The chemistry of branched condensed phosphates

Condensed phosphates may exist as linear, cyclic or branched structures. Due to their important role in nature, linear polyphosphates have been well studied. In contrast, branched phosphates (ultraphosphates) remain largely uncharacterised, because they were already described in 1950 as exceedingly unstable in the presence of water, epitomized in the antibranching-rule. This rule lacks experimental backup, since, to the best of our knowledge, no rational synthesis of defined ultraphosphates is known. Consequently, detailed studies of their chemical properties, reactivity and potential biological relevance remain elusive. Here, we introduce a general synthesis of monodisperse ultraphosphates. Hydrolysis half-lives up to days call the antibranching-rule into question. We provide evidence for the interaction of an enzyme with ultraphosphates and discover a rearrangement linearizing the branched structure. Moreover, ultraphosphate can phosphorylate nucleophiles such as amino acids and nucleosides with implications for prebiotic chemistry. Our results provide an entry point into the uncharted territory of branched condensed phosphates. The “anti-branching rule”, introduced in 1950, excludes branched polyphosphates from biological relevance due to their supposedly rapid hydrolysis. Here, the authors synthesize monodisperse branched polyphosphates and demonstrate their unexpected stability in water, as well as provide evidence for their competence in phosphorylation.

In recent years, branched oligophosphates caught attention again: cyclic ultraphosphates like 11 with modifications on the terminal phosphate can now be obtained and applied in the syntheses of linear nucleoside, dinucleoside and inorganic polyP [29][30][31][32][33] . Cummins et al. synthesised 7 as its [PPN] (bis(triphenylphosphine)iminium) salt, which allowed the isolation of the product 34 . Application of 7 was demonstrated in the tetraphosphorylation of nucleotides and enabled the synthesis of another ultraphosphate species containing four phosphates in the cyclic subunit 35 . Although cyclic ultraphosphates have thus recently become accessible, there is no synthesis of ultraphosphates available that are devoid of cyclic substructures and therefore are true constitutional isomers of linear polyP 36 . This fundamental type of condensed phosphates remained unstudied.
Here, we report the synthesis of non-cyclic ultraphosphates using phosphoramidite chemistry. This approach provides access to both symmetrically modified ultraphosphates containing three equal modifications on each terminal phosphate, including the smallest possible unmodified ultraphosphate uP 4 (2) as well as unsymmetrical analogues containing two different residues. The synthetic approach enables the generation of thio-and selenoultraphosphates. To interrogate the antibranching-rule, we report hydrolysis studies including enzymatic degradation. Furthermore, we show the phosphorylation of nucleosides with inorganic ultraphosphate with implications for prebiotic chemistry (see Fig. 1d). We also study the reactivity of modified ultraphosphates in organic solvent by using a combination of 31 P-NMR and capillary electrophoresis mass spectrometry (CE-MS) and discover an ultraphosphate rearrangement, which we name the phosphate walk.

Results
Symmetrical ultraphosphates. Phosphordiamidites are used in linear polyP syntheses by twofold activation and reaction with (modified) phosphates 37 . A phosphortriamidite should therefore enable threefold activation and reaction with three phosphates to produce a mixed P(III)-P(V)-anhydride intermediate 18 (hereafter, called ultraphosphite, Fig. 2a), which can further be oxidised resulting in an ultraphosphate (12).
