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  1. Phosphates and polyphosphates play ubiquitous roles in biology as integral structural components of cell membranes and bone, or as vehicles of energy storage via adenosine triphosphate and phosphocreatine. The solution phase space of phosphate species appears more complex than previously known. We present nuclear magnetic resonance (NMR) and cryogenic transmission electron microscopy (cryo-TEM) experiments that suggest phosphate species including orthophosphates, pyrophosphates, and adenosine phosphates associate into dynamic assemblies in dilute solutions that are spectroscopically “dark.” Cryo-TEM provides visual evidence of the formation of spherical assemblies tens of nanometers in size, while NMR indicates that a majority population of phosphates remain as unassociated ions in exchange with spectroscopically invisible assemblies. The formation of these assemblies is reversibly and entropically driven by the partial dehydration of phosphate groups, as verified by diffusion-ordered spectroscopy (DOSY), indicating a thermodynamic state of assembly held together by multivalent interactions between the phosphates. Molecular dynamics simulations further corroborate that orthophosphates readily cluster in aqueous solutions. This study presents the surprising discovery that phosphate-containing molecules, ubiquitously present in the biological milieu, can readily form dynamic assemblies under a wide range of commonly used solution conditions, highlighting a hitherto unreported property of phosphate’s native state in biological solutions. 
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    Dynamic nuclear polarization (DNP) by the cross effect (CE) has become a game changer for solid-state nuclear magnetic resonance (NMR) spectroscopy. The efficiency of CE-DNP depends on the strength of the electron–electron coupling in biradical polarizing agents. Hence, the focus lately has been on designing biradicals with a large net exchange ( J ) and dipolar ( D ) coupling. In this study, we reveal that the crucial factor for CE-DNP is not the large sum, J + D , but rather the relative magnitude of J and D , expressed as the J / D ratio. We show that the mechanistic basis of this interference lies in the isotropic vs. the anisotropic nature of the J and D couplings, respectively. This interference can lead to a small (effective) electron–electron coupling for many orientations even when J + D is large, resulting in non-adiabatic rotor-events. We find that when 0 < | J / D | < 1 the CE-DNP efficiency is attenuated for the majority of orientations, with greater attenuation observed at higher magnetic fields and faster magic-angle spinning (MAS) frequency. The interference effect of J and D coupling introduced in this study can explain why many biradicals with high or comparable J + D still show significantly divergent DNP performances. We debut J / D as a consequential criteria for designing efficient biradicals to robustly perform across a large range of B 0 fields and MAS frequencies. 
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