Retraction Note: New insights into the microscopic interactions associated with the physical mechanism of action of highly diluted biologics

In this investigation, we report the effect on the microscopic dynamics and interactions of the cytokine interferon gamma (IFN-γ) and antibodies to IFN-γ (anti-IFN-γ) and to the interferon gamma receptor 1 (anti-IFNGR1) prepared in exceptionally dilute solutions of initial proteins. Using both THz spectroscopy and molecular dynamics simulations we have uncovered that the high dilution method of sample preparation results in the reorganization of the sample surface residue dynamics at the solvent–protein interface that leads to both structural and kinetic heterogeneous dynamics that ultimately create interactions that enhance the binding probability of the antigen binding site. Our results indicate that the modified interfacial dynamics of anti-IFN-γ and anti-IFGNR1 that we probe experimentally are directly associated with alterations in the complementarity regions of the distinct antibodies that designate both antigen–antibody affinity and recognition. A number of crystal structures 1–3 of antigen in the bound state have revealed an essential role of the solvent molecules in the hydration shell in stabilizing the complexes and have provided a detailed molecular basis for understanding the thermodynamics forces that drive the association between the antigen–antibody interactions. Analyses have revealed that the main force stabilizing the complexes stems from hydrogen-bonding (H-bonding) but other weak forces such as van der Waals interactions and the enthalpy from hydration also contribute to conformational stabilization. Hydration of molecules depends on the properties of the solution, which, according to the recently published data, can significantly change as a result of various physical effects 4–6 and, consequently, should alter the conformation and properties of proteins. The conformational transformation of IFN-γ exposed to high dilutions (HD) of antibodies to IFN-γ has recently been shown using the 2D-NMR method 7 . The technology of HD implied a number of serial dilutions accompanied

A number of crystal structures 1-3 of antigen in the bound state have revealed an essential role of the solvent molecules in the hydration shell in stabilizing the complexes and have provided a detailed molecular basis for understanding the thermodynamics forces that drive the association between the antigen-antibody interactions. Analyses have revealed that the main force stabilizing the complexes stems from hydrogen-bonding (H-bonding) but other weak forces such as van der Waals interactions and the enthalpy from hydration also contribute to conformational stabilization. Hydration of molecules depends on the properties of the solution, which, according to the recently published data, can significantly change as a result of various physical effects [4][5][6] and, consequently, should alter the conformation and properties of proteins.
The conformational transformation of IFN-γ exposed to high dilutions (HD) of antibodies to IFN-γ has recently been shown using the 2D-NMR method 7 . The technology of HD implied a number of serial dilutions accompanied by intense physical (mechanical) stress, which, according to the results of physical-chemical studies, can affect not only the properties of water, but even change the parameters of piezoelectric crystals 8 .
Among the non-specific effects, it has been shown that turbulent stirring involving the formation of nanobubbles intensifies the generation of reactive oxygen species, and, in particular, hydrogen peroxide, whose concentration increases from dilution to dilution 5 . Also, adding substances in ultra-low concentrations leads to a change in the structure of water, i.e. to a change in its hydrogen bonds [9][10][11] . Also, it has been shown that the process of repeated dilution of antibodies to IFN-γ combined with external physical stress leads to the formation of unique nano objects 6 , which were further detailed as flotation-affected nanobubbles that aggregated the antibodies retained on their surface even after sequential HD 4 .
Thus, the ability of the solvent to affect the properties of protein molecules, along with the possibility of altering the properties of the solvent through technological processing, formed the basis for the development of drugs based on HD antibodies 12 . However, the nature of this effect from a physical standpoint remained unknown until Johnson's papers were published, which theoretically demonstrated that transient structures in water can alter the properties and activity of proteins 13 . Here it was shown that "surface" THz-vibrational modes of water clusters "resonate" with THz-frequency "bending" vibrations of amino acid residues in proteins 14 . These results confirmed the ability of HD of antibodies to form structures that could be characterized by a broadening of the energy distribution of intermolecular bonds in the HD solution of antibodies compared to the control solution 15 .
Therefore, in this study, we have used TeraHertz (THz) spectroscopy to investigate HD samples of an antigen (IFN-γ and antibodies (anti-IFN-γ and anti-IFNGR1) in an effort to comprehend how solvent environment may OPEN Lehrstuhl  www.nature.com/scientificreports/ alter the binding regions of protein association. We have also conducted a series of molecular dynamics (MD simulations) on crystal structures of antibody and antigen complexes with the aim of providing a basis for the interpretation of our experimental measurements. The interpretation of the results obtained is consistent with the data of previously performed structural studies of the action of HD proteins on the conformation of IFN-γ 7 , and for the first time explains the physical features of the molecular mechanism of the modifying action of HD samples.

Experimental THz spectra on HD of anti-IFN-γ, anti-IFNGR1 and IFN-γ and standard solutions of IFN-γ and IFNGR1.
We have performed experimental THz spectroscopy measurements on the antibody of interferon gamma (anti-IFN-γ), the antibody to the interferon gamma receptor 1 (anti-IFNGR1) and of IFN-γ prepared in exceptionally dilute solutions (HD). Our measurements also include a HD prepared sample of liquid water (HD-water) that is contrasted with distilled liquid water (water). Additionally, we have also performed measurements on IFN-γ and anti-IFN-γ in more concentrated solutions in a standard phosphate buffer. The global fluctuations, which reside in the < 100 cm −1 region of the THz spectrum, describe the intrinsic dynamics of a system 16 . These globally, correlated associations reflect the sampling of the ensemble of conformations that comprise the free energy landscape of all possible conformations. Therefore, experimental measurements in this region of the spectrum provide direct information about the sampling of conformational substates in proteins as well as transient structures in hydrogen-bonding liquids like water. On the other hand, the motions detected in the 100-250 cm −1 spectral region reflect local relaxations that are sensitive to specific intramolecular and intermolecular induced correlated fluctuations in the system. For the HD-sample solutions, we detect motions that are mostly associated with localized intermolecular interactions such as inter-and intra-protein contacts as well as protein interactions with the solvent in the 40-240 cm −1 region of the experimental spectrum.
In Fig. 1a, we detect a very broad envelope in the spectrum of water and HD-water that extends from approximately 90-200 cm −1 but peaks at about 160 cm −1 . The THz spectrum of liquid water has been extensively studied and it is believed that the broad envelope is associated with various intermolecular hydrogen-bonding (H-bonding) associations in water. For instance, a broad, prominent band peaking at about 180 cm −1 in numerous investigations [17][18][19][20] of liquid water has been ascribed to hindered translational oscillations of water molecules in with water. IFN-γ is a dimerized soluble cytokine that is critical for innate and adaptive immunity predominately against viral infections. The IFN-γ monomer consists of six α-helices and an extended unfolded sequence in the C-terminal region. The biologically active dimer is formed by anti-parallel association of two interacting monomers. Our MD simulations have been performed on the crystal structure of the active dimer. Explicitly, we have used a full correlation analysis (FCA) 28 of the MD simulation to investigate the correlated, internal protein fluctuations of the IFN-γ dimer. Using this method we determine that IFN-γ has primarily two main conformational states that form the dynamical conformational landscape of the unbound cytokine dimer (Fig. 2). The two detected minima (conformational states) on the energy surface have different energy levels with a low energy barrier separating the two distinct conformations-indicating that "hopping" between the two states is probable by means of low energy, thermal fluctuations. Further analysis allows us to associate the dynamics of the lower energy conformation (the conformation associated with the deeper energy basin) with a global torsional fluctuation that comprises correlated oscillation of all of the α-helical regions of the dimer (Fig. 2). The dynamics of the dimer in the shallower well (higher energy conformational state) involves oscillation of only a subset of the helices in distinct regions on the dimer structure. It is likely that the second mode is associated with a binding mode of the dimer complex.
Aqueous solvent containing 10% mole fraction ethanol (χ EtOH = 0.10). Conformation, mean square diffusion (MSD) and long-range correlations. We have also performed MD simulations of the IFN-γ dimer in a solution of water mixed with ethanol. Our aim is to identify protein intra-and inter-molecular interactions that may be altered in a mixed aqueous solvent that resembles the HD prepared samples discussed in the experimental section of this investigation. In Fig. 3a-c we observe that the addition of ethanol to the dimer hydration shell seemingly has a strong influence on the dynamics of IFN-γ. The plot of the root mean square fluctuation (RMSF) of the dominant (single) conformation in Fig. 3a and the corresponding C α− representation in Fig. 3b clearly display that the regions most affected in the mixed solvent environment are the loops connecting helices A and B (A-B loop) as well as a centralization of dynamics within the C-terminus on the first monomer making up the dimer. The A-B loop is necessary for receptor-ligand binding, indicating that the change in solvent may affect the biological activity of the cytokine. In an effort to gain further insight into the nature of the protein internal interactions that are altered with the change in solvent, we have calculated the root mean square deviation (RMSD) of the C α− atomic distances from the MD simulation of IFN-γ in water versus that in the water-ethanol mixture in Fig. 3c. These internal sub-nanosecond timescale fluctuations are central for protein function and are also the motions coupled with the dynamics of the surrounding solvent. At first glance it becomes immediately clear that the protein internal fluctuations in the mixed solvent differs dramatically from the protein dissolved in water. The RMSD of IFN-γ in the water-ethanol mixed solvent exhibits a sharp rise at around 3 ns and that sub-    www.nature.com/scientificreports/ sequently reaches a higher amplitude plateau at longer times, suggesting that a dynamical transition has taken place. The steep curve in the water-ethanol mixture RMSD signifies large-scale molecular motion. After a finite time (> 4 ns), the system adapts to a new diffusive equilibrium. IFN-γ in water on the hand, is more characteristic of a system with thermal fluctuations at equilibrium. Interestingly, we have also calculated the distance correlation coefficient from the C-α atom distances in IFN-γ in the two solvent environments. This analysis reveals that the collective dynamics within the protein is also altered in the mixed solvent. Figure 3d illustrates that the protein containing only water in its hydration shell is dominated by C α -C α interactions that extends only as far as the closest nearest neighbor. IFN-γ in the water-ethanol solvent environment comprises a heterogeneous environment with two distinct distributions: a smaller population with nearest neighbor correlations similar to what we have uncovered in the IFN-γ system containing only water and a secondary, larger population with long-range atomic correlations that incorporate at least second nearest neighbor interactions.