Initially, the reaction of three equivalents of tetrabutylammonium (TBA) phenyl phosphate with tris(diethylamino)phosphine (16) and ethylthiotetrazole (ETT) was studied: 31 P{ 1 H}-NMR of the mixture showed consumption of 16 within a few minutes, giving rise to the ultraphosphite intermediate. The absence of peak splitting due to homonuclear P-P coupling for this mixed P(III)-P(V)-anhydride is in accordance with earlier observations for P-amidite couplings 37 . Oxidation with mCPBA gave phenylmodified ultraphosphate 20, which was isolated by precipitation with Et 2 O (71% yield, 78% purity, measured by 31 P{ 1 H}-NMR). As decomposition products, diphenyl triphosphate (10%) and phenyl phosphate (10%) were detected. The central ultraphosphate signal, now showing the expected multiplicity (quartet) with a chemical shift of ca. δ = −35 ppm, was detected in water. This finding is in sharp contrast to the antibranching-rule, claiming the instantaneous hydrolysis of ultraphosphates 3, 10, 24 . Purification was possible in aqueous buffer (NH 4 HCO 3 ) using strong anion exchange chromatography (SAX) and 31 P{ 1 H}-NMR analysis of fractions showed pure 20 in solution. Lyophilization resulted in significant decomposition. We also studied NaClO 4 or LiCl solutions as eluents in SAX and attempted to isolate the product by precipitation from acetone 32 . Although we were unable to isolate trisphenyl uP 4 20 using this procedure, trisadenosine ultraphosphate (21) precipitated and afforded the product in 55% yield. 31 P{ 1 H}-NMR of the precipitate showed pure ultraphosphate, but after drying, decomposition (>15%) was detected.
Next, we evaluated the scope of ultraphosphate synthesis (see Fig. 2b) by changing modifications on the terminating phosphates. Since not all products precipitated readily, reaction yields as derived for 21 cannot be given and Fig. 2b lists the purities of crude products according to 31 P{ 1 H}-NMR. Alkyne modified ultraphosphates (24 and 25) were readily accessible. Efforts towards the synthesis of amino-acid-and carbohydrate-modified ultraphosphates using O-phospho-L-tyrosine or α-D-glucose-1phosphate resulted in side-reactions of the phosphoramidite with the amine or the primary alcohol, respectively. Application of Fmoc-O-phospho-L-tyrosine followed by deprotection of the amine gave access to amino-acid modified ultraphosphate 27. The use of D-glucose-6-phosphate enabled access to a carbohydrate-containing ultraphosphate 28. Thiamine-derived ultraphosphate 29 could be obtained from the tetrakis[3,5bis(trifluoromethyl)phenyl]borate salt of thiamine phosphate. Modification of the oxidation (S 8 or KSeCN) facilitated entry into thio-(in green) and seleno-(23) ultraphosphates.
Unmodified and unsymmetrical ultraphosphates. We envisioned the synthesis of inorganic ultraphosphate uP 4 (2) as the defining minimal unit of this substance class. Reactions of phosphoric acid with 16 were unsuccessful thus requiring protected precursors for 2. Different cleavage strategies for the protected phosphates were considered, including hydrogenolytic (30), enzymatic (31, discussed later), phototriggered (32)(33)(34)(35)(36) and basic (37) deprotection (see Fig. 2b). We found that (9H-fluorenyl-9-yl)methyl (Fm) dihydrogen phosphate was readily accessible 38 and that the corresponding ultraphosphate 37 could be synthesised under ambient conditions. 37 could also be stored indefinitely in solution at −20°C after purification, enabling screening of several bases for deprotection. Only DBU enabled deprotection to 37, but precipitation of uP 4 2 resulted in decomposition.
