Interfacial water is ubiquitous on Earth, playing a crucial role in biology, chemistry, physics, materials science, and environmental science. Multiscale, hierarchical water motions on the surface of different materials under different conditions (temperature, hydration extent, pressure, etc.) and the coupling of this motion with the substrate/solute dynamics and the influence of these couplings on the material functions are complex, long lasting, interdisciplinary research topics. We herein focus on the coupling between the picosecond dynamical onset of substrates and their surface water at temperatures lower than the freezing point (273 K) and discuss the recent progress in the study of its molecular mechanisms.

The behavior and properties of interfacial water in contact with material or bio-molecular surfaces play a crucial role in various scientific disciplines.1–8 For instance, chemical reaction rates, adsorption processes, and the stability of intermediates are affected by the interfacial water effect, which leads to modified reaction pathways and selectivity.9–11 Biological processes such as protein folding, enzymatic activity, and the transport of ions and other small molecules across cell membranes, as well as the interaction between bio-molecules, are influenced by the interfacial water.12–16 The presence of interfacial water can also influence the mechanical properties, such as elasticity or strength, of materials, and it is also relevant in fields such as surface chemistry, thin films, and nanotechnology.17–28 

One important topic in the interfacial water study is to understand the coupling between the complicated, multi-scale, and hierarchical dynamics of the interfacial water and the solute/substrate material.3,14,29–38 Interfacial water dynamics couples with substrate material dynamics through complicated mechanisms including hydrogen bonding, surface wetting/dewetting, interfacial diffusion, surface restructuring, and thermal effects.3,13,14,39–42 It is a complex phenomenon involving the interaction and exchange of energy, momentum, and mass between the two systems.

The microscopic machinery underlying the water–substrate and water–solute dynamical coupling mechanisms has been studied by numerous experimental, theoretical, and computational tools. For instance, two distinct water dynamic processes (18ps and 20200ps) were detected in the protein hydration layer using time resolved fluorescence measurements,43 which represent the initial local relaxation and the subsequent collective network restructuring, respectively. By measuring the bulk/interfacial water dynamics using dielectric spectroscopy and protein internal fluctuations using the Mossbauser effect and neutron scattering, it was found that large-scale protein backbone motions are driven by the bulk solvent fluctuations and the solvent viscosity, while small internal (sidechain) protein motions are driven by the beta fluctuations of the interfacial water.42 Molecular couplings between DNA and water, together with the accompanying energy exchange processes, are also studied via the femtosecond infrared pump–probe experiments.14,44–46 NMR relaxation measurements were used to study water dynamics in the hydration layers of peptides and globular proteins, as well as in the living cells of micro-organisms.47 A general slowdown of water dynamics in all kinds of concentrated ionic solutions is found to be largely due to the coupling of the slow, collective component of water motion with the motion of large hydrated ion clusters ubiquitously existing in the concentrated ionic solutions.48 Using the elastic incoherent neutron scattering on the colloidal poly-N-isopropylacrylamide (PNIPAM) microgels, the low-temperature dynamical transitions were found to occur simultaneously for PNIPAM and its hydration water dynamics, suggesting a dynamical coupling between these two processes.21 

At temperatures much below 0 °C, the significant inhomogeneity of substrate surface structure, chemistry, and morphology often prevents the ice formation of the interfacial water.4,6–8,22,23,25 The low-temperature motion of non-freezing surface water then couples with the substrate dynamics and renders much flexibility and mobility to the substrate. Consequently, various material functions at subzero temperatures, including the preservation of tissues and organs, keeping the functioning of water-based electronic devices, and maintaining the electronic conduction in the aqueous battery, are activated.6 Rational design and production of the relevant functional materials require an in-depth study of the molecular mechanisms underlying the low temperature dynamical coupling phenomena. The knowledge of universality and diversity in these mobility rendering processes across different substrate materials at specific spatial and temporal scales, for instance, becomes useful in extracting function-related structural features and designing related material functional motifs.