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Van Hove correlation function and collective diffusion. Further insight into the microscopic dynamics of diffusion in the differing IFN-γ environments can be attained by analysis of the self-part of the van Hove correlation function. The van Hove correlation function is defined as And the function P(r,t) = 4πr 2 G s (r,t) describes the likelihood that a particle at r = 0 has moved a distance r in time t. In the hydrodynamic limit the atoms have a Gaussian peak that broadens spatially as a function of time. The Gaussian behavior is attributed to the structural relaxation time of a particle in a liquid-like state. The presence of multiple peaks in the probability distribution signifies a diffusion mechanism driven by "hopping" or correlated jumps involving neighboring particles to neighboring sites. A particle and its neighbors remain "trapped" for finite period of time before undergoing a (collective) thermally-activated structural relaxation that is based on the initial hop. In Fig. 3e, the self-part of the van Hove function for IFN-γ in water is shown. There is little change in the position of the r value of the peak maximum but the amplitude decays as a function of time. This consistent with the decay of spatially arranged set of particles, such as protein in a confined environment, although it does not display the characteristics of an equilibrium liquid with a typical Gaussian probability distribution. IFN-γ with ethanol in the hydration shell in Fig. 3f has a primary peak that has negligible change with time indicating a very rigid or "caged" structure of a glassy or supercooled-like material 29 . At 400 ps a secondary peak emergences at approximately r ~ 1.8 Å corresponding to the distance between the protein and water molecules in the first hydration shell. So the presence of the secondary peak suggests that the solvent water in the hydration shell is somehow involved with the "hopping" between caged sites. The secondary peak continues to migrate with increasing time signifying a thermally-activated hopping (diffusion) mechanism utilizing correlated jumps involving neighboring particles to nearest neighbor sites in a glassy or supercooled-like state. The main non-evolving peak of IFN-γ in the ethanol mixture and the secondary "hopping" peak that emerges and evolves as a function of time are consistent with dynamic heterogeneity in the dynamics of the protein.
IFN-γ microscopic transport and relaxation dynamics. To gain a better understanding about the microscopic nature of the dynamical motion of the molecules in the systems being considered, we have calculated the means square displacement (MSD) r 2 (t) of the molecules in the system In Fig. 4a, it becomes more apparent that both samples have confined motion in the system but the cytokine with the ethanol in its solvation shell has significantly slower relaxation at long times when compared with the cytokine dissolved in just water. The MSD provides a dynamical picture of microscopic interactions and the effect on particle motion. At short times, the MSD increases according to r 2 (t) ≈ (3K B T/m)t 2 where m is the mass of the monomer and t is time. The particles at early times (≤ 0.1 ps) have uncorrelated motion both with other particles and their environment and this is called the ballistic regime. Repeated collisions with other particles eventually slows the displacement of the tagged particle where it becomes trapped in the potential well produced by neighboring particles. At later times a quasi-plateau region is observed in the MSD that signifies an increased caging of the particle-this intermediate caged-time motion is associated with β-relaxation. In many glass forming systems, the β-relaxation time scale is often extended at low temperatures. At long times, particle leaves the cage after an average time τ α , referred to as α-relaxation and during this period the particle enters the diffusive regime.
We have also analyzed the time dependence of the relaxation dynamics of the system with the self-intermediate scattering function (ISF) F s (q,t), where q is the wave-vector N is the number of particles in the system and < > denotes a thermal average over the position r(t) of particle j at time t. The self ISF is the spatial Fourier transform of the self-part of the particle van Hove correlation function. In Fig. 4b, a plot of the self ISF of IFN-γ at q max (the maximum peak in the static structure factor) in pure water and in the water/ethanol mixture clearly demonstrates that the mixed-solvent cytokine has "damped" motion www.nature.com/scientificreports/ in the cage of its nearest neighbors. The presence of a peak in this intermediate time scale suggests dynamic heterogeneity and clustering in terms of particle mobility. We notice a prominent peak in the self ISF at about 0.8 ps in the mixed solvent system which is directly related to the highly structured local environment of the particle. The presence of this peak is typically associated with the boson peak in glassy type materials and is attributed to an excess of the vibrational density of states. The conspicuous presence of the 0.8 ps boson peak in the IFN-γ mixed-solvent sample and the weak presence in the pure water sample may also explain the slower relaxation of IFN-γ in the presence of ethanol as observed in the MSD in Fig. 4a.
Water dynamics in the protein hydration shell. There have been numerous studies 30-32 that have clearly demonstrated that water in the protein hydration shell and protein dynamics are intricately connected. Principally, the protein and the water in its hydration shell are connected by an extensive network of hydrogen bonds that promote functionally important protein motions. The picosecond time fluctuations of the water molecules particularly have been found to have a large influence on protein biological activity. From our MD simulations on IFN-γ, we have also investigated the collective dynamics of water in the protein hydration shell in the two distinct solvent environments. Specifically, we have used MD simulation to calculate the properties of the hydrogen-bond network of water that supports propagating modes on the picosecond time scale that have been linked with energy transfer and modulation of the biological activity of proteins [33][34][35] . We use an approach that utilizes a distant-dependent calculation of the dielectric function of the water molecules in the protein hydration shell, where the distance (d) is the distance from the protein surface. The distant-dependent dielectric constant is subsequently used to calculate the absorption coefficient (α(ν)) which can be used to characterize the collective propagating modes of water in the MD simulation hydration shell. In Fig. 5a, we plot the distance-dependent absorption coefficient (α(ν)) of the hydration water of IFN-γ dissolved in water. At all of the distances probed we find a weak mode ~ 175 cm −1 . The ~ 175 cm −1 mode has been previously identified as a low frequency translational mode of pure liquid water in a number of THz 18,36,37 and Raman 38 experimental measurements. There is no dispersion (propagation) in the translational mode as a function of distance indicating that it is an optical-like mode in the water hydration shell. In the IFN-γ system in the mixture of water with ethanol ( Fig. 5b) we observe a more prominent translational water band at ~ 175 cm −1 in the absorption spectrum. Previous computational investigations 33,35 on the translational diffusion of water in the presence of a protein have determined that the translation component of water is closely tied with the dynamical transition in proteins (at approximately 240 K), anharmonic dynamics and functionality. It is also interesting to note that the dynamical behavior of the hydration water in the two samples is considerably different in the extended hydration shell. Again, using the self -part of the van Hove correlation function to this time analyze the dynamics of the water in the hydration shell, we find that in the pure water sample the equilibrium dynamics in the extended hydration shell (≥ 1.9 nm) is of a fast decaying liquid with a typical Gaussian-like probability distribution (Supplementary Figure S1). On the other hand, the water molecules in the equivalent hydration layer in the ethanol-mixed solvent displays slow relaxation dynamics that mirror the dynamics of water molecules in the hydration layers that reside much closer to the protein surface. The slow relaxation dynamics of the water molecules so distant from the protein surface suggests that the enhanced translational diffusion of water molecules in response to ethanol in the protein hydration shell promotes long-distance correlations that may provide insight into how alterations in hydration dynamics may alter the propensity of the cytokine to interact with other macromolecules. For instance, in Fig. 5c, it is clear that the overall global dynamics of IFN-γ is dramatically red-shifted in the ethanol-mixed solvent. This distinctive change in the low-frequency modes may indicate that the cytokine has an altered binding dynamics or interaction dynamics when interacting with other macromolecules. www.nature.com/scientificreports/ Water-protein H-bonding interactions and protein methyl group fluctuations in the presence of ethanol. Our analysis of the MD simulation of IFN-γ also includes an examination of the H-bonding interactions coupling the protein motions with the solvent. Although our main focus has been on the water dynamics in the hydration shell, we have also monitored the ethanol dynamics in the mixed solvent environment in the MD simulations. From our analyses we have deduced that the ethanol molecules in the hydration shell have only a very modest/ weak interaction with the protein in general. We have calculated the H-bonds between the ethanol molecules in the hydration shell and IFN-γ and have found only a minor contribution of direct H-bonds between the two groups. Rather, we have found that the ethanol molecules have a tendency to self-associate into long, linear chains that form clathrate-like structures around the mobile loops and helical regions of the protein, particularly regions with clusters of amino acids with large, hydrophobic side chains. The ethanol-protein interactions are largely electrostatic in nature. One such region is the A-B loop, which is surrounded by chain-like assembly of ethanol molecules that interact weakly with the proline and lysine amino acids that form part of the interfacial loop region in both monomers making up the IFN-γ dimer. We have previously noted that the dynamics of the A-B loop is strongly modulated in the ethanol-mixed solvent when contrasted with the same region in an all-water solvent (Fig. 3a, b). Interestingly, we also observe that the water density and H-bonding interactions between the protein and water are enhanced in the regions adjacent to the ethanol chains. Analyses of the water-protein H-bonding fluctuations from the MD simulation reveal that in the ethanol-mixed solvent, water H-bonds with IFN-γ strongly modulate the methyl group fluctuations of the protein. For instance, in Fig. 5d a comparison of the calculated water-protein H-bonding spectrum of IFN-γ in ethanol-water versus that in water shows a new band at 1375 cm −1 , attributed to δ(CH 2 ) twisting/bending, that indicates a greater mobility of methyl group fluctuations 39 when ethanol is added to the hydration shell. Similarly, there is definitive red-shift of the1460 cm −1 peak in the ethanol-mixed solvent when compared with the same peak in the water-only hydration shell. The peak at 1460 cm −1 stems from δ(CH 2 ) scissoring vibrations coupled with CH 3 antisymmetric bending-again indicating that the methyl groups are more mobile in the cytokine system with a mixed ethanolwater hydration shell. On the other hand, we detect the loss of peaks at ~ 1410 cm −1 and 1515 cm −1 in IFN-γ in  www.nature.com/scientificreports/ the heterogenous solvent environment signifying that polar side chains, particularly those found prominently on the cytokine surface, are more tightly bound by water H-bonds. The peak in the spectrum at 1410 cm −1 is attributed to symmetric stretching vibrations of side chain COO − groups 40 . The diminished presence of the 1410 cm −1 band is primarily associated with increased water H-bonding to (charged) polar side chains on the cytokine surface in the ethanol-mixed solvent. Likewise, the 1515 cm −1 in the Amide II region is strongly associate with N-H bending and is a good indicator of protein-water coupling. The near absence of the Amide II band is strongly suggestive that the water H-bonding to amino acid residues is stronger/more rigid when ethanol is added to the hydration shell. Overall, our analysis suggests that the methyl group fluctuations in IFN-γ are enhanced when ethanol is introduced into the protein hydration shell, while at the same time we detect an increase in the strength of the H-bonding between the water molecules in the hydration shell and residues on the protein surface. It is likely that the enhanced dynamics of the methyl groups of IFN-γ in the ethanol solution has significant ramifications on the sampling of the protein conformational landscape. For instance, the results from a number of separate investigations 41-44 focusing on protein conformational dynamics have determined that methyl group fluctuations play a central role in regulating the low-temperature onset of anharmonic protein dynamics. The activation of the local diffusive process afforded by methyl group fluctuations at low temperatures is the precursor for global diffusive protein dynamics that take place at the protein dynamical transition.