Unsymmetrically modified ultraphosphates were accessible by orthogonal activation strategies using chlorophosphoramidites (39 or 41, see Fig. 3a). Although over-reaction in the first and unselective phosphate exchange in the second step was observed, a series of unsymmetrical ultraphosphates were obtained after purification. Fm-modified structures further allowed deprotection by the addition of DBU to yield twofold or singly modified ultraphosphates (50-54, see Fig. 3c). The number of  61 . c Monodisperse ultraphosphates detected by Glonek in the condensation reactions of orthophosphoric acid or metaphosphates using carbodiimides or trichloroacetonitrile [24][25][26][27][28] . The structures in dashed boxes were further described in publications by Klein 62 , Taylor 29 , Jessen 31, 32 and Cummins 33 . d General structures of ultraphosphates in this work and suggestion for prebiotically plausible phosphorylation reactions using ultraphosphates: uP 4 (2) was used as a model substrate for polydisperse ultraphosphates arising from reactions of P 4 O 10 in the presence of water 59 . The prebiotic phosphate cycle including phosphorus pentoxide from volcanic activity has already been proposed and meets the challenge of making phosphate available from low-solubility minerals 56 31 P{ 1 H}-NMR spectra of the intermediary ultraphosphite 19 and the ultraphosphate 21 after oxidation and purification for R = adenosine. b Synthetic scope of the synthesis of symmetrically modified ultraphosphates and modification of the oxidation step to yield thio-and seleno analogues. The purity of the crude products is given in percent according to the 31 P{ 1 H}-NMR spectra. Yields were not determined due to uncertain quantities of counterions but the respective crude masses are reported in the supporting information along with the spectra. modifications influenced the stability of the ultraphosphate towards hydrolysis, showing faster decomposition for twofold modified structures. For example, 54 was completely hydrolysed in the deprotection mixture (5% DBU in water, pH 13.9) within 30 min while 52 had a half-life of 180 min. Copper-catalysed click reactions on 49 were performed with biotin and fluoresceinconjugates and allowed the preservation of the ultraphosphate (Fig. 3d).
Salt metatheses and crystallisation. To obtain a single crystal of an ultraphosphate, we examined salt metatheses reactions to yield [PPN] salts, as [PPN] is well-known for its high crystallinity and its capability to stabilise anions 39 . We developed a method to isolate the ultraphosphate [PPN] salts from fractions after SAX purification ( Supplementary Fig. 2) and found that they can be dried and stored indefinitely, in contrast to non-[PPN] salts. Only uP 4 [PPN] decomposed as soon as residual water was removed.
Although no crystals of sufficient quality for crystal structure analysis could be obtained from the [PPN] salts, it was found that Fm-protected 37 can be salted out from solutions after reversedphase purification (55% water, 35% MeCN, 10% TEAA (100 mM, pH 7.0)) by addition of NaCl and that these conditions supported the formation of single-crystals. X-ray diffraction studies established the identity of 37 (Fig. 2). The packing along the a-axis ( Supplementary Fig. 3) shows that the ultraphosphate is arranged along a chain of water-bridged sodium cations to form distinct layers where hydro-and lipophilic interactions are maximised. We attribute the increased stability of 37 compared to other symmetrically modified ultraphosphates to a steric shielding of the ultraphosphate moiety. Accordingly, the comparably lower stability of singly or twofold modified ultraphosphates can be explained. However, as a counter-effect, the higher negative charge enables longer half-lives of singly compared with twofold modified structures. Although [PPN] salts are stable storage forms for ultraphosphates, their insolubility in water can be disadvantageous. The metathesis to water-soluble sodium salts was possible using NaOTf. Only for uP 4 , the salt metathesis was unsuccessful and led to the formation of inorganic mono-and triphosphate. Unexpectedly, also pyro-(14%) and linear tetraphosphate (12%) were detected.
Stability of ultraphosphates in water. The antibranching-rule describes ultraphosphates as exceedingly unstable in the presence of water 12,13 . Our observations, however, revealed significant hydrolytic stability for short-chain ultraphosphates expressed in half-lives ranging from several hours to days. The decomposition of uP 4 and trisadenosine uP 4 21 was tracked by 31 P{ 1 H}-NMR at different pH values and in the presence of different cations (see Fig. 4a and Supplementary Fig. 4). There is a high pHdependency on the decomposition rates, with longer half-lives obtained with increasing pH values. In the presence of Mg 2+ , the decay was about twice as fast, and Ca 2+ accelerated the decay even further. In contrast, monovalent cations had only little effect.
The stability of ultraphosphates suffices to subject them to polyacrylamide gel electrophoresis on dense gels (PAGE; Supplementary Fig. 5 and Supplementary Fig. 6) without significant decomposition followed by staining with toluidine blue 40 . Such separations take several hours in aqueous buffer. Threefold modified ultraphosphates gave clear bands without any observed decay and even uP 4 could be analysed by PAGE, pointing towards a possible analytical approach to detect ultraphosphates in biological samples. Singly or twofold modified structures 52 and 54 decomposed under these conditions.