The presence of interfacial water layers often leads to a dynamical onset in the material substrates, in which the substrate transforms from a rigid harmonic state to a flexible, material function related, an-harmonic state across a specific temperature range.12,39,49–57 This dynamical onset is absent when the material is dehydrated. In this Perspective, we focused on the coupling between the picosecond dynamical onset of substrates and their surface water at subzero temperatures and discussed the recent progress in the study of their molecular mechanisms. Diverse quantities of interest, such as the dynamic structure factor S(q), the mean-square displacement MSD, and the dynamic propensity DP, were calculated and analyzed in order to elaborate on the molecular details of the dynamical onset. The displacement correlation functions along the average hydrogen bond switch event trajectory were calculated to generate a real time picture of how the mobility in the interfacial water dynamical onset is rendered into the underlying substrate and triggers the material-specific dynamical transitions therein. Various ways of estimating the thermal transport across the solute–water interfaces, which are closely related to the aforementioned mobility rendering process, are then further discussed.

Previous studies have suggested that the dynamical onset of hydrated material is driven by the thermal activation of its surface water dynamics. Recently, temperature dependences of the dynamics of water and the underlying substrate have been explored independently using neutron experiments over a broad range of materials, including proteins, DNA, tRNA, polymers, and graphene oxide.57 The measurements were carried out with different oxidation rates, in different forms, and at different levels of hydration. The dynamic structure factor, S(q, Δt), measured in the neutron experiment, estimates the average amplitude of the atomic motions up to Δt. The rapid decrease in S(q, Δt) measured for the interfacial water on substrate surfaces that starts at a certain temperature marks the harmonic-to-anharmonic transition. Distinct materials exhibit vastly diverse dynamical onset temperatures varying from 200 to 260 K. Intriguingly, for different substrate materials, the interfacial water therein shows approximately the same onset temperature in S(q, Δt) as well as the mean-square displacement (MSD) in both experimental and simulation results.57, Figure 1(a) presents the simulated MSD of interfacial water adjacent to the Cytochrome P450 (CYP) protein and Graphene Oxide Membrane (GOM), both of which have the same onset temperature. Furthermore, the MSD of interfacial water near different categories of residues (therefore in different local chemical environments) on the surfaces of CYP and GOM also has the same onset temperature. The diverse, material-specific functional dynamics in the substrate were, therefore, considered to be activated by a water process that appears to be universal in all systems so far investigated.57 

FIG. 1.

Dynamical onset of hydration water obtained from MD simulations. The dynamic structure factor S(q, Δt) of hydration water (a) on the surface of CYP and GOM and (b) at distinct types of surface sites on the CYP and GOM surfaces are presented.

FIG. 1.

Dynamical onset of hydration water obtained from MD simulations. The dynamic structure factor S(q, Δt) of hydration water (a) on the surface of CYP and GOM and (b) at distinct types of surface sites on the CYP and GOM surfaces are presented.

Close modal

There has been a long lasting debate about whether the dynamic onset of interfacial water arises from a critical phenomenon or a kinetic phenomenon. In an early molecular dynamics simulation study on the hydrated bio-molecules (lysozyme and DNA),58 the dynamic transition of the macromolecules and their hydration water was found to coincide with the maxima of the isobaric specific heat and the temperature derivative of the orientational order parameter. This observation was interpreted as that the protein glass transition results from crossing the Widom line59 (the locus of correlation length maxima originated from the hypothesized second critical point of water). Neutron scattering measurements on hydrated bio-molecules showed a sudden change in the interfacial water dynamics,60 which was interpreted as the experimental support of the liquid–liquid critical point. The same relaxation probed by dielectric spectroscopy,61 on the other hand, shows no turning point as seen in neutron scattering when the characteristic relaxation time exceeds the neutron time window. Moreover, the transition also disappears when the neutron data are fitted using different analytical models.62 These observations implied that the dynamic onset of water might not be a critical phenomenon; instead, the turning in the curve occurs as the characteristic relaxation time of water enters the resolution window of the neutron scattering spectrometers at the onset temperature. A simple way to decide whether this water process is a critical or kinetic phenomenon is to check how Ton depends on the neutron spectrometer resolution Δt. A critical phenomenon should have its Ton independent of the instrument resolution. Ton for a kinetic process, on the other hand, would increment with a decreased Δt since it requires a higher temperature to activate the system and make the molecules move faster (so that the characteristic relaxation time enters the resolution time window). Figure 2 shows the simulation results of the dependence of Ton on the resolutions (Δt). A varying Ton is observed with respect to Δt, and similar observations were also presented in the experimental measurements.56 These results support the kinetic scenario.

FIG. 2.

Dynamical onset of hydration water obtained from MD simulation at different resolutions Δt. (a) MSD of interfacial water at the surface of graphene oxide membrane and (b) MSD of interfacial water at the surface of cytochrome P450 protein.