MD simulation of the antibody fragment antigen-binding (Fab fragment) A6 of the insulin-like growth factor 1 receptor (IFNGR1). Aqueous solvent with water.
In this investigation we have also performed MD simulations on the antibody Fab fragment A6 in solution. The neutralizing antibody (nA6) is one of the ligands known to be recognized in the extracellular region of the interferon-gamma receptor (IFNGR). The Fab fragment is the region of the antibody that binds to antigens. It is comprised of one constant domain and one variable domain-with each domain consisting of a heavy and a light chain. Consequently, the domains of the fragment are what shape the antigen-binding site. We again analyze the conformational dynamics of the antibody by analyzing the FCA of correlated motions. In Fig. 6a the antibody dynamics reveals an energy landscape consisting of only one major conformational state. The largest displacement entails a hinge-bending type motion that primarily involves the CC′ loop that resides close to the binding site with the receptor.  www.nature.com/scientificreports/ Aqueous solvent containing 10% ethanol mole fraction (χ EtOH = 0.10). Solvation shell distortion and altered amino acid methyl chain and aromatic ring dynamics. We have also performed MD simulations of the antibody in a solution of water mixed with ethanol. Unlike IFN-γ, the correlated fluctuations are not substantially altered with the addition of ethanol into the antibody hydration shell. Similar to the antibody in an all water environment, there is only a single dominant conformation that we detect during the course of the MD simulation (Fig. 6b, c). Likewise, the principal motion of the conformation can be described as a hinge-bending type mode that is centered around the CC′ loop close to the receptor binding site. Interestingly, there are two regions of the antibody in the ethanol solution that differ significantly from the dynamics observed in the pure water solution. Namely, the interior β-sheets close to the N-terminal region of the antibody (residues 24-29 and residues 83-85, respectively) have substantially reduced dynamics compared with the antibody in water. The reduced dynamics equate to a rigid core-like region in the center of the antibody structure. On the opposite side of the antibody, we also note an increase in the dynamics of the β-sheet region closest to the C-terminus, which consequently forms a substantially more flexible region on the opposing surface. It is interesting to point out that the dynamical changes in the antibody appear to be closely connected with modifications in the hydration shell structure that take place when the ethanol is added to the antibody system. In Fig. 6 d, e, the distribution of both water molecules and ethanol molecules within a 5 Å distance from the antibody surface clearly reveals that the water hydration shell is noticeably distorted in the water-ethanol mixture. Analogous to what was previously observed in IFN-γ, we discern that the ethanol molecules do not strongly interact directly with the antibody-but rather self-associated into long, chain-like assemblies that form clathrate-like structures around the solvent-exposed helical regions of the protein. Additionally, we determine that the water molecules immediate to the protein surface are skewed such that the majority of the water molecules in the first hydration shell shift toward the C-terminal region while the N-terminal region is left exposed. It is likely that the altered distribution of water molecules in the antibody hydration shell-particularly on the N-terminal side-is correlated with the reduced dynamics in that region. For instance, analyses of the water-protein H-bonding fluctuations from the MD simulation in Fig. 6f reveal that in the ethanol-mixed solvent, water H-bonds strongly modulate the methyl group fluctuations of the protein as well as aromatic amino acid sidechains. The calculated H-bonding spectrum of protein-water interactions exposes new water H-bonding bands in the water-ethanol mixed solvent that are not present in the pure water spectrum. Namely, we uncover a new band close to 1375 cm −1 and another weaker band at 1290 cm −1 . The first is attributed to a water-induced δ(CH 2 )/C-OH side-chain bending dynamics and the second is associated with solvent-induced aromatic sidechain fluctuations of amino acids such as tryptophan or histidine that are typically found in type I and type II β-turns. Interestingly, we also notice the loss of the band at 1330 cm −1 , which is prominent in the pure water spectrum. This band is associated with solvent-induced torsional oscillations of amino acid backbone atoms. It is well known that proteins are energetically coupled with the torsional oscillations of water molecules in the hydration shell. More precisely, the molecular rotational degrees of freedom of the water in the solvation shell have been shown to be closely linked with the energy dissipation pathways of the protein 31 . Hence, the loss of the peak at 1330 cm −1 in the water-ethanol mixed solvent may indicate that there is a decoupling or reduced coupling of the water torsional oscillations in the hydration shell that may alter the relaxation dynamics of the protein. Interestingly, we find no clear indication from the calculated H-bonding spectrum that there is a change in the strength of the water-protein H-bonds in the distinct antibody systems. There is a discernible band at approximately 1515 cm −1 in the pure water antibody solution that appears to be absent in the mixed ethanol solvent. Previously, we have identified the 1515 cm −1 band as one of the spectral marker for assessing the strength of water-protein backbone H-bonding interactions. Unfortunately the possible band is obscured by the noise in the spectrum making assessment difficult. The noise level in the calculated spectra is relatively high due to the overall weaker water H-bonding in the antibody solution when compared with the IFN-γ solution samples discussed in the previous section.

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Long-range dipole interactions of water molecules in the protein hydration shell. In the previous section, we observed that the ethanol-mixed solvent of the antibody had a strong effect on the distribution of water molecules in the protein hydration shell. To investigate further, we again analyze the dielectric properties of the water molecules in the antibody hydration shell to determine how the collective dynamics of the water molecules may affect the overall dynamics of the protein. In Fig. 7a, we plot the distance-dependent absorption coefficient of the hydration water of the antibody dissolved only in water. At a distance of 1.9 nm from the protein surface we find a prominent water band at 380 cm −1 that is assigned to a (hindered rotation) libration associated with a intermolecular twisting-like motion in the water H-bonding network. As the distance to the protein surface is reduced (d gets smaller) we observe a red-shift of the 380 cm −1 mode. At a distance equivalent to the first hydration shell of the antibody (d = 0.5 nm), we witness the emergence of a new peak close to180 cm −1 . We have previously identified the ~ 180 cm −1 band as a water (restricted) translational mode. The shift of the peak position in the complex refractive index spectrum as a function of distance suggests that the librational mode is a propagating mode. In the water H-bonding network the twisting motion of water molecules in the extended hydration shell couple with the restricted translational motions of water molecules at the protein surface. Several experimental and computational investigations have previously uncovered a connection between the coupling of the intermolecular degrees of water and the dissipation of excess energy via the water H-bonding network 30,31,45,46 . Specifically, with excitation the excess energy in the water network is initially distributed locally through the rotational modes and subsequently on a picosecond time scale transferred to the restricted translational motions of neighboring molecules in the extended hydration shell. It has been proposed that ultimately molecular relaxation is attributed to the intermolecular translational motions 34 of the interacting molecules in the water H-bonding network. www.nature.com/scientificreports/ In the antibody system with a mixed water-ethanol solvent in Fig. 7b, we discern a visible band at 180 cm −1 at a distance of 1.9 nm from the protein surface. The 180 cm −1 band becomes noticeably more distinct as the distance to the protein surface is approached and is maximum at a distance equivalent to the protein-water interface. The long-distance spatially correlated translational motions observed throughout the entire hydration shell indicates the presence of coherent long-range dipole interactions in the water network. Further, the disappearance of the 380 cm −1 mode from the distance-dependent dielectric spectrum suggests a decoupling of the water rotational and translational intermolecular degrees of freedom in the water hydration shell dynamics. Several ultrafast spectroscopy experiments focusing on protein-water interactions in the protein hydration shell have observed that the strengthening of the H-bonds 31,35 between the protein and the hydration water retards the orientational motion of water. The decoupling of the rotational and translational degrees of freedom results from water molecules interacting with charged/polar groups on the protein surface that become confined. The confined water molecules become correlated with the translational motions of neighboring, adjacent water molecules ultimately leading to long-range spatial correlations in the water H-bonding network. Femtosecond spectroscopy experiments 47 have identified that ultrafast flow of energy into the H-bonding network requires anharmonic coupling between the translational and librational degrees of freedom. Hence, disturbance of the H-bonding structure within the hydration shell caused by increased restricted translations leads to slow modulation of the librational motions and consequently, has been shown to lead to a marked "slowing down" of molecular relaxation. In our case, the increased interaction of water molecules on the antibody surface in the mixed water-ethanol solvent is heterogeneous. Water molecules in the ethanol mixed solution have increased binding to selective regions on the antibody surface. This primarily effects the water-induced amino acid side-chain orientational motions on the protein surface that are typically associated with the protein "dynamical transition". Consequently, we identify surface regions with reduced water interaction with high mobility and regions with increased water interaction with less mobility.

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Long-range intra-protein interactions in the antibody and the effect of hydration dynamics on protein motions. The MSD of the antibody in both solvent environments in Fig. 7c shows displacement typical of a particle in a confined environment. Although, the long-time relaxation behavior of the antibody in the ethanolmixed solvent is more characteristic of a sub-diffusive system indicating a more crowded environment and consequently a slower long-time α-relaxation. Correspondingly, the self ISF of the antibody in Fig. 7d reveals a similar short-and intermediate-relaxation regime although the ethanol-mixed antibody system has a more prominent peak in the β-relaxation region indicating a stiffer cage of the trapped particle. The self-part of the van Hove correlation function for nA6 in pure water and in the water-ethanol mixture is shown in Fig. 7e, f. In both cases we find that there is little change in the r value of the first peak in both position and amplitude. These www.nature.com/scientificreports/ characteristics in the self correlation function with time are indicative of colloidal type system in which strong self interactions form in a high viscosity environment. Correspondingly, the second peak in the self correlation function is indicative of a trapped particle oscillating in a cage of its nearest neighbors.