Enzymatic digestion of ultraphosphates. Ultraphosphates have not been reported to occur in biological systems 41 . Since polyP extraction protocols usually include acidic conditions, nucleophilic reagents, divalent cations and drying-all of which accelerate ultraphosphate decomposition-one would not expect to detect ultraphosphates. The publication by Hong provides evidence for this case already for the more stable metaphosphates 9 . In accordance, we could not find any ultraphosphate signal at ca. δ = −35 ppm in 31 P{ 1 H}-NMR analyses of polyP extracts from different yeast strains modified in their polyP metabolising enzymes (the polyP overexpressor GPD-vtc5, the polyP devoid Δ vtc4, and polyP accumulating Δ ppn1, ppn2, ppx1, that lack phosphatases degrading polyP; Supplementary Fig. 7 and 8). We hypothesised that in addition to chemical conditions, enzymes might also degrade ultraphosphates, which would further complicate strategies to extract them from biological sources. We studied the enzymatic digest of ultraphosphates using alkaline phosphatase (ALP). We initially examined the hydrolysis of paranitrophenylphosphate and its ultraphosphate 31. We synthesised ultraphosphate 31 as its [PPN] salt and tracked the decomposition in the presence and absence of ALP by 31 P{ 1 H}-NMR (Fig. 4b) 42 . 31 showed a half-life of t 1/2 = 159 min in the absence of the enzyme, which was significantly reduced upon its addition (t 1/2 = 29 min). We were interested as to whether the ultraphosphate 31 binds to the active site or whether surface effects are responsible for the accelerated hydrolysis. We measured additional kinetics using either heat-denatured enzyme or enzymetreated with ethylenediaminetetraacetic acid (EDTA) to remove Mg 2+ and Zn 2+ ions. The decay of 31 in presence of heatinactivated enzyme copies the kinetics of the blank. Only a low residual hydrolytic activity in the presence of EDTA was found. We conclude that ultraphosphate 31 binds to the active site and is enzymatically digested, providing evidence for an ultraphosphate-enzyme interaction. Similar results were obtained for the adenosine-modified ultraphosphate 21 ( Supplementary  Fig. 9). However, it was still unclear whether ALP first hydrolyses the branching point of ultraphosphates, or one of the three phosphoester bonds (path A or B in Fig. 4b). The latter would result in an unstable twofold modified ultraphosphate 60 that would rapidly decay further. uP 4 2 was enzymatically digested as well ( Supplementary Fig. 10), pointing towards the cleavage of the anhydride bond. To further study the enzymatic digestion of modified ultraphosphates, we envisioned the synthesis of the nonhydrolyzable analogue 63 with a CH 2 -group as an oxygen replacement, which the enzyme cannot cleave, whereas still being capable of hydrolysing the central anhydrides (Fig. 4c). para-Nitrobenzyl phosphonic acid was transformed to ultraphosphonate 63. After oxidation, 31 P{ 1 H}-NMR suggested a clean reaction to the product, but after precipitation, ultraphosphonate 63 was no longer present ( Supplementary Fig. 11). We identified the usual hydrolysis products 61 and 62 but also another product, which was purified by AIEX chromatography and found to be a linearised mixed tetraphosphonate/phosphate analogue 64. This is reminiscent of the linear tetraphosphate we found for uP 4 2 decomposition described earlier and pointed towards a rearrangement typical for ultraphosphates.
