Protein dynamics is strongly influenced by the surrounding environment and physiological conditions. Here we employ broadband megahertz-to-terahertz spectroscopy to explore the dynamics of water and myoglobin protein on an extended time scale from femto- to nanosecond. The dielectric spectra reveal several relaxations corresponding to the orientational polarization mechanism, including the dynamics of loosely bound, tightly bound, and bulk water, as well as collective vibrational modes of protein in an aqueous environment. The dynamics of loosely bound and bulk water follow non-Arrhenius behavior; however, the dynamics of water molecules in the tightly bound layer obeys the Arrhenius-type relation. Combining molecular simulations and effective-medium approximation, we have determined the number of water molecules in the tightly bound hydration layer and studied the dynamics of protein as a function of temperature. The results provide the important impact of water on the biochemical functions of proteins.

Dynamic fluctuations in hydrogen-bond network of water occur from femto- to nano-second timescale and provides insights into structural/dynamical aspects of water at ion-water interfaces. Employing terahertz spectroscopy assisted with molecular dynamics simulations, we study aqueous chloride solutions of five monovalent cations, namely, Li, Na, K, Rb and Cs. We show that ions modify the behavior of surrounding water molecules and form interfacial layers of water around them with physical properties distinct from that of bulk water. Small cations with high charge densities influence the kinetics of water well beyond the first solvation shell. At terahertz frequencies, we observe an emergence of fast relaxation processes of water with their magnitude following the ionic order Cs>Rb>K>Na>Li, revealing an enhanced population density of weakly coordinated water at ion-water interface. The results shed light on the structure breaking tendency of monovalent cations and provide insights into the properties of ionic solutions at the molecular level.

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Water is vital for life, and without it, biomolecules and cells cannot maintain their structures and functions. The remarkable properties of water originate from its ability to form hydrogen-bonding networks and dynamics, which the connectivity constantly alters because of the orientation rotation of individual water molecules. Experimental investigation of the dynamics of water, however, has proven challenging due to the strong absorption of water at terahertz frequencies. In response, by employing a high-precision terahertz spectrometer, we have measured and characterized the terahertz dielectric response of water from supercooled liquid to near the boiling point to explore the motions. The response reveals dynamic relaxation processes corresponding to the collective orientation, single-molecule rotation, and structural rearrangements resulting from breaking and reforming hydrogen bonds in water. We have observed the direct relationship between the macroscopic and microscopic relaxation dynamics of water, and the results have provided evidence of two liquid forms in water with different transition temperatures and thermal activation energies. The results reported here thus provide an unprecedented opportunity to directly test microscopic computational models of water dynamics.

We study the large-N limit of the Segal-Bargmann transform on S N −1 ( √ N ), the (N − 1)-dimensional sphere of radius √ N , as a unitary map from the space of squareintegrable functions with respect to the normalized spherical measure onto the space of holomorphic square-integrable functions with respect to the normalized quadric measure. In particular, we give an explicit formulation and describe the geometric models for the limit of the domain, the limit of the range, and the limit of the transform when N tends to infinity. We show that the limiting transform is still a unitary map from the limiting domain onto the limiting range.