FIG. 2.

Dynamical onset of hydration water obtained from MD simulation at different resolutions Δt. (a) MSD of interfacial water at the surface of graphene oxide membrane and (b) MSD of interfacial water at the surface of cytochrome P450 protein.

Close modal

Previous research suggested that the relaxation of the substrate–water hydrogen bond network and the thermal activation of the translational motion of water play a crucial role in activating the dynamics of the underlying materials around the dynamical transition.6,39,41,51,63 In a simulation of myoglobin-in-water, for instance, the protein–water hydrogen bonding interactions are recognized as one main reason for collective protein fluctuations at low temperatures.39 In another study, a phenomenological two-state model, proposed based on the neutron and Mossbauser measurements of hydrated proteins, suggests that the onset of interfacial water motion triggers the relaxation of the protein–water hydrogen-bond network and enables the protein dynamical transition to occur.64,65 For the hydrated maltose binding protein (MBP), neutron measurement showed an intimate coupling between protein and hydration water dynamics. The simulated MBP–water hydrogen bond relaxation rate increases rapidly with the temperature at the dynamical transition of the protein, suggesting that the protein transition is associated with the relaxation of the protein–water hydrogen bond network.63 In a simulation of the RNase crystal with restrained hydration water oxygen atoms, water translational diffusion was largely reduced while rotational freedom was mostly preserved. At the same time, protein structural relaxation is significantly reduced.51 In another molecular dynamics simulation investigation of the hydrated myoglobin protein, the excess water translational diffusion constant and the excess mean-square fluctuation of the protein are demonstrated to have similar temperature dependences.41 

On the other hand, the characteristic time of the local water translational motion can be defined as the residence time τres of the water molecules staying around a position before moving away by a cut-off distance. This characteristic residence time, however, was demonstrated in the recent study57 to strongly depend on the local chemistry and is, therefore, not a universal property of interfacial water. It takes much longer for water adjacent to the charged protein surface sites to move away with respect to those around the non-charged residues. The charged-site-bound water also exhibits a much steeper temperature dependence and, therefore, a higher energy barrier. This observation can be understood in a cage effect picture, as the water molecules require different amounts of energy to escape from the cages formed by different local environments.

We can apply iso-configurational analysis (ISOCA)66–69 to gain further insight into the molecular details of water motion in different local protein environments. In ISOCA, a number of hydrated protein initial configurations were first generated using, for instance, molecular dynamic simulations. For each initial configuration, an ensemble of equal length trajectories was then shoot with randomly assigned moments satisfying the Boltzmann distribution at the corresponding temperature. Based on this trajectory ensemble, we can quantify the mobility tendency of a water molecule with a dynamical propensity (DP),
DPi=ri(t0)ri(0)2MSDISO,
where ri(t) is the position vector of water oxygen atom i at time t0 and MSD is the mean-square displacement of all oxygen atoms. ISO indicates that the outcome is averaged over many trajectories starting from the same initial configuration but with different sets of random velocities. If there is no correlation at all between an initial configuration and the subsequent dynamics of the water molecules, each water oxygen atom’s squared displacement, averaged over many trajectories with the same initial system configuration, would be the same as that of every other water oxygen atom. The features of the propensity distribution, therefore, contain information about the dynamics that can be directly attributed to some aspect of the initial configuration.

Figure 3 shows the calculated ISOCA DP distribution of water oxygen atoms at a series of t0 for water molecules initially adjacent to different kinds (charged, polar, and non-polar) of protein sites for cytochrome P450 protein (therefore, sitting in different local chemical environments) and bulk water. The converged DP values were averaged over 50 initial configurations, with 200 short trajectories shooting out from each configuration. DP distributions are pretty much identical in different local environments before t0 = 10 ps, while clearly different at longer times, such as t0 = 50 ps and t0 = 100 ps. A comparison of protein hydration water with bulk water (Fig. 3) further shows that the DP distributions before t0 = 10 ps are fairly close even between hydration/bulk water, while significantly different at the times beyond (t0 = 50 ps and t0 = 100 ps). The universal process of water is, therefore, probably related to the rattling motion of the water molecules within their confining cages instead of the translational motion defined by the aforementioned residence time τres, which is related to escaping from local cages. In a typical mode coupling theory (MCT) picture,70 the intermediate time rattling motion of the particles transiently trapped in cages is considered the β-relaxation, while the full relaxation with the particle breaking free from the cage is the α-relaxation. Mapping the molecular details observed in the ISOCA analysis with the different relaxation modes in the MCT framework and exploring the possibility of applying MCT to the description and prediction of interfacial water motions, such as the dynamical onset, on the material surfaces is a challenging but important research topic.