Ultraphosphates rearrange by phosphate walk. Apart from linearised products such as P 4 from uP 4 [PPN] 2 and the synthesis of an ultraphosphonate (63 and 64, Fig. 4c and Supplementary Fig. 11), trisadenosine ultraphosphate [PPN] (21) also showed another decay mechanism accompanying simple hydrolysis of the branching point after several days in DMF. Next to AMP and Ap 3 A as expected products of hydrolysis, further signals were detected and 1 H-31 P-HMBC cross-peak analysis revealed that internal phosphates must carry adenosine (Fig. 5a). The mixture was analysed by CE-MS, which enabled the separation of different components and determination of their mass. We confirmed masses matching Ap 2 A, a threefold modified triphosphate 65 as well as a threefold modified tetraphosphate 66. Since 21 was analytically pure, a rearrangement must lead to linearization of the ultraphosphate that walks into the line 43 , which we dub the phosphate walk (Fig. 5b). We propose, that the ultraphosphate linearises by an attack of one terminal phosphate at another accompanied with the cleavage of either a phosphoanhydride or phosphoester bond. The latter would form a cyclic ultraphosphate intermediate and requires a second nucleophilic attack of the released alcoholate to form 66 as the central intermediate of the mechanism. Depending on the nucleophile (AMP or H 2 O) and the attacked phosphate of 66 (Fig. 5b), both the internally modified phosphate 65 and Ap 2 A, as well as standard decomposition products, can be explained.
Computation was invoked to corroborate the feasibility of the internal phosphate walk mechanism. The electronic states and chemical bonding of branched phosphates in phosphate glasses have been discussed based on computational results for various model clusters 44 . However, the history of mechanistic disputes surrounding substitution reactions at phosphorous includes a myriad of experimental results and ab initio computations [45][46][47] . The energy of highly charged species, with variable counterions in high vs moderate dielectrics involving hydrogen bond donors, are sensitive to intricate changes in speciation, constitutional and conformation isomerism, and explicit vs continuum environmental effects [47][48][49] . Mechanistic computational studies involving trimethyl ultraphosphate (67) at the B97D/Def2-TZVPD(water) level of theory support the ultraphosphate 67 and linearised product 69 having energies compatible with both species being accessible under normal conditions. A cyclic intermediate 68 (Fig. 5c) was found that results formally from the loss of methoxide and the formation of a six-membered ring by the association of formally negative oxygen of one phosphate to the phosphorous where methoxide is removed. These three states (67-69) were the basic minima considered. The walk could occur through this higher energy cyclic state that serves as a possible bridge between branched and linear forms and has transition states leading to the ring-formation and -opening. Alternatively, the association could form a ring with a pentavalent phosphorous atom (70); however, numerous attempts to identify such an intermediate by DFT calculations were unsuccessful. Mono-and dihydrates were considered, where the explicit waters were placed in positions consistent with prevailing models 47 bringing down the relative activation energies. The data support a trend where reaction in water coupled to specific acid catalysis would show fast substitution rates. Considering effective molarities, relative nucleophilicities and the high concentration of water in water (55 M), hydrolysis as the dominant reaction path is not surprising. Taken out of the context of water, the effective molarity of internal nucleophile remains constant; the nucleophilic strength of solvent is reduced and the concentration of solvent molecules as nucleophiles in bulk solvent drops to on the order of 10 M 50, 51 . All these factors presage parallel rates of acceleration in the presence of acid but a product distribution in which internal attack becomes competitive if not fully dominant. This shift in product distribution opens the way for the phosphate walk. For the ultraphosphonate analogue 63, however, the one-step mechanism must be energetically favoured.
