and analysed using the SAXSutilities software package provided by ESRF 75 .
High pressure NMR and DOSY NMR. All NMR spectra were acquired on a Bruker Avance III 600 MHz spectrometer with a standard 5 mm O.D. ceramic tube from Daedelus Innovations. Hydrostatic pressure was applied to the sample using the Xtreme Syringe Pump (Daedelus Innovations). A commercial ceramic zirconia high-pressure NMR cell and an automatic pump system (Daedalus Innovations, Philadelphia, PA) were used to vary the pressure in the 0.1 to 240 MPa range 76 . Longitudinal relaxation times T 1 were measured for the H8 protons using an inversion recovery experiment, and the data were analysed using the relaxation module of Bruker's Topspin software. The T 1 values at various temperatures and pressures are given in Supplementary Table S1. The range of T 1 values varied from 1.9 s at 35 °C to 0.8 s at 5 °C for the tetramer, and from 1.4 s at 35 °C to 1 s at 5 °C for the monomer. Conversely, pressure had a very little effect on T 1 . Standard 1 H NMR experiments were performed with the zgesgp pulse sequence using excitation sculpting for solvent suppression. At each pressure, 16 scans were collected with a recycle delay of 10 s at 15, 25 and 35 °C and 32 scans were collected with a recycle delay of 5 s at 5 °C. The data were processed and analysed on Bruker Topspin software version 3.5 pl 5. For 1 H diffusion experiments, the stebpgp1s pulse sequence was used. The pulsed field gradient duration (δ) was 10 ms, the diffusion period (Δ) was 250 ms and the variable gradient strength (G) was 34.05 T/cm. For the gradient, 32 scans were collected for each of 32 linear incremental steps from 2% to 95% of the gradient strength, with a recycle delay of 5 s. The data were analysed using the 'eddosy' tool on Bruker Topspin software version 3.5 pl 5. The temperature and pressure dependence of water's dynamic viscosity was considered 77 .
The standard-state free energy of dissociation, ∆G D 0 , was determined by where the apparent equilibrium constant, K app , for the disassembly reaction is given by the ratio of the mole fractions of monomer and hydrogen-bonded 5′-GMP assemblies (dimers and G-quartets), f m and f hb . The standard-state molar volume change of the disassembly process of 5′-GMP, ∆V D 0 , was calculated from Data availability. The data that support the findings of this study are available from the corresponding author on reasonable request.