FIG. 3.

Probability density distribution of the DP for interfacial water on the surface of the CYP protein (charged: square, polar: circle, and non-polar: triangle) and for bulk water molecules (bulk: inverted triangle) with different run times [(a) t0 < = 10 ps and (b) t0 > 10 ps] labeled as different colors in ISOCA.

FIG. 3.

Probability density distribution of the DP for interfacial water on the surface of the CYP protein (charged: square, polar: circle, and non-polar: triangle) and for bulk water molecules (bulk: inverted triangle) with different run times [(a) t0 < = 10 ps and (b) t0 > 10 ps] labeled as different colors in ISOCA.

Close modal

When categorizing the water in the different local environments in the aforementioned ISOCA analysis of the hydrated CYP protein, we defined the protein–water interface based on the first peak of the protein–water pair correlation functions. It has been demonstrated in soft matter systems,69 such as water–vacuum and water–graphene, that the definition of interfaces can be critical in the study of interfacial water dynamics. The referenced atom sites on soft matter systems might be very flexible, and this may shift the peak position of the pair correlation function and subsequently influence the intricate interface dynamics. An alternative interface definition (e.g., the Willard–Chandler model,71 which generates a water density field by summing over the Gaussian density functions created from smearing out the discrete position of the water molecules and defines the instantaneous interface as the set of points on the density field whose value is equal to half the average equilibrium bulk water density) can be applied as well. How does the change in interface definition influence the interpretation of the subtle structure–dynamics correlation is topic that needs to be systematically addressed.

When varying the q values (up to qmax = 1.76 Å−1) in the neutron measurement, S(q, Δt) is averaged over different spatial ranges. On the other hand, Ton of the hydration water was found to be unchanged. The universal water process observed, therefore, has a spatial range smaller than 3–4 Å (2π/qmax). This is a rather local process with a length close to the scale of the hydrogen bonds. The interfacial water–water hydrogen bond correlation function CH(t) around distinct protein–surface residues and GOM surface sites was found to be invariable with the local chemistry. Furthermore, a significant similarity was presented between CHt) and S(q, Δt) in terms of their dependence on temperature, local chemistry, and the associated energy barrier. The universal dynamical onset of surface water, therefore, results from the switching of hydrogen bonds between the neighboring water molecules.56 

A somewhat simplified real time picture of the coupling between the dynamical onsets in the interfacial water and the underlying substrate can be generated by calculating the displacement correlation functions r(t)=αt,xαt1,x (we herein used the hydrated CYP protein as an example). Here, αx,t represents the position vector of the chosen atom at time t for the x switching events. Protein surface nitrogen [Fig. 4(a)] and oxygen [Fig. 4(b)] atoms, which form the hydrogen bond with the interfacial water, are chosen for this calculation. Time zero here is the moment that the specific water–protein hydrogen bond breaks. At this moment, these protein oxygen/nitrogen atoms have significant displacements.

FIG. 4.

Displacement time correlation function of the nitrogen atom (a) and oxygen atom (b) on the surface of CYP. (c) The average number of hydrogen bonds attached to oxygen atoms of donor water molecules when water–protein hydrogen bonds are exchanged. (d) The average number of hydrogen bonds attached to the oxygen atoms of the water molecules in the hydration layer of water–oxygenprotein donor water molecules.

FIG. 4.

Displacement time correlation function of the nitrogen atom (a) and oxygen atom (b) on the surface of CYP. (c) The average number of hydrogen bonds attached to oxygen atoms of donor water molecules when water–protein hydrogen bonds are exchanged. (d) The average number of hydrogen bonds attached to the oxygen atoms of the water molecules in the hydration layer of water–oxygenprotein donor water molecules.