Reactivity of uP 4 as phosphorylating agent. Ultraphosphates could potentially serve as phosphorylating reagents if suitable nucleophiles are present, as has been previously studied for polyand metaphosphates [52][53][54][55] . Earlier studies suggested the formation of branched phosphates on primitive earth as partial hydrolysis products of P 4 O 10 , which in turn can be volatilised from magma 7, 56-58 . uP 4 2 was used as a model substrate for polydisperse ultraphosphates arising from P 4 O 10 in the presence of water 59 to study the potential contribution of branched phosphates to prebiotic phosphorylation reactions ( Fig. 6a and Supplementary  Fig. 15). Aliphatic nucleophiles were studied for general reactivity patterns of ultraphosphates. Ethanolamine was used to screen the required stoichiometry to favour the phosphorylation reaction over simple hydrolysis by water. We observed monophosphorylation of the amine moiety with a phosphorylation ratio of up to 85:15 (phosphorylated ethanolamine vs. orthophosphate as hydrolysis product) with 3000 eq. ethanolamine. Decreasing ethanolamine gave ratios of 70:30 for 500 eq. and 27:73 phosphorylated ethanolamine for 100 eq., respectively. For secondary amines and alcohols, we additionally detected a phosphoramidate arising from the reaction of DBUwhich was present due to the deprotection conditions -with uP 4 . This side-reaction was avoided using polymer-bound DBU for the deprotection, affording DBU free uP 4 in 81% purity (see Supplementary Fig. 15). Interestingly, uP 4 2 was found to be less stable in the absence of DBU. Thus, further experiments were performed with DBU in solution due to the better repeatability. For different amino acids, the primary or secondary amine andif presentthe alcohol or thiol moiety were phosphorylated ( Supplementary Fig. 15). For glycine, only 8% phosphorylation of the amine was observed at pH 8.8 but the adjustment to pH 13.0 increased the phosphorylation to 66%, in accordance with the longer half-life of uP 4 at higher pH (see Fig. 4a). Although it is unclear whether this pH condition is relevant to prebiotic chemistry 60 , the result still shows a general reactivity trend. Freeze-drying experiments increased the phosphorylation of glycine to its phosphoramidate to 52% at a pH of ca. 9.
For all canonical (deoxy)nucleosides, even 10 eq. were sufficient to detect phosphorylated nucleosides by CE-MS after freeze-drying. For full consumption of uP 4 2 in one single freeze-drying experiment, 500 eq. were necessary. These conditions allowed phosphorylation of up to 54%, whereas evaporation of solvent at room temperature resulted in 33% nucleoside phosphorylation. The product distribution was analysed by CE-MS, and spiking experiments revealed product identities (Fig. 6b). We found phosphorylation in the 5′-and also 2′-and 3′-positions. To rule out phosphorylation arising from inorganic mono-and triphosphate, these compounds were lyophilised with 3000 eq. uridine, leading to no phosphorylation. Ultraphosphate 2 as a model substrate-and by extension other branched polyP-may thus have served as phosphate donors in prebiotic chemistry.
Life relies on condensed phosphates, but ultraphosphates as a fundamental type and true constitutional isomers of the linear polyP remained unstudied. In this study, we disclose the synthesis of defined monodisperse ultraphosphates containing zero to three modifications. For those short-chain ultraphosphates, we found significant hydrolytic stability expressed in half-lives up to days, which calls the antibranching-rule into question. We provide evidence for the interaction of an enzyme with ultraphosphates and describe the phosphate walk, which linearises branched phosphates. Ultraphosphate was applied as a phosphorylating reagent for nucleophiles such as amino acids and nucleosides with implications for prebiotic chemistry. With synthetic access to this class of molecules, the chemistry-and potential biology-of the branched phosphates can finally be studied.
General procedure for the salt exchange of ultraphosphates to [PPN] salts. The crude ultraphosphate is either purified by anion exchange chromatography using Q Sepharose® Fast Flow and a NaCl (1 M) gradient or by using a PuriFlash Column (30 µ C18 AQ; water, MeCN gradient (0-45%), 10% TEAA (100 mM, pH 7.0)). Fractions containing ultraphosphate were analysed for their concentration by addition of a defined volume of a PMe 4 Br solution in D 2 O (1 mg/ml) and 31 P{ 1 H}-NMR. Fractions were combined and heated to 55°C.
[PPN]-Cl (2-3 eq.) was dissolved in H 2 O (yielding~2-5 mM solution) at 55°C and added to the ultraphosphate solution. The precipitate was collected by centrifugation and washed with warm water (~55°C). The residue was dissolved in acetone, dried over Na 2 SO 4 and the solvent removed in vacuo.

Data availability
All data supporting the findings of this study are available in the article and Supplementary Information file or from the corresponding author upon reasonable request. The X-ray crystallography data have been deposited at the Cambridge Crystallographic Data Centre (CCDC), under accession number CCDC: 2032762. These data can be obtained free of charge from The Cambridge Crystallographic Data Centre via www.ccdc.cam.ac.uk/data_request/cif.