One interesting question to consider is how the dynamics in the hydration shell may directly affect the dynamics of the antibody. Recent femtosecond spectroscopy experiments 48 on protein hydration water have demonstrated that the dynamics around a global protein surface is hierarchical in nature. The ultrafast dynamics of hydration water in the protein hydration shell, which forms the initial response to excitation, takes place on the hundreds of femtosecond time scale and corresponds to water molecules in the outer layer bulk-like region of the molecule. This is followed by the collective water/side-chain orientational dynamics that take place on the few picosecond timescale. And lastly, the cooperative water/side-chain structural changes that restructure the collective network as whole and take place on a time scale of hundreds of picoseconds. The findings from these time-resolved studies made it apparent that the coupled solvent-protein motions are intimately tied with the hydration water relaxation processes. We note that in our MD investigation of nA6 that the most substantial changes that we observe in the distinct solvents are those associated with the extended hydration shell distant from the protein surface. For instance, the prominent 380 cm −1 librational mode found in the distant-dependent refractive index of the bulk-like hydration layer of the antibody (Fig. 7a) in pure water is absent in the sample with a minor component of ethanol in the hydration shell. An analysis of the hydration water vibrational density of states (VDOS) at a distance of 1.9 nm from the protein surface in Fig. 8 reveals that the lowest frequency mode in the spectrum (at about 50 cm −1 ) is blue-shifted in the antibody with an ethanol-mixed solvent. This lowest frequency mode has been attributed to an intermolecular H-bonding mode in the liquid water protein hydration shell network and the blue shift in the VDOS reflects the coupling between solute and solvent modes 49 . Additionally, it is also apparent that the overall shape of the VDOS spectrum within the equivalent hydration layer differs in the two samples. In the water-only antibody system, we find three distinct modes in the spectrum at approximately 430 cm −1 , 180 cm −1 , and 50 cm −1 that correspond to the librational, intermolecular stretching, and intermolecular bending modes of the interacting water molecules. In the water-only VDOS antigen spectrum we note that the librational and intermolecular stretching mode have a lower intensity than the 50 cm −1 bending mode. The shape and intensity of the antibody VDOS is in line with a coupled succession of modes that transfer excess energy initially through the rotational modes of the water network and subsequently (on a picosecond time scale) to the restricted translational motions of neighboring molecules in the hydration shell, where it is eventually deposited into the lowest frequency modes. The analogous VDOS spectrum in the antibody with a mixed-solvent hydration shell exhibits a decoupled or weakly couples set of states. The prominent librational mode at 430 cm −1 in the water spectrum signifies that the excess energy due to the protein perturbation is not being effectively distributed to the lowest frequency mode. One would expect a much slower relaxation of the water network, which correspondingly would affect the overall dynamics of the antigen. We have analyzed the dynamical behavior of the hydration water in the two antibody samples through computation of the van Hove self correlation function and have found that indeed the water in the mixed-ethanol solvent has considerably slower relaxation in the longer time diffusive regime (Supplementary Figure S2) when compared with the pure water sample.
Conformational dynamics of IFN-γ bound to IFNGR1 and IFNGR2 from MD simulation. Aqueous solvent with water. We have also conducted MD simulations on the cytokine IFN-γ when in complex with the receptors interferon gamma receptor 1 (IFNGR1) and interferon gamma receptor 2 (IFNGR2). The interferon gamma receptor is a heterodimer of two chains (IFNGR1 and IFNGR2) that bind IFN-γ. The binding of www.nature.com/scientificreports/ the cytokine to the receptor heterodimer induces dimerization that activates the receptor complex. Our interest in performing the simulations is to gain a deeper understanding about the role that IFN-γ sample preparation may play in binding associations. In our experimental sample preparations, IFN-γ is dissolved in the presence of dilute proportions of ethanol that may affect the interfacial region or binding interfaces of the cytokine and/or its receptors. In Fig. 9, we provide an image of the crystal structure of the receptor complex and the corresponding single, dominant conformation computed from the FCA of the MD simulations of the separate molecules forming the complex. In the complex, IFN-γ has an overall rigid dynamics with the largest amplitude motion confined to the C-terminal helix of the molecule. IFNGR1 and IFNGR2 have distinct dynamics that implies that they have non-equivalent roles in the binding interaction with IFN-γ. For example, IFNGR1 has minimal large-amplitude motion in the center core of the molecule but possess prominent elongation motion at the poles. IFNGR2 on the other hand has small-scale fluctuations throughout the majority of the protein but features localized large-amplitude fluctuations in an inner surface loop close to the IFN-γ binding site and also in an outer surface loop (Ser55-Arg59) that does not appear to have direct role in binding IFN-γ. Hence, it appears that only IFNGR1 has an active role in the ligand-binding activity while IFNGR2 appears to fulfill a more structural role in the binding assembly.
Aqueous solvent containing 10% mole fraction ethanol. Conformational heterogeneity and modifications of the dynamical landscape of the receptor complex. We have also performed MD simulations of the IFN-γ/ IFNGR1-IFNGR2 complex in a solvent containing a water-ethanol mixture. One of the most noticeable changes in dynamics with addition of ethanol to the hydration shell is that the dynamics of the receptor complex becomes conformationally heterogeneous (Fig. 10). The Gibbs free energy landscape map of the FCA analysis of from the MD simulation displays two distinct conformations with similar energy that the cytokine adopts during the course of the simulation (Fig. 10a). One conformation is comparable to the dominant conformation already observed in the sample dissolved in pure water and mostly involves fluctuation of the C-terminal helix (conformation 1). The second prominent conformation in IFN-γ comprises a motion that is almost entirely confined to the C-terminal region of the cytokine (conformation 2). We also detect changes in IFNGR1 in the presence of ethanol (Fig. 10b). The two conformations of similar energy involve a principal conformation (conformation 1) where the molecule is mostly rigid with the exception of a surface loop opposite from the IFN-γ binding region and a secondary conformation that is limited to motion involving the N-terminus of the protein (conformation 2). Interestingly, the receptor with the greatest modification in dynamics in the ethanol-mixed solvent is IFNGR2. IFNGR2 dynamics features three distinct conformations with unequal energy. The principal conformation (conformation 1) of IFNGR2 involves a correlated motion between the surface loop involved with binding IFN-γ and the dynamics of a loop involved with phosphorylation on the opposite site of the receptor. The secondary conformation in IFNGR2 (conformation 1a) involves the localized fluctuation of the N-terminal region of the receptor. And the third conformation (conformation 2) is similar to the dominant IFNGR1 conformation in water (Fig. 9b) and involves minimal motion in the receptor core but large-amplitude elongation motion at the receptor poles. It is interesting to note that IFNGR2 conformation 1 and conformation 2 have similar energy but can only exchange by migrating through conformation 1a, forming a type of bottleneck pathway making exchange between the two conformations rare. Closer analyses of the conformations reveal that they reflect the dominant conformations before a dynamical transition has taken place in the complex as a whole (Supplementary Figure S3) and then a conformational hopping mechanism is observed after the transition. The conformations marked as (1) in IFN-γ, IFNGR1, and IFNGR2 in Fig. 10 represent the dominant conformation before the transition takes place-while the conformations marked as (2) represent a secondary conformation in the population of confomers in the receptor components after the transition has taken place. IFNGR2 presents a distinctive case. In IFNGR2, in addition to  IFN-γ complex). Also interesting, is that conformation 2 in IFNGR2 appears to be the active receptor in IFN-γ binding. More specifically, the transition that has taken place in the complex has for the most part produced a heterogeneous mixture of both rigid-like and more "conformationally flexible" regions in the receptor complex and additionally has switched the "active" receptor in ligand-binding from IFNGR1 to IFNGR2.
Superdiffusion, caging and long-range protein interactions. In Fig. 11a, we plot the MSD of the overall receptor complex motion from the MD simulation in both water and in the ethanol-water mixture. A comparison of the long-time dynamics clearly reveals that the diffusion of the complex in ethanol can be described as superdiffusive while the complex in water is more indicative of a subdiffusive system in a confined or highly viscous environment. An interesting question to consider is if the conformational heterogeneity observed from the conformational analyses performed in the previous section has anything to do with the origin of the superdiffusive motion in the MSD of the complex in the ethanol-mixed solvent. For instance, observation of the corresponding calculated self ISF in Fig. 11b shows that the intermediate time scale of the complex in the mixed solvent has two different β-relaxation times. A pronounced, fast relaxation time is detected in the self ISF at about 0.7 ps and a secondary, less distinct relaxation time is found at approximately 2.2 ps. Multiple β-relaxations are often associated with dynamical heterogeneity in glass forming liquids 50 . In the cytokine receptor complex in water we only observe a single β-relaxation time at approximately 3.6 ps in the plot of the self ISF. So overall, we observe that β-relaxation in the ethanol-mixed solvent is significantly faster than in the water-only complex. Interestingly, a plot of the non-gaussian parameter in the inset of Fig. 11b clearly highlights the differences in peak position in the two distinct systems. The non-Gaussian parameter is a measure to characterize deviations from Gaussian particle displacement dynamics where r 2 (t) and r 4 (t) are the mean square displacement and quartic displacements of the particle at time t.