Close modal

To examine the correlation between water–oxygenprotein (taking the hydrogen bonding of water with protein oxygen atoms as an example) and water–water hydrogen bond switches, the numbers of all water–oxygenprotein hydrogen bond switch events are collected and statistically averaged [Fig. 4(c)] at different moments along the switching event within 50 ps before and after the time zero. Before the water–oxygenprotein hydrogen bond is disconnected, the number of hydrogen bonds connected to the oxygen atom of the donor water molecule significantly decreased, which indicates a clear correlation between the water–protein hydrogen bond switch event and the water–water hydrogen bond switch event on the adjacent donor water molecule. It can be speculated that the energy released from the disconnection of the hydrogen bond connected to the donor water molecule is transferred to the hydrogen bond connected to the oxygen atom on the CYP, causing it to break and further transferring the energy to the CYP, causing the oxygen atom on the CYP to have a large displacement.

The hydrogen bond switch is largely affected by the accessibility of the surrounding potential receptors. For water molecules in the first hydration shell of the water–oxygenprotein hydrogen bond donor water, Fig. 4(d) shows the average number of hydrogen bonds on their oxygen atoms during the water–protein hydrogen bond switch. Shortly before the switching moment, the number of hydrogen bonds on donor water’s first hydration shell water decreases, and the potential vacancies that can form hydrogen bonds increase, which enhances the accessibility of the surrounding potential receptors and consequently induces the water–protein hydrogen bond switch.

The calculated energy barriers, assuming the Arrhenius temperature dependence,57 support as well the picture that water–water hydrogen bond relaxation couples to the substrate–water hydrogen bond relaxation and further to the substrate dynamics. The water–substrate hydrogen bond relaxation has the same energy barrier as that of the water–water hydrogen bond. Relaxation time τIqt of the intermediate scattering function for the interfacial water also shows the same energy barrier as that of hydrogen bond relaxation time, which is further inherited by the τIqt of the surface as well as the inner core atoms of the substrate. The characteristic relaxation of water captured by τIqt is, therefore, the result of water–water hydrogen bond switching. Water–substrate hydrogen bonds are the important channels transporting the surface water fluctuations to the connected substrate sites and then spreading out to other regions of the substrates.

On the other hand, the water–substrate hydrogen bond has a longer relaxation time compared to the water–water hydrogen bond. The τIqt of substrate inner atoms is also longer than that of substrate surface atoms, while the τIqt of interfacial water is shorter than that of the substrate. Therefore, although the interfacial water, the substrate surface, and its inside regions have a similar energy barrier for fluctuations, the rate of fluctuation differs significantly as the inner-core of the substrate is further away from the mobile surface water and, thus, shows a slower response, which will require a higher temperature to be activated. Similarly, while the fast relaxations in different substrate materials inherit the same energy barrier from their universal surface water hydrogen bond switching processes, their dynamical rates can differ significantly due to their distinct material nature, such as structures, packing, and substrate–water interaction strength, which leads to a significant diversity in the dynamic onset temperature.

We herein limit our discussions on the universality and diversity of interfacial water dynamical onset to a timescale of up to dozens of picoseconds. Due to the multi-scale, complex structure of the water hydrogen bonding network, water dynamics has a hierarchical nature. Some other water dynamical modes, such as the collective water–water reorientations on the surfaces of different hydrated systems, detected using other tools such as dielectric measurement, can also present a universal nature. These collective water motions might have their characteristic time up to 1000 times slower than the water dynamical onset discussed herein. Moreover, the collective water–water motion has a surface-dependent relaxation time, while the relaxation time of the process observed in the neutron experiment is substrate independent. Therefore, in order to discuss the dynamical couplings between water and substrate/solute and analyze the underlying molecular mechanism, the nature of the water and substrate dynamics/fluctuations chosen to investigate, including their spatiotemporal scales, needs to be clearly addressed. A further, revealing investigation along this thread is to compare the molecular details in the coupling/driving mechanisms of different water/substrate dynamical mode pairs and to rationalize their possible correlations and causalities.

The coupling observed between the subzero temperature interfacial water dynamical onset and the substrate dynamical onset through the temperature dependent neutron scattering measurements has a potentially distinct difference with respect to what was observed, for instance, in the room temperature bulk solution femto-second fluorescence measurements.57 In the neutron measurements of low temperature water/substrate dynamical onset, with the increment of temperature, the dynamical transition of the interfacial water molecules starts at a lower temperature where the substrate remains in its rigid harmonic state until a higher temperature. This suggests a picture that water molecules are activated first and drive substrate dynamics, and the energy is then transferred from the water molecules to the substrate. In the bulk solution processes observed by fluorescence, on the other hand, the dynamics of the interfacial water couple with the much more sophisticated, flexible anharmonic solute structural fluctuation and dynamics. The anharmonic dynamics of water molecules and warm substrate interfere with each other, leading to a much more sophisticatedly entangled mechanism. In the femto-second infrared pump–probe study of hydrated DNA.14,44–46 The formation of a hot ground state of the interfacial water shell is reflected by a one-picosecond component in the signal, while a slower contribution of tens of picoseconds is detected and attributed to a flow of excess energy from the water shell to DNA, followed by the warming up of DNA as well as the energy redistribution in the whole DNA molecule. Theoretical studies with abundant molecular details are desired for this category of energy and mobility rendering processes.

