Solvation dynamics of biomolecules: modeling and terahertz experiments

Abstract

The role of water in biomolecule dynamics has attracted much interest over the past decade, due in part to new probes of biomolecule-water interactions and developments in molecular simulations. Terahertz (THz) spectroscopy, among the most recent experimental methods brought to bear on this problem, is able to detect even small solute induced changes of the collective water network dynamics at the biomolecule-water interface. THz measurements reveal that proteins influence up to 1000 water molecules in their surroundings, and that even small saccharides influence the dynamics of hundreds of surrounding water molecules. The THz spectrum of a protein is sensitive to mutation and depends on the surface charge and flexibility of the protein. Influence on the solvation shell appears most pronounced for native wildtype proteins and decreases upon partial unfolding or mutation. THz spectra of solvated saccharides reveal that the number of water molecules coupled dynamically to a saccharide, forming a dynamical hydration shell around it, is related to the number of exposed oxygen atoms on the solute. The thickness of this layer appears correlated with the bioprotection efficiency of the saccharide. All findings support the thesis of a long-range dynamic coupling between biomolecule and solvent.

Is there any water in a living cell? This may seem like a strange question, but water as we know it, that hydrogen-bonded bulk liquid melting at 0 °C and boiling at 100 °C may not exist within cells. With a cytoplasmic packing density of up to 400 mg∕ml of protein, nucleic acids, lipids, carbohydrates, and small molecules or ionic compounds, there is not much distance from any one molecule to its nearest neighbors; about 20–30 Å only, depending on the molecular size (Cameron and Fullerton, 2006). The 10–15 water layers that can be fitted into these spaces may be highly perturbed from the bulk and could have entirely different properties. This is true not just in the living cell, but also in model systems, such as water-filled reverse micelles (Rosenfeld and Schmuttenmaer, 2007).

Freezing point depression is just one simple example of solute-modified water properties, familiar from chemistry textbooks. Just how strongly water is perturbed is a question of how you look at it. The density of water may lie near the bulk value five layers from the surface of a protein, while the ever-changing orientation of its dipoles (negative at the oxygen atom, positive at the hydrogen atoms) still differs in fundamental aspects from the bulk at that distance. Debates about the number of hydrogen bonds per water molecule in bulk water, whether this number is between 3 and 4 or less, stem from the fact that any one bond survives only briefly, due to the liquid’s rapidly changing hydrogen bond network (Kumar et al., 2007). This water dynamics changes profoundly when proteins are present, beginning with the collective dipole moment fluctuations of all the solvation water molecules. Such perturbations of the dynamics of water will decrease with increasing distance from the biomolecule, but at the same time, the number of molecules in a shell around the protein grows as the square of that distance. For this reason, even subtle effects can add up to a significant change in behavior.

Just what measurement techniques can give us insight into how much water surrounded by biological molecules differs from the bulk?

Neutron scattering can look at the structure of water, and it has been shown that hydrophobic amino acid sidechains lead to greater ordering of immediately adjacent water molecules (Pertsemlidis et al., 1996). Water forms cage-like structures around small hydrophobic sidechains, similar to the clathrates of water that engulf methane molecules in some natural gas sources (Head-Gordon, 1995).

Nuclear magnetic resonance (NMR) and x-ray crystallography have probed water molecules bound to proteins (Gallagher et al., 1994). X-ray crystallography has shown that certain sites in or on the surface of a protein are always occupied by a water molecule, mediating for example binding to an active site (Evans and Brayer, 1990). NMR has been used to measure the slowing of exchange rates of waters from the immediate vicinity of the protein out to larger distances (Halle, 2004). NMR (Persson and Halle, 2008) and neutron scattering (Tehei et al., 2007) have both been used to study water dynamics in the living cell. NMR provides a good example of how the deviation from bulk depends on the probe: magnetic relaxation dispersion yields a mobility only a factor of 2 below bulk for water molecules near a protein, while intermolecular nuclear overhouser effects (nuclear overhauser effect—a method to measure the distance between polarized spins, such as protons in water and protons in proteins) yield a greater mobility loss (Otting and Wüthrich, 1989).