The maximum of the non-Gaussian parameter is closely related to the characteristic time of α-relaxation (τ α ). We find that in the complex with ethanol in the hydration shell that τ α is significantly faster. A similar picture emerges from the analyses of the of the self van Hove correlation function of the cytokine/ receptor complex in the two distinct solvent environments from the MD simulation in Fig. 11c, d. It is clear that in the pure water solvent that there is little change in the position of the r value of the peak maximum but the www.nature.com/scientificreports/ amplitude decays as a function of time signifying a particle in a viscous environment. Similar to the dimer of the cytokine when not bound to the dimer receptors, we also identify a secondary peak in the self van Hove correlation plot at approximately r ~ 1.8 Å that suggests that the liquid water in the hydration shell plays a significant role in the diffusion mechanism. The self van Hove correlation function of the complex in the mixed ethanol-water solvent depicts an entirely different dynamics. Here, we see a number of translational peaks in the diffusion function ("hopping") suggesting a more heterogeneous set of structures or regions in the ethanol-enriched solvent. In Fig. 11e, we see that in the plot of the RMSD of the C α -atoms that there is a definitive rise in the RMSD in the cytokine complex from the MD simulation with the water-ethanol mixed solvent that is not observed in the complex dissolved in water. This rise at about 25 ns is associated with the large-scale molecule fluctuations that precede a dynamical transition. Once the transition has taken place (> 30 ns) we discern that the system adapts to a new equilibrium. It is interesting to point out that the steep rise in the mixed-solvent RMSD is coincident with the onset of superdiffusive motion of the complex in the MSD in Fig. 11a. The cytokine complex in water comprises thermal motion that is more characteristic of a system at equilibrium. Analogous to what we have previously observed in the unbound cytokine dimer in the mixed solvent (Fig. 3d), we find that a plot of the distribution of C α atoms from the RMSD in Fig. 11f reveals a complex with heterogeneous associations. The cytokine complex with ethanol in the hydration shell has both long-range associations that are on a length scale comparable to the system size and shorter-range nearest neighbor associations. The complex in water has a distribution of associations that are governed by nearest neighbor interactions.
Surface packing deformations, dynamically correlated clusters and strain propagation in the IFN-γ complex. In the IFN-γ receptor complex we have determined that ethanol in the hydration shell modifies the packing distribution of water molecules on the protein surface and consequently also alters the fluctuations of side-chain methyl groups primarily on the protein surface. A plot of the calculated protein-water H-bonding spectrum in Fig. 12a closely mirrors the equivalent spectrum calculated from the IFN-γ dimer in Fig. 5d. What becomes even more apparent in the analyses of the IFN-γ complex is the central role that the long-range translational dynamics of water molecules on the protein surface play in stabilizing the specific interactions within the protein complex structure. For instance, the enhancement of methyl group fluctuations in the ethanol-mixed solvent is directly associated with the formation of dynamically correlated clusters of amino acids that propagate through the protein complex. Although, the details of how the clusters are propagated within the complex structure is not entirely clear. To further elucidate the underlying mechanism(s) creating this heterogeneous environment within the receptor complex, we have extended the MD simulations to include force distribution analyses (FDA) 51 on the complex in both solvent environments. The aim of these analyses is to deduce the mechanical strain that is both distributed and propagated within the interior of the receptor as a result of the solvent-induced  www.nature.com/scientificreports/ interactions on the protein surface in the two distinct samples. In Fig. 12b, c the 3-D the structure of the IFN-γ complex in each solvent environment is depicted along with an illustration of the distribution of mechanical strain coupling the distinct protein components. In the complex with only water in the hydration shell (Fig. 12b), we find that the propagation of the strain energy is local such that it is confined to the contact boundaries of the individual proteins forming the receptor complex. In the ethanol-mixed solvent (Fig. 12c) we also find that the strain energy shared between IFN-γ and IFNGR2 is local in nature (contained within the boundaries of the two proteins) but the propagated strain between IFN-γ and IFNGR1 results in a pathway formed by a dynamically correlated cluster of hydrophobic amino acids that span a large shared segment of the two proteins. It is interesting to point out that the analysis of the conformational populations in the IFN-γ complex in the ethanolmixed solvent from FCA in Fig. 10 are line with the analysis of strain propagation presented in this section. A comparison of the FCA and FDA of the complex makes it apparent that the conformational fluctuations detected are linked with rearrangements that involve a population with greater conformational mobility and a population with a more ordered structure. In Fig. 12d we plot the spectrum of the vibrations associated with the collective displacement of the individual components making up the cytokine complex and find a unique peak in the ethanol-mixed spectra of each close to 50 cm −1 that is not prominent in the water only components. In the protein complex the ~ 50 cm −1 mode represents a solvent-induced backbone fluctuation in which the protein is integrated into the collective network dynamics of the water in the hydration shell. Coincidentally, the hydration shell water VDOS also contains a very strong vibrational band close to 50 cm −1 . The nature of the ~ 50 cm −1 mode in liquid water is still not entirely clear, but there is growing evidence that it is likely attributed to the frustrated translation of water molecules around a given atom or molecule that produces the so-called cage effect 52 . Therefore, it appears that the strong interaction with translational water molecules on the protein surface not only stabilizes the dynamically correlated clusters of molecules but may also play a central role in synchronizing the collective mobility that brings about the transition thus, returning the protein complex to equilibrium 53 .

Conformational dynamics of the antibody bound dimer of IFNGR1.
Aqueous solvent with water. We have performed a similar set of MD simulations on the extracellular interferon-γ receptor 1 dimer (IFNGR1 (1) and IFNGR1 (2)) bound to the neutralizing antibody A6 as shown in Fig. 13a. Analyses of the  www.nature.com/scientificreports/ conformational dynamics of the antibody-receptor complex in Fig. 13b reveals an antibody with limited dynamics within the region of contact with IFNGR1 (1). IFNGR1 (1) and IFNGR2 both have dynamics that extends throughout the entire receptor but the greatest amplitude is largely confined to the protein terminal regions. This symmetry in the overall dynamics of the two binding receptors may indicate that both have significant roles in the ligand-binding process.

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Aqueous solvent containing 10% mole fraction ethanol (χ EtOH = 0.10). Conformational dynamics and modified ligand-binding associations. Similar to the MD simulations that we have previously described for the IFN-γ complex, we perform a similar set of simulations for the antibody complex such that ethanol is now included in the receptor hydration shell. In the analysis of the conformational dynamics of the antibody complex, the Gibbs energy landscape map in Fig. 13c displays two distinct conformations that the antibody adopts during the course of the simulation-a low energy conformation (conformation 1) that is characterized by a bending type motion of a C-terminal loop that enhances the binding interface created by the two bound receptors and a higher energy conformation (conformation 2) that resembles the antibody dynamics under normal solvent conditions (Fig. 13b) and features dynamics almost entirely restricted to the C-terminal region. Analogous to what we observed in the IFN-γ complex, the lower energy conformation (conformation 1) is dominant before a transition takes place and the higher energy conformation (conformation 2) is found within the mixture of conformational states after the transition has taken place. We also detect changes in IFNGR1 (1) in the presence of the ethanol in Fig. 13d when compared with receptor in water. In general, the dynamics in the ethanol-water mixed solvent results in a weakened H-bonding interfacial region in the space separating antibody with the heterodimer receptors. In IFNGR1 (1) the lower energy conformation of the receptor (conformation 1) is the principal conformation adopted before the transition and involves a shearing type motion of the N-terminal region of the receptor toward the bound antibody. Conformation 2 of IFNGR1 (1), present after the dynamical transition, displays dynamics that is mostly confined to C-terminal region and acts to maximize the packing interaction of the C-terminal interface shared between IFNGR1 (1) and IFNGR1 (2). Interestingly, the receptor with the greatest modification in dynamics in the ethanol-mixed solvent is IFNGR1 (2). The IFNGR1 (2) dynamics in Fig. 13e feature two distinct conformations with an almost barrier-free region separating the substates. Unlike the antibody or IFNGR1 (1) within the complex, IFNGR1 (2) arbitrarily hops between the two substates during the course of the entire simulation. The lower energy conformation (conformation 1) resembles the lowest energy conformational state of IFNGR1 (1) in the pure water solvent (Fig. 13b) and consists of compression-type motion that concentrates the largest amplitude motion to the protein terminal regions. It is interesting to point that IFNGR1  (2) has generally rigid dynamics with motion localized on a single loop in the C-terminus. Analogous to our observation in the IFN-γ we note that after the transition has taken place that the receptor complex consists of heterogeneous regions containing immobile, solid-like regions mixed with localized domains with more flexible dynamics.
Solvent fluctuations and dynamical heterogeneity. In the MD simulations we also detect distinctive changes in the water-protein and protein-water interactions in the ethanol-mixed solvent when compared with the antibody-receptor complex in only water. For example, an examination of the calculated distant-dependent (distance from the protein) absorption coefficient from the MD simulation of the water-only solvent complex in Fig. 14a reveals a prominent librational mode in the hydration shell that spans from approximately 300-700 cm −1 at a distance of 1.9 nm from the protein surface. The broad librational band narrows as the distance to the protein surface is reduced and eventually shifts to about 200 cm −1 at a distance equivalent to the first hydration shell of the protein complex. The dynamics of the water molecules in the complex are closely tied with the dynamics of the protein side-chains. Particularly, we note that the solvent-coupled polar side-chains on the exterior of the protein surface are strongly coupled with librational modes of water on the blue-er side of the spectrum (~ 660 cm −1 ) while the side-chains closer to the protein-interior have a broader range of interactions with the librational modes of water that include a smaller component in the 650-700 cm −1 region and a more substantial interaction with a redder component in the 450-550 cm −1 range (Supplementary Figure S4). This suggests that the protein-water interactions involve a complex set of associations that may play a significant role in both conformational stability and shaping the conformational landscape of the protein complex. In the ethanol-mixed solvent in Fig. 14b, we also discover that the distance-dependent water dynamics is drastically altered when compared with the dynamics in the pure water solvent. Similar to what we observed in the antibody A6 in solution, we find that the water dynamics in the mixed solvent consist of long-range translational motions that have the effect of reducing the overall solvent-side chain coupling in the protein complex while selectively enhancing methyl group fluctuations on the protein surface. Consequently, the modifications in protein-water surface interactions also appear to be directly related to the detected increase of protein-protein interactions within the antibody-antigen complex. www.nature.com/scientificreports/ The analyses of the of the van Hove self correlation function of the antibody receptor complex in the two distinct solvent environments from the MD simulation in Fig. 14c, d mirrors that uncovered in the analyses of the cytokine receptor in Fig. 11. In the pure water solvent, the r value of the peak maximum is constant but the amplitude decays as a function of time indicating a molecule in a tightly packed environment. In addition to the main peak, we also detect a secondary peak in the self van Hove correlation plot at approximately r ~ 1.8 Å that suggests that the liquid water in the hydration shell plays a significant role in the diffusion mechanism. The self van Hove correlation function of the complex in the mixed ethanol-water solvent possesses multiple translational peaks in the diffusion function denoting dynamical heterogeneity in the structural diffusion of the complex in the ethanol-mixed solvent.