Thermal transport across the solute–water interfaces in the room temperature bulk solutions, which is closely related to the aforementioned energy and mobility rendering processes, is mediated by vibrational dynamics and energy relaxation.35 In some works on the thermal transport across the protein–water interfaces, for instance, the stationary non-equilibrium molecular dynamic simulations were carried out72 with a temperature gradient placed in a direction perpendicular to the interface. The temperature relaxation was monitored along the way and fitted to a solution of the heat diffusion equation to calculate the interface thermal conductance and conductivity. In some other cases, the interface thermal conductance was calculated in an analytical model35,73,74 as the heat flow Q̇ divided by the difference in temperature ΔT and the interface area A: hBd=Q̇AΔT. Heat flow across the interface was then expressed in terms of the vibrational excitations that passed through it. The diffuse mismatch model was applied to eliminate the transmission probability, which assumes that after crossing the boundary, a vibrational excitation has no memory about which side of the interface it initiated from. The final model is expressed as hBd=14kBdω(βω)2×ν1(ω)ν2(ω)ρ̄1(ω)ρ̄2(ω)ν1(ω)ρ̄1(ω)+ν1(ω)ρ̄1(ω)×eβω(eβω1)2, in which νi is the speed of propagation on side i and ρ̄i(ω) is the vibrational mode density on side i.

Energy conductivity calculation with more molecular details was carried out for the interface between protein and the water cluster at its interface,75 in which the inter-residue energy flow was evaluated by an energy current Jij=12Fij(vi+vj), where vi is the velocity for atom i and Fij is the pairwise inter-atomic force from atom j to i. The inter-residue energy current between residues A and B is then calculated as JAB=iANAjBNBJij, where NA and NB are the number of atoms in residues A and B, respectively. The discrete autocorrelation of the inter-residue current reveals the inter-residue energy conductivity. The energy transfer rate calculated was found to be proportional to the inverse of the fluctuations around the average distance between the protein–water contact.

For substrates with less complicated atom arrangement structures, such as graphene or graphene oxide, a state-of-the-art potential energy surface of water–substrate and water–water can be constructed based on high level ab initio calculations and machine learning techniques.76–80 An accurate description of energy and flexibility transfer between water and the substrate can be generated from the dynamical simulations using these potential energy surfaces.

Multiscale, hierarchical water motions on the surface of different materials under different conditions (temperature, hydration extent, pressure, etc.) and the coupling of this motion with the substrate/solute dynamics and the influence of these couplings on the material functions are complex, long lasting, interdisciplinary research topics. We herein mostly focus on a specific coupling process, namely, the coupling between the picosecond dynamical onset of substrates and their surface water in temperatures lower than the freezing point (273 K), and discuss the recent progress in the study of its molecular mechanisms, which lays out a neat platform for developing new experimental, theoretical, and computational tools for the investigation in this field.

This work was supported by the NSFC Grants (Grant Nos. 22273106 and 22063007). Q.Z. acknowledges the support of the Basic Scientific Research Foundation for Universities of the Inner Mongolia (Grant No. GXKY23Z080) and the Scientific Research Foundation of IMUN for doctors (Grant No. BS581).

The authors have no conflicts to disclose.

Tan Jin: Data curation (equal); Investigation (equal); Writing – original draft (equal). Qiang Zhang: Conceptualization (equal). Wei Zhuang: Conceptualization (equal); Funding acquisition (equal); Writing – original draft (equal); Writing – review & editing (equal).

The data that support the findings of this study are available within the article. Some of the computational details about the intermediate structure factor S(q, Δt), MSDt), the hydrogen bond relaxation time, and the residence time of water within the solvation shell of protein, as well as the details of molecular dynamic simulations, are reported in Ref. 57.

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