Dielectric relaxation spectroscopy, using frequencies in the up to the gigahertz range, has detected changes in relaxation of water containing biomolecules such as small peptides. Amphiphilic peptides (polar on one side, nonpolar on the other) interact with water molecules and restrict their motions, effectively “frustrating” the free motion of the water (Murarka and Head-Gordon, 2008; Nandi et al., 2000). The concept of slaving was introduced by Frauenfelder to describe such feedback between solvent motions and biomolecule motions (Fenimore et al., 2002).

Fluorescence of biological functional groups such as tryptophan sidechains depends strongly on the aqueous environment. The high dielectric constant of water leads to a redshift in fluorescence by stabilizing large excited state dipole moments. Ultrafast pump-probe experiments have used such dynamical shifts to reveal how rapidly water molecules can rearrange around a sidechain (Zhong et al., 2002). Of course, adding such sidechains to probe many locations around a protein may also perturb the water structure.

Such perturbation can be used in a controlled manner. Site-directed mutagenesis of surface exposed residues has provided clues that water ordering near the protein surface depends on the nature of the sidechains present. Unfolding free energies of proteins generally change little upon surface mutation (<4 kJ∕mole for the most part), but the change is significant on the energy scale of hydrogen bonds (20 kJ∕mole). Thus, surface mutations can map out how sensitive water structure is to changes in polarity, charge, and hydrophobicity at the protein surface, or how important protein flexibility controlled by interior mutations is (Ebbinghaus et al., 2007; Evans and Brayer, 1990).

Recently a new window has opened up onto water dynamics around biomolecules. Terahertz light, at frequencies (10¹² H=1 THz) between microwaves and the infrared, can excite collective motions of solvent molecules and of biomolecules whose time scales are on the order of a picosecond (Dexheimer 2007; Leitner et al. 2006). Modern terahertz instrumentation, building on decades of progress in far infrared spectroscopy of solid samples and films, is now powerful enough to penetrate water layers and look at fully solvated proteins, carbohydrates, lipids, or nucleic acids (Chen et al., 2005; Dexheimer, 2007; Ebbinghaus et al., 2008; Xu et al. 2006). As we shall show, terahertz absorption can detect subtle changes in the dynamical orientation of water molecules that are washed out in radial distribution functions from scattering experiments, and it can report on distance scales beyond current NMR experiments (Ebbinghaus et al., 2008; 2007; Heugen et al., 2006; Heyden et al., 2008). Mutagenesis can be used to ask questions about site specificity, but is not required to obtain a signal (Ebbinghaus et al., 2008). In effect, terahertz light extends the dielectric regime from nanosecond motions down to picosecond motions, just the time scale where important librational, diffusional, and other collective motions of hydration water, and large amplitude motions of biomolecules, come into play.

A small but growing number of researchers, including the groups of Durbin, Markelz, Plaxco, the groups of Plusquellic, Heilweil, and Siegrist at the National Institute of Standards and Technology, and ours, are now looking at the terahertz response of hydrated to fully solvated large biomolecules (Chen et al., 2005; Ebbinghaus et al., 2007, 2008; Heugen et al., 2006; Knab et al., 2007; Markelz et al., 2008; Plusquellic et al., 2007; Xu et al., 2006; Zhang and Durbin, 2006). From this work over the past 5 years we now know that the frequency dependence of the absorbance is largely featureless in the terahertz (THz) regime (Ebbinghaus et al., 2007; Plusquellic et al., 2007; Zhang and Durbin, 2006), that hydration substantially enhances the THz absorbance of protein systems (Ebbinghaus et al. 2007; Zhang and Durbin, 2006), and that the absorbance depends sensitively on protein configuration and flexibility (Ebbinghaus et al., 2008; Markelz et al., 2008; Whitmire et al., 2003). For a thin film of hen egg white lysozyme sudden increase of THz absorption was found when the hydration exceeded 23% gwater∕g protein (Knab et al., 2006). This was taken as evidence for an increase in conformational flexibility of the protein itself upon increasing hydration. A similar rapid increase in THz absorption was found when increasing the temperature above the dynamical transition (around 200 K) (Markelz et al., 2007). These results can be directly related to the results from neutron scattering measurements which also probes the flexibility of the water-protein network (Wood et al., 2008). All these data were obtained in relatively highly concentrated protein-water samples.

Measurement of the THz absorbance as a function of protein concentration in solution provides clues about dynamic coupling between protein and water; it is this information that we focus on in this perspective. At relatively high concentration, the absorbance has been observed to decrease approximately linearly with increasing protein concentration (Xu et al., 2006). A study of the THz absorption of hydrated myoglobin over a range from 3.6 to 98% wt showed considerable changes. A significant increase in the absorption was found in the range from 1 to 42 wt %, which was obtained by measurements on hydrate powders. At higher water concentrations in protein solutions (above 50 wt %) an even higher overall absorption coefficient was found, as was expected for an increasing amount of water. [However, their results demonstrated that an interpretation using a simple model with two noninteracting species—protein and water—is not possible (Zhang and Durbin, 2006). Instead we have to assume a strong coupling.]

We have investigated lower concentration protein-water solutions with great precision. We could thereby detect an interesting nonlinear variation of the absorbance with protein concentration (Ebbinghaus et al., 2007). This variation reveals a crossover from dilute protein solutions to solutions where the solvation layers around the proteins overlap and bulk water disappears.

At the same time, computational methods provide estimates for vibrational spectra of biomolecules at low frequencies (Leitner et al., 2006; Whitmire et al., 2003). For large biomolecules force field models have been adopted to compute THz absorption spectra in harmonic approximation (Whitmire et al., 2003), using normal mode analysis, and by computation of dipole fluctuations using molecular dynamics simulations (Ebbinghaus et al., 2007). In addition to extracting THz spectra, simulations have also been carried out to model the behavior of water molecules as a function of distance from the biomolecule, to gain insight into the dynamic coupling between the biomolecule and nearby water, which underlies the THz spectra (Heyden et al., 2008; Leitner et al., 2006). These studies, both experiment and theory, are revealing a number of interesting concepts which we discuss in the next section, followed by a review of theoretical and simulation approaches towards understanding long-range hydration shells around water molecules, and finally some of the experiments that are interpreted by such models and simulations

BIOMOLECULE SOLVATION AND TERAHERTZ DYNAMICS: IMPORTANT CONCEPTS

We begin by reviewing some of the important concepts that have emerged from terahertz studies of biomolecular solvation. Some of these ideas confirm what one would have suspected, others are rather surprising. The subsequent sections will discuss in more detail the technical basis in modeling, theory, and experiments from which these concepts emerged.

Complex macromolecules have a great many vibrations, at different frequencies ω, so it makes sense to invoke as a central concept the spectral density ρ(ω), rather than accounting for every one of thousands of vibrational peaks separately. A plot of ρ(ω) for the five-helix bundle protein, ${\lambda }_{6–85}^{*}$, in the region from 0 to 110 THz is shown in Fig. 1. At the highest frequency, one finds vibrations from the lightest nuclei (hydrogen) and most localized vibrational modes. Further down (∼30 THz) come various small amplitude stretching and bending modes of the backbone and sidechains. Only below 10 THz do we begin to get modes delocalized to large numbers of atoms. In the region between 1 and 5 THz, water absorption (shown as a thin black line in Fig. 1) plays a significant role. At the very lowest frequencies, the absorption declines towards zero as some power of the frequency, or A∼ω^a (Elber and Karplus, 1986; Herrick and Stapleton, 1976; Leitner, 2008). Such a power-law scaling of the spectral density has been observed in low-temperature electron-spin relaxation measurements (Herrick and Stapleton, 1976). At first glance, a power-law variation of the absorbance at low frequency is not particularly surprising; the Debye theory of elastic materials predicts just such a variation, where the power a is just 1 less than the dimension of the material; for a three-dimensional object a is 2. What is surprising is that experiment and theory reveal an altogether different value of a, between about 0.3 and 1.0, for vibrational frequencies out to about 3 THz. This very simple functional form and the power a associated with it contain very interesting information. The fractional powers observed in low-temperature electron-spin relaxation measurements and computational studies of the low-frequency motion of protein molecules indicate that vibrational couplings and energy transport in the biomolecule are lower-dimensional than one might think—certainly not three-dimensional (Elber and Karplus, 1986; Herrick and Stapleton, 1976; Leitner, 2008).

Figure 1. Protein and water spectral density.

The spectral density (gray curve) of the five-helix bundle protein ${\lambda }_{6-85}^{*}$, shown in the inset, describes how its vibrations are distributed as a function of frequency or energy. Only modes below a few THz correspond to collective motions of many atoms or residues within the molecule. Such motions are prime candidates for folding and function. Also shown is a spectral density for bulk water (black), for comparison.

Another key concept in terahertz spectroscopy of biomolecules in water is the “terahertz defect.” Biomolecules absorb less THz light than water over part of the frequency range, and when biomolecules are dissolved in water, the absorption coefficient of the solution often decreases at certain frequencies (e.g., 2.5 THz for proteins in water). In some cases, a simple model assuming that biomolecules behave like empty cavities in the water gives good agreement with experimental data! The missing absorption arises because biomolecules, although large and extended, do not extend in the same way as the full water network. Being bounded in size, they lack some of the lowest frequency motions that can be found in the bulk aqueous solvent. Thus at sufficiently low frequencies, water will absorb more. The difference can range from a few percent to percentages close enough to 100% that the biomolecule-as-hole-in-water concept provides a first approximation.

A third key concept is the “terahertz excess.” Despite the fact that pure biomolecule solids or films generally absorb less than bulk water between 1 and 3 THz, there are still many situations where the biomolecule+water mixture does absorb more than either the biomolecule or a bulk water sample. This can be explained only by invoking a third substance—biological or hydration water. If the presence of biomolecules perturbs nearby water molecules, this could have an effect on many of the measurable properties of water: density, relaxation rates, reorientation rates.

Water has a built-in probe of its orientation: its dipole moment, with a negative charge at the oxygen end and positive charge at the hydrogen end of the molecule. The dynamical reorientation of the water dipole moment turns out to be affected over particularly long distances, up to several nanometers from the surface of a biomolecule. This reorientation arises as water molecules within the hydrogen bonding network tumble around and diffuse, constantly making and breaking hydrogen bonds. Couple that with the radius-squared increase of the number of water molecules as one moves outward to more remote solvation shells, huge numbers of water molecules can be affected by a single biomolecule. Terahertz measurements and simulations, and theories studying the terahertz spectrum, are exquisitely sensitive to the dynamical reorientation of dipole moments on the picosecond time scale—this is precisely what a terahertz spectrum measures (1 THz=10¹² Hz=1 ps⁻¹). A simple picture of a protein in water thus has to include the protein, nucleic acid or carbohydrate (causing a terahertz defect), bulk water (if far enough away), and hydration water with new physical properties, including a propensity for enhanced terahertz absorption—the terahertz excess. The thus defined hydration water is not identical to the sterically bound water molecules probed by x-ray crystallography, NMR, or neutron crystallography. We will therefore define a dynamical hydration shell, which includes all water molecules that show water network dynamics distinct from the bulk, and thus a distinct THz absorbance. The influence of the protein can reach much further than the static hydration radius since it involves only a change in the motions and not a fixed H-bond to the protein.

Our work has shown that this simple picture can work quantitatively for some cases, for instance water molecules surrounding small sugar molecules (Heyden et al., 2008), but breaks down in other cases, for instance hydration water around crowded proteins (Ebbinghaus et al., 2007). In the latter case, the effect of proteins on the surrounding water shell reaches out so far that water molecules begin to “see” more than one protein, which implies that many-body interactions become important even away from the surface of the protein. Such a continuum of different types of water also emerges from molecular dynamics simulations of the solvation water around biomolecules (Bagchi, 2005).

BIOMOLECULE SOLVATION: THEORY AND SIMULATION

Computer simulations provide a means to explore the detailed dynamics and structure of water near the surface of a biomolecule, including translational and rotational diffusion of water molecules as a function of distance from a protein as well as hydrogen bond dynamics. These processes, notably hydrogen bond rearrangements, occur at THz frequencies. We observe in Fig. 1 that the spectral density of a protein rises and is relatively large at such frequencies, so that oscillations of the water network and hydrogen bond rearrangements are resonant with and dynamically coupled to collective motions of the protein molecule. THz fluctuations of the collective dipole moment of the solvent water and thus the THz spectrum are exquisitely sensitive to the presence of nearby protein molecules.

Water molecules in the bulk hydrogen bond with 3–4 other water molecules at any given time, as deduced from, e.g., neutron diffraction studies, but these hydrogen bonds are in a constant state of flux (Kumar et al., 2007). Water molecules rotate in solution on a subpicosecond time scale, so that within a picosecond a hydrogen bond between any two molecules may break and reform many times. Diffusion of water molecules occurs on a picosecond time scale. Over this longer time scale a given hydrogen bond between two water molecules may no longer reform, as reorientation and translation of a given water molecule favors new bond formation. These two main contributions which lead to a fluctuation in the water network are visualized in Fig. 2.

Figure 2. Illustration of hydrogen bond rearrangements in water.

In bulk water we find a constant breakage and formation of hydrogen bonds due to the rotation and diffusion of the water molecules in bulk water. Curved arrows indicate the oxygen atom to which a new hydrogen bond is formed following rotation of the water molecule.

A detailed picture of this collective dance has emerged from computational studies, which have also elucidated the nature of the hydrogen bond and criteria for hydrogen bonding between a given pair of water molecules in the bulk. One way to quantify hydrogen bond rearrangement is calculation of time-dependent survival probabilities for bonds between water molecules (Bagchi, 2005).

The THz fluctuations of the hydrogen bond network of water arising in part from the breaking and reformation of hydrogen bonds between water molecules are influenced by the presence of solute. Molecular dynamics simulations reveal that hydrogen bonds between exposed O atoms on a protein or saccharide and surrounding water molecules survive on average significantly longer than the hydrogen bonds between water molecules in the bulk (Lee et al., 2005; Tarek and Tobias, 2002), mimicking the effect of cooling of the water near the protein surface. The relatively sluggish rearrangement of hydrogen bonds is not merely limited to bonds between the water and the solute. Computer simulations reveal a retardation of the rearrangement of hydrogen bonds between water molecules out to 3 or 4 solvation layers from a protein molecule, even to about two layers for a small saccharide (Heyden et al., 2008).

The THz absorption spectrum of the solvated protein is thus related to the fast fluctuations of the water dipole moments (more in detail: The THz absorbance is proportional to the Fourier transform of the dipole moment autocorrelation function). The spectrum is not merely a separable spectrum of water and protein, due to the strong dynamic coupling between them. Since the fluctuations of the collective dipole of the water are sensitive to the environment, the spectrum is influenced by the presence of nearby proteins. Molecular dynamics simulations reveal that the THz oscillations of the water dipole moments are tuned by the presence of a protein as far as 10 Å away, or perhaps even farther (Ebbinghaus et al., 2007). If the protein concentration is sufficiently high such that the distance between protein surfaces in solution is about 20 Å or even less, the collective THz oscillations in the water network no longer resemble the fluctuations of water in the bulk. The collective protein-water dynamics give rise to a new medium in which bulk water is absent.

As we observe in Fig. 1, protein molecules exhibit a significant spectral density in the THz region. As discussed in the previous section, the absorbance, A, of a protein molecule varies with frequency, ω, as a power-law, A∼ω^a, where a≈0.3−1. If we naively separate protein and water absorbance, then such a modest rise in the absorbance with increasing frequency is not enough to compete with the much stronger absorbance of water at 1–3 THz. Indeed, as we increase the concentration of protein in molecular dynamics simulations of the protein—water system while fixing the frequency of the dipole moment oscillations in this range, the absorbance is computed to generally decrease, albeit nonlinearly. As the concentration increases such that the surfaces of two protein molecules lie on average within 18–24 Å of each other, the decrease of the absorbance with increasing concentration changes more gradually than it does at higher concentration, when the proteins are closer together (Ebbinghaus et al., 2007).

Another surprise is the influence of mono- and disaccharides on the THz spectrum of water. A small, isolated saccharide absorbs THz radiation at only a few specific frequencies. Nevertheless, introducing saccharides to water tunes the fast oscillations in the water network and thus the THz spectrum. Molecular dynamics simulations of the hydrogen bond dynamics between water molecules around a disaccharide such as lactose are more sluggish than the hydrogen bond rearrangements between water molecules in bulk water to about 6 Å away from the solute. Similarly, the predicted THz absorbance of water molecules around lactose is distinct from the THz oscillations of bulk water (Heugen et al., 2006; Heyden et al., 2008).

BIOMOLECULE SOLVATION: TERAHERTZ EXPERIMENTS

THz spectroscopy is still a great challenge. For a long time, this spectral region between microwave and infrared technology was known as the “THz gap,” indicating a lack of powerful THz radiation sources. The previous inherent lack of bright THz sources can be attributed to the fact that it lies in the frequency range where classical electronic devices end and photonics devices such as diode laser do not work because the corresponding frequency is smaller than the band gap of a semiconductor. The state of the art of THz sources has been reviewed recently by Tonouchi (2007).

In general, the precise measurement of THz absorbance of (strongly absorbing) liquids is very difficult because they require data acquisition over a series of very short and precisely determined path lengths. Moreover, when measuring a liquid fixed between two windows, these windows will also absorb and reflect part of the radiation. While the reflection factor at the window surfaces remains unchanged when varying the layer thickness, the absorption will exponentially increase with the layer thickness of the liquid, thus strongly reducing any systematic error. It is therefore highly advantageous to measure a thick layer of the liquid; however, this requires a sufficient laser power in order to be able to still penetrate through the sample to the detector.

In Bochum we have realized a new table-top THz spectrometer using a p-Ge laser as a radiation source (Bergner et al., 2005), with an output power that is increased by an order of magnitude over other available table-top THz sources. The p-Ge laser is a pulsed laser source with a duty cycle of up to 5% and a laser power of approximately 10 W.

The absorption of a sample can be described by Beer’s law

$$I\left(\nu \right)=I_0\exp [-\alpha \left(\nu \right)d]+C,$$ (1)

with I₀, α(ν), d, C corresponding to the intensity before the probe, the absorption coefficient of the probe, the layer thickness of the probe, and the detector offset, respectively. Even with absorption coefficients on the order of α=100–400 cm⁻¹, as is typical for solvated solutes in the THz range our new setup yields good signal-to-noise spectra in a matter of minutes. We are able to penetrate water to a depth of over 200 μm, thereby allowing a reliable measurement of the absorption coefficient of water or solute-solvate mixtures in the THz with an accuracy of less than 1%, not possible before.

Any change in the fast water network oscillations is connected with a change in THz absorbance. This