Superdiffusion and dynamical transition. In the plot of the calculated MSD of the antibody complex in water and in the ethanol-mixed solvent from the MD simulations in Fig. 14e we detect that the complex with ethanol in the hydration shell has superdiffusive dynamics. The motion under normal solvent conditions can be described as subdiffusive or in other words the molecules diffuse in a confined (viscous) environment. In the previous section, one of the biggest changes that we observed under the two solvent conditions is the manner in which the water in the hydration shell interacts with the protein surface(s). In this context, it is tempting to correlate changes in the coupling of the density fluctuations of water in the protein complex with the observed changes in sample viscosity. We again use the calculated self ISF as a means to investigate the intermediate time scale of the relaxation of the complex in the two different solvents. Similar to what we observed in the IFN-γ complex, we find that the mixed solvent sample in Fig. 14f has multiple β-relaxations-indicating a heterogenous environment-and a largely faster relaxation time when compared with the complex in water. Specifically, we detect a fast β-relaxation time at ~ 0.47 ps and a slower relaxation time at 1.25 ps in the self ISF. For the sample in water, we detect a single β-relaxation time at 3.6 ps. Assuming that the β-relaxation is a precursor to the longer time α-relaxation 54 , we tentatively attribute the consequent faster α-relaxation of the complex in the ethanol mixture, as detected in the plot of the non-Gaussian parameter in the inset of Fig. 14e, to the relation between the two distinct (α-and β-) relaxation times.
We also note the connection with the onset of superdiffusive motion in the MSD of the antibody complex in the ethanol environment (Fig. 14e) and the steep rise in the RMSD of the C α atom distances in the complex as a function of MD simulation time in Fig. 14g. The rapid rise in the RMSD is characteristic of a dynamical transition. Hence, our results indicate that the superdiffusive motion detected in the MSD is directly correlated with a dynamical transition in the antibody complex with the mixed solvent as demonstrated in the RMSD of the complex. Further, a plot of the distribution of C α -C α distances (inset in Fig. 14g) uncovers a heterogeneous set of association in the ethanol-mixed solvent that are largely absent in the water-only hydrated sample. We find a diverse set of association in the complex in the ethanol-mixed hydration shell that range from nearest-and second-nearest neighbor associations to long-range associations that are equivalent to the length of the entire molecule. In the antibody complex in water the associations are mainly restricted to closest nearest-neighbor interactions.
Strain propagation, localized correlated fluctuations and protein vibrational density of states (VDOS). We find that the deformation in structural conformation in the mixed-solvent complex, attributed to the altered solvent distribution on the protein surface, is the source of long-distance strain propagation that acts to correlate the fluctuations of large clusters of amino acids such that they move as cohesive unit. Compared with the IFN-γ complex, the interactions underlying the dynamical heterogeneity in the sample is more transparent. Specifically, the structural deformation caused by the solvent distribution of interactions on the protein surface induces a redistribution of interactions that propagate throughout the entire complex to alleviate the surface-induced strain. The large-amplitude fluctuations at the protein-solvent interface propagate as correlated hydrophobic side chain fluctuations through the protein interior-forming interconnect pathways of localized, oscillating regions that continue to grow until a new equilibrium is established. Curiously, the regions with strong water H-bonding on the protein complex surface are somehow associated with the formation of structured domains in the protein that move as rigid units. In the latter case, we have uncovered that the strong interaction of the translational water molecules alters the packing interactions within the protein structure that leads to long-range intra-protein interactions that may foster the formation of the rigid domains in the molecule.
The changes in protein interactions are visible in the plot of the VDOS of the protein complex in water and in the water-ethanol solvent in Fig. 15a. In the < 100 cm −1 region of the spectrum there is a weak peak close to 70 cm −1 that is associated with out of plane backbone torsional deformations 22 (C-C-N and C-O) that are not present in the complex dissolved only in water and is also not directly associated with ethanol H-bonding to protein residues in the complex. It is interesting to point out that ~ 70 cm −1 mode matches well with the 0.47 ps fast, intermediate time scale relaxation (β-relaxation) found in the protein complex in the ethanol-mixed solvent in F s (q, t) in Fig. 14f. We also find a secondary, slower relaxation in the intermediate time scale of the self ISF at 1.25 ps (27 cm −1 ). Incidentally, there is a small shoulder in the in the ethanol-mixed antigen complex VDOS at a similar frequency (~ 32 cm −1 ). The ~ 30 cm −1 mode is also present as a discernible shoulder in the pure water spectrum in Fig. 15a-but is significantly less defined. Further analyses have allows us to ascribe ~ 30 cm −1 mode in the VDOS to correlated side-chain fluctuations in the protein complex. The two coexisting relaxation mechanisms relate to the distinct local structural arrangements of molecules in the protein complex in the mixed-solvent environment-a fast relaxing one and a slower one. The water-only solvent sample has a single prominent relaxation time at intermediate times at 3.6 ps (~ 9 cm −1 ) that is significantly slower than that found in the ethanol-mixed solvent. This relaxation time is characteristic of molecule in a viscous medium. Coincidentally, we do identify a peak in the VDOS of the complex in water at a similar frequency (9 cm −1 ) that is not  Fig. 15b, c shows the differences in the induced-weak forces in the antibody complex in the two different solvents. In the water-only solvent complex (Fig. 15b), the induced strain is limited to the contact regions separating the individual protein components forming the receptor complex. In the ethanol-mixed solvent in Fig. 15c an entirely different picture emerges. Here we find that the distribution of mechanical strain is transmitted via a collection of dynamically correlated hydrophobic side-chain residues that are localized in various regions within the protein complex. These correlated residues have high mobility at the protein/solvent interface but diminish in amplitude as they disseminate through the protein structure. In Fig. 15c a plot of the strain-propagation from the FDA reveals long-distance correlated fluctuations that connect residues in the C-terminal domain of the antibody with a subset of residues in both the N-and C-terminal region of IFNGR1 (1). A similar pattern of correlated sidechain fluctuations can be seen to connect a C-terminal loop of the antibody with the N-terminal region of IFNGR1 (2). The propagation of strain energy between IFNGR1 (1) and IFNGR1 (2) is local such that it is predominantly restricted to the contact regions shared between the individual proteins.
A plot of the vibrational modes associated with weak interactions within the complex reveal an overall redshift of the modes in the ethanol-mixed solvent when compared that in only water in Fig. 15d, e. The observed shift to lower energy is mostly a reflection of the enhancement of the collective sidechain reorientation motion in the protein complex and a shift away from more localized protein-protein and protein-solvent interactions when ethanol is present in the hydration shell. The underlying reason for the change in dynamics is twofold: (1) There is an increased amplitude (superdiffusive motion) of sidechain fluctuations associated with the exploration of the molecular cage of neighbors. We have witnessed this development in the antibody complex as localized, large-amplitude methyl group fluctuations that promote the formation of free space or packing perturbations in the closely packed system when the solvent is changed from pure water to a water-ethanol mixture. In the water-only solvent, the complex is typical of a colloidal-like system. The residues are tightly packed with little room for movement although their interactions are governed by forces acting directly between the individual molecules (nearest neighbor interactions). The induced large-amplitude sidechain fluctuations on the protein surface in the mixed solvent weaken the forces between the interacting molecules and allow significant localized motion within the confine of forces created from their neighbors. (2) The red-shift of protein modes is also www.nature.com/scientificreports/ associated with the exploration of the conformational space of the protein complex via conformational hopping. The correlated oscillation of side-chain fluctuations that propagate through the protein structure is instrumental in creating heterogeneous domains of both flexible and rigid (solid)-like regions within the complex. More specifically, after a dynamical transition has taken place within the protein complex, we observe a "hopping" between the individual (sub)states on the PEL. This conformational hopping ultimately creates domains within the protein structure that contain localized regions or pathways where the residues have greater flexibility and short-range interactions and other regions where the residues behave more like they are in a solid environment (less mobile) and contain long-range interactions-an example of dynamical heterogeneity. The sampling or hopping from one configuration to another necessitates crossing a low energy barrier, which requires collective dynamical rearrangements within the protein complex.
In this context, it is interesting to also point out that in our analyses we have also identified a spectral marker associated with the correlated side-chain fluctuations within the localized, flexible regions detected in the antigen complex in the water-ethanol mixed solvent. The coupled sidechain oscillations within the flexible regions peak at approximately 220 cm −1 in the THz region of the calculated spectrum. The analogous regions in the complex in pure water produce a broader, lower amplitude signal at approximately 260 cm −1 . Perhaps this provides some insight into the nature of the unidentified, large-amplitude band identified in the experimental HD-IFN-γ spectrum in Fig. 1a. Here we observed a prominent band in the HD-IFN-γ spectrum at 217 cm −1 that was not present in either of the other HD samples nor in the untreated samples of IFN-γ and IFNGR1. We also note that in the MD simulation of the antibody complex we find that the hydration shell water has a strong intermolecular anti-symmetric stretching band located about 220 cm −1 in the calculated VDOS that is considerably blue-shifted ( by 40 cm −1 ) when compared with the hydration shell stretching mode in the antibody hydrated in a pure water solution (Fig. 15f). In addition, both the twisting and wagging librational modes in the antibody complex hydration shell water VDOS are also considerably blue-shifted indicating an overall change in the water local structure in the hydration shell when compared with the antibody in water or when contrasted with the hydration shell dynamics of the other MD simulation systems investigated in this study. Previous spectroscopy studies on liquid water 17 have demonstrated that there is a coexistence of two local configurations of water molecules in solution-a high-density form and low-density water form. The high density form corresponds to a highly tetrahedral water molecular arrangement that absorbs around 220 cm −1 while the lower-density form absorbs close to ~ 180 cm −1 and is ascribed to a compressed configuration with a distorted H-bond network. It has been proposed that relaxation induced reorganization between the two structures may potentially affect vibrational mode delocalization in liquid water that consequently, may also play a role in specific biological processes.

Discussion and conclusion
In this work we have explored the underlying microscopic interactions and molecular changes that are associated with HD protein samples that have recently been shown to be effective in the treatment of a number of biological disorders [55][56][57] . These studies were also strongly motivated in response to the unexpected strong protein signals that the HD samples emit in the experimental THz region of the spectrum. Such highly diluted samples would typically be expected to spectroscopically resemble liquid water. But on the contrary, we have detected discernible collective and intermolecular protein (inter-protein and protein-solvent) bands in the spectra prompting us to explore further with analogous computational models of the experimental samples.
Explicitly, from our computational analyses of HD-inspired solutions of IFN-γ and the neutralizing antibody A6 (nA6), we propose that the ethanol added in the hydration shell as part of the dilution process induces dynamics in the protein that ultimately leads to the arrangement of long-range interactions of water translational motions at the protein surface along with chained assemblies of ethanol molecules that interact weakly with protein surface sidechains. Here, "HD-inspired" refers to the MD simulations that are based on the experimentally prepared HD samples. In subsequent MD simulations on HD-inspired receptor complexes of IFN-γ and nA6 we witnessed an analogous ordering of hydration shell molecules around the protein complex surface as we previously observed in the solution samples of the IFN-γ dimer and nA6. In all but one case of the performed MD simulations, we have observed that the arrangement of solvent molecules in the protein (complex) hydration shell directly leads to protein surface deformation that prompts large-amplitude mobility fluctuations (superdiffusion) of protein surface methyl groups. In our analyses we have related this solvent-induced superdiffusive motion to a fast β-relaxation identified in the self-intermediate scattering function in the MD simulations.
We have also determined that the strain deformation resulting from the solvent-induced pockets of enhanced mobility on the protein surface are further propagated as a series of smaller-scale correlated sidechain rearrangements that disseminate throughout the protein or protein-complex structure resulting in fractured regions of mobility, while other regions of the protein maintain limited mobility. We attribute this propagation or dissemination of localized oscillations to a secondary, slower β-relaxation that we have also detected in the dynamics of the MD simulations. Specifically, the secondary β-relaxation process is associated with the conformational hopping between distinct protein conformational substates driven by collective sidechain fluctuations that act to connect or link the individual islands of mobility concomitant with the initial, faster β-relaxation. In both of the protein complexes that we studied, we found that a particular receptor forming the complex had a more significant or active role in the propagation process-IFNGR2 in the IFN-γ complex and IFNGR1 (2) in the nA6 complex. In both cases, the particular receptor can be seen to evoke a motion that appears to be efficient in extending the localized excitations from the most mobile local sites to the extended surrounding. The properties that we observe in the computational studies of the HD systems are similar to the evolution of nanoscale structural heterogeneity that arises in metallic glasses when cooled down from room temperature to the supercooled regime 58,59 . Although, in our case the structural dynamic heterogeneity that develops in the HD samples is a function of solvent heterogeneity rather than temperature. www.nature.com/scientificreports/ In nearly all cases, we detect a point where the systems appear to reach a new equilibrium after undergoing a dynamical transition. We equate this equilibration to α-relaxation. At this point, the local relaxations associated with the longer secondary β-relaxation have coalesced such that there are distinct segments within the protein structure consisting of highly mobile domains and less mobile regions that no longer resemble a crowded colloid but behave more like a disordered solid with long-range interactions (Supplementary Figure S5). Both the correlated fluctuations and the long-range protein interactions appear as prominent modes in the long-wavelength region of the experimental THz spectrum where collective motions in the protein system are most apparent.

R E T R
It was previously mentioned that one of the HD-inspired samples that we explored with MD simulation did not undergo the dynamical transition. This was the nA6 sample in solution. The model antibody used in the MD analyses is a relatively small macromolecule with a structure comprised of two β-sheets packed tightly against each other in a compressed antiparallel β-barrel. Similar to the other HD-inspired MD simulation samples, we did witness a change in the protein-water coupling at the protein surface in the ethanol-mixed solvent-yet there was no dynamical transition. This may indicate that for the transition to occur there must be a build-up of critical energy or a threshold before the transition can take place. We also notice that the manner in which the water in the hydration shell couples to the dynamics of the amino acids in the protein differ significantly in the IFN-γ and nA6 systems. For example, the caging dynamics of water molecules around the solvent-exposed residues on the protein surface in the IFN-γ systems are principal in the formation of structural regions along the pathway leading up to the secondary β-relaxation in the IFN-γ systems. This is most apparent in the MSD of the hydration shell water hydrogen atoms in the IFN-γ complex (Supplementary Figure S6) where we observe much stronger caging dynamics in the time scale preceding the slower α-relaxation. Specifically, the caging regime represents weak protein-water associations that result in large-amplitude rearrangements of methyl group side chain fluctuations on the protein surface. This rattling in the cage motion of the protein residues within the cage formed by the nearest neighbors represents local diffusion central in intra-basin transitions within the conformational landscape of the molecule. Both in the plot of the self ISF and in the calculated spectrum of weak associations in the IFN-γ systems we find a prominent ~ 50 cm −1 mode associated with the caging dynamics of water-coupled associations with protein residues in the system. We associate the longer-time scale escape processes from the cage with the growth of mobile fluctuating domains within the protein housed within regions of low mobility. On the other hand, we have found that in the nA6 systems the protein-water H-bonding couples the dynamics of the solvent with the collective, torsional (restricted twisting) oscillations of protein backbone atoms. In this case, the excitation of the collective torsional oscillations of the protein play a more significant role in altering the barrier heights that eventually lead to the cage-breaking process in the longer-time scale secondary β-relaxation (Supplementary Figure S6). These differences in mechanism are likely apparent in the experimental THz measurements of the HD systems. In Fig. 1c we find clear distinctions in the detected collective dynamics of the HD-IFN-γ sample when compared with the HD-anti-IFNGR1 sample. The HD-IFN-γ sample exhibits a central peak at 50 cm −1 in the global dynamics region of the spectrum that is linked with solvent-induced protein fluctuations associated with caging dynamics of the solvent molecules in the hydration shell, while the principal mode in the HD-anti-IFNGR1 sample is blue-shifted to 80 cm −1 . The blue-shifted 80 cm −1 mode in the HD-anti-IFNGR1 sample reflects solvent-induced torsional 22 backbone fluctuations in the protein that are coupled with the dynamics of solvent molecules in the extended 49 hydration shell. These observed differences in the investigated samples indicate that specific associations with water molecules in the protein hydration shell provide mechanistically distinct pathways to a seemingly equivalent dynamic phase transition. This suggests that THz spectroscopy is not only sensitive to the specific intermolecular interactions associated with the individual HD samples but it may also provide unique insight into the underlying mechanism(s) driving the evolution of the dynamical and structural heterogeneity within the systems.
One interesting aspect of the results of this study is the possible functional role of the changes that we observe in the HD samples. The dynamics of both the HD cytokine and antibody systems that we have investigated can no longer be accurately represented with equilibrium type models when describing the underlying nature of protein fluctuations and macromolecular interactions. Rather, we find that the dynamics within the HD systems, driven by the ordering of solvent molecules on the protein surface, promote spatial heterogeneity within the macromolecule that alters the conformational populations that ultimately determine ligand-binding associations and possibly ligand recognition. For instance, we find that in both of the receptor complexes that we have studied with MD simulation that there is stronger association of the ligand with the receptor. Additionally, we also found in the MD simulation of the HD-IFN-γ dimer that the greatest modifications in dynamics takes place at the dimer interface and in a C-terminal surface loop (Fig. 3c), where both regions play a critical role in binding IFN-γ receptors and for signaling. Our findings are in line with recent experimental measurements on HD prepared antibodies 7 to IFN-γ that have confirmed that interaction with IFN-γ induces conformational changes in the cytokine that were conjectured to alter its biological activity as well as its interactions with other macromolecules. These induced changes were mainly localized at the IFN-γ dimer interface and in the C-terminal region. These same set of experiments also revealed that HD anti-IFN-γ increases specific binding of IFN-γ to its receptor.
In summary, the results of our investigation uncover distinct differences in the experimental THz properties of HD samples of various proteins when compared with either liquid water or with their higher concentration protein equivalents. Moreover, with the aid of MD simulation we are, for the first time, able to unravel the physical mechanism(s) that correlate these detected differences with observable alterations in protein dynamics and dynamical interactions that directly impart novel binding associations and enhanced functional activity in the HD samples.
The results from this investigation form a methodological basis for future research into the structural and functional properties of HD samples. Our aim is that this work will provide an initial foothold that will help to expand the possible applications of HD technology. Based on our initial results, we can clearly conclude that the www.nature.com/scientificreports/ technology used for the preparation of HD samples plays a key role in the formation of the physical and chemical properties of the proteins and consequently, activity.

Materials and methods
Sample preparation. The following reagents were used: antibodies to IFN-γ (2.5 mg/ml, Angel Biotechnology Holdings, Penicuik, U.K.), antibodies to IFN-γ receptor 1 (1 mg/ml, Abcam, cat.number Ab61179-100), IFN-γ (1 mg/ml, Prospec Protein Specialists, cat.number CYT-206), distilled water (solvent). The highly diluted antibodies to IFN-γ (HD-anti-IFN-γ), to IFN-γ receptor 1 (HD-anti-IFNGR1), highly diluted IFN-γ (HD-IFN-γ) were produced by the GMP manufacturing facility of OOO "NPF "Materia Medica Holding" in accordance to the technology described in the United States patent 8,535,664 60 . Briefly, to produce each test sample the respective initial antibodies were mixed with the solvent (water-ethanol solution) at a ratio of 1:100 and underwent intensive vibration treatment to produce the first dilution (i.e. 100-fold dilution). All subsequent dilutions were comprised one part of the previous dilution and 99 parts of solvent (ethanol-water solution for intermediate dilutions and purified water for the preparation of the final dilutions), with intensive vibration treatment between the dilution steps. As a result, the HD-anti-IFN-γ, HD-anti-IFNGR1, and HD-IFN-γ samples consists of mixture of 12th, 30th, and 50th 100-fold dilutions. Thus, the theoretical concentration reduction is corresponded to at least 10 24 times. Therefore, if we do not take into account the physical aspects of heterogeneity of solutions described in the scientific literature 4,6,61 , the theoretical concentration of initial antibodies might be 2.5 * 10 −24 mg/ml (HD-anti-IFN-γ) or 1.0 * 10 −24 mg/ml (HD-anti-IFNGR1 and HD-IFN-γ). The HD water (as a control) was prepared by applying an identical procedure to distilled water. All HD-samples were prepared by OOO "NPF "MATERIA MEDICA HOLDING" (Russia) in glass vials and stored without constant light, at room temperature. The samples were tested blindly.
TeraHertz (THz) spectroscopy experiment. The THz spectroscopy experiments were carried out on a Jasco FTIR-6000 series spectrometer. We conducted 3 separate experiments on each HD sample. For each experiment, a 50 ml aliquot of the HD solution sample was taken from the main sample stock and allowed to warm up to room temperature (18 to 21 °C) before measurement. The entire 50 ml aliquot of sample was subsequently placed between two-2 mm silicon discs separated by a 6 micron mylar spacer. The silicon discs were subsequently used to form the windows of a sealed sample cell. The HD solution samples were collected using a liquid helium cooled bolometer in the 40-250 cm −1 spectral range using a 12 micron beam splitter. A more detailed description of the experimental set-up and measurement parameters can be found in a previous publication 22 .

Computation. Molecular dynamics (MD) simulations of IFN-γ, the neutral antibody A6 (nA6) and receptor
complexes. Each MD simulation consisted of a starting x-ray crystal structure taken from the PDB database. PDB structure 1d9c was used for the IFN-γ dimer and 1jrh was used to obtain nA6 from the crystal structure of the interferon gamma receptor (IFNGR1) dimer complex. The crystal structure 1jrh was also used as a starting structure for the MD simulation of the IFNGR1 receptor complex. The pdb structure 6e3l was used as a starting structure for the MD simulation of the IFN-γ complex with IFNGR1 and IFNGR2. In all simulations, the receptor was hydrated with a 2.5 nm layer of water and sufficient ions (sodium and chloride) were added to neutralize the net charge of the system. In the mixed solvent (water-ethanol mixture), ethanol molecules were added to the simulation box to make a 10% mole fraction (χ EtOH = 0.10). For the small antibody nA6, χ EtOH = 0.10 equated to 5400 water molecules and 600 ethanol molecules in the mixed solvent system. The IFN-γ complex with IFNGR1 and IFNGR2 contained 800 ethanol molecules and 7200 water molecules. The IFN-γ dimer in the mixed solvent environment was hydrated with 6120 water molecules and 680 ethanol molecules and the antibody-bound IFNGR1dimer was hydrated with 6840 water molecules and 760 ethanol molecules. Initial MD simulations were conducted with larger fractions of ethanol in the hydration shell but a value greater than χ EtOH = 0.25 was found to create instability in the protein dynamics. We found a 10% mole fraction of ethanol to be optimal in maintaining an overall stable system and also served as the best representation of the experimental samples described in the experimental section of the manuscript.
MD simulations were performed at 300 K using the Gromacs package (www. groma cs. org) version 2020. The all-atom CHARMM36m force field parameters were utilized for the protein, ethanol, and ion parameters. The SPC water model was used for hydration shell water. We decided on a non-polarizable water model for hydration mainly because we were primarily interested in the librational and lower frequency dynamics of liquid water-and for this a classical treatment is sufficient. In cases where the receptor structures contained thermostabilizing mutations, they were mutated back to the wildtype sequence. In all MD simulations carried out in this work energy minimizations were initially carried out to reduce the number of unfavorable contacts between added solvent molecules and the receptor by using a steepest descent method to a convergence tolerance of 0.001 kJ mol −1 . The energy minimization was followed by a MD run with constraints for 200 ps in which an isotropic force constant of 100 kJ mol −1 nm −1 was used on the protein atoms. During the restrained dynamics simulation, the temperature and pressure of the system were kept constant by weak coupling to a modified velocity rescaled Berendsen temperature 62 and pressure baths and in all cases the protein, water, and ions were coupled to the temperature and pressure baths separately. The output conformation from the MD simulation with constraints was used as the starting conformation for an initial 10 ns equilibrium MD simulation.
Five subsequent simulations were conducted where randomized conformations from the last 10 ns of the equilibrium simulations were used as starting point conformations for each distinct simulation. These subsequent simulations were carried out with a 2 fs time step for an additional 50 ns and were eventually used to assess the dynamical transition in the mixed solvent systems. All of the simulations were continued for an additional www.nature.com/scientificreports/ 8 ns with a smaller 1 fs time step and a more frequent output of dynamical properties (Δt = 4 fs) so that in our long-time dynamical analyses we could access the mid-infrared region of the spectrum. In the simulations, the bonds between the hydrogen and the other heavier atoms were restrained to their equilibrium values with the linear constraints (LINCS) algorithm 63 . Particle mesh Ewald (PME) method 64 was used to calculate the long-range electrostatic interactions in the simulation and was used with a real-space cutoff of 1.0 nm, a fourth order B-spline interpolation and a minimum grid spacing of 0.14 nm. The convergence of the simulations was assessed by block averaging of the root mean square deviation (RMSD) of the C α− atom distances in the separate simulations. A representative plot of the convergence of a MD simulation is shown in Supplementary Figure S7.
Analyses. GROMACS tools. The mean square displacement (MSD), the root mean square displacement (RMSD), the vibrational density of states (VDOS) and velocity autocorrelation function (VACF) of molecules or atoms, and the self part of the van Hove correlation function were calculated with the standard analyses tools within the GROMACS software package. The self intermediate scattering function (self ISF) was obtained from a spatial Fourier transform of the van Hove correlation function. The GROMACS set of analyses tools were also utilized to calculate the normalized dipole correlation function where Φ is the correlation function as a function of time (t) and M is the dipole moment. We detected two decay times in the correlation function-a very fast, initial decay followed by a significantly slower, single exponential decay. With the time resolution that we employed we were not able to accurately resolve the fast decay time, hence we modeled the correlation function as a single exponential where A is the amplitude of the exponential and τ D is the Debye relaxation time. The relationship between the Debye relaxation and the dielectric constant allows us to express the relaxation time as where ε(ω) is the frequency-dependent dielectric constant, ε(0) the static dielectric constant, and ε(∞) is the dielectric constant at optical frequencies. A value of 65 was used for the static dielectric constant, ε(0) and a value of 1 for ε(∞)since we use a nonpolarizable water model in our computations. The frequency dependent dielectric constant is complex and can be further written in terms of its real and imaginary parts which can be alternatively expressed in terms of the index of refraction n(ω) and extinction coefficient k(ω) from which the frequency dependent absorption coefficient (α) can be expressed in terms of the extinction coefficient (k) as where λ is the wavelength. In this investigation, we have plotted the calculated frequency dependent dielectric constant in terms of α.
Principal component analysis (PCA). Our PCA analyses of MD simulation trajectories has been described previously 22 . In brief, principal component analyses (PCAs) were carried out by diagonalzing the covariance matrix C ij=�(x i −�x i �)(x j −�x j �)� , where x denotes protein atomic positions in the 3N-dimensional conformational space and the angular brackets represent the averages over the MD trajectory. The eigenvectors of C were determined by diagonalization with an orthonormal transformation matrix. The resulting eigenvectors from the transformation were used to determine the PCA modes with eigenvalues ( ) equivalent to the variance in the direction of the corresponding eigenvector. The MD trajectory was projected onto the principal modes to determine the principal components. The eigenvalues i of the principal components denote the mean square fluctuation of the principal component i and are arranged so that 1 ≥ 2 ≥ · · · ≥ 3N . Using this arrangement, the trajectories were filtered along the first principal component to analyze the collective dynamics taking place within the protein.
Full correlation analysis (FCA). The full correlation analysis (FCA) algorithm 28 based on mutual information (MI) was used to detect correlated motions of the proteins from the MD simulations. The g_fca tool used in GROMACS utilizes a previously calculated PCA as a starting point for the optimization. FCA minimizes the coupling between the coordinates and the FCA modes are ranked by anharmonicity (rather than fluctuation ǫ(ω) = ǫ ′ (ω) − iǫ ′′ (ω), (9) ǫ ′ (ω) = n 2 (ω) − k 2 (ω) (10) ǫ ′′ (ω) = 2n(ω)k(ω) www.nature.com/scientificreports/ amplitude). In this case, the anharmonicity of a FCA mode is defined by the difference in the informationentropy of the observed density and that of a Gaussian function with the same variance. The visualization of the essential FCA modes and a description of the dynamics within the protein conformational subspace were conducted by selecting the FCA modes with the highest pairwise correlation. The free energy surface plots of the selected pair of FCA modes were created with the gmx sham tool in GROMACS and further visualized with gnuplot.
Calculation of pair-wise forces from MD simulation. A modified version of Gromacs 4.5.3 was used to write out the pair-wise forces 51 , Fij, between each residue pair i and j from the MD simulations. The force distribution analysis (FDA) provides a method for visualizing strain propagation in macromolecules. In our FDA, forces include contributions from the electrostatic and van der Waals interactions involving protein-protein interactions that are calculated below a certain cut-off distance. In this work, FDA was performed in a post-processing step on trajectories obtained from the production MD simulation runs. Hence, the cut-off for both van der Waals forces and Coulomb forces were set to 1.0 nm These non-bonded pairwise forces of the residue pairs in close proximity comprise a force-propagation network involving short-range to medium-range connections that are averaged over the simulation time. The averaged forces were saved every 10 ps and convergence was reached when an equilibrium value for the forces was attained. The stored forces were written out as force trajectories and the average of those forces were used later for further analysis in R (https:// www.r-proje ct. org/) as well as visualization in VMD (http:// www. ks. uiuc. edu/ Resea rch/ vmd/). Covariance matrices and principal component analyses (PCA) were used on the averaged residue forces to identify correlated changes in the pair-wise forces within and between protein structures.

Funding
Open Access funding enabled and organized by Projekt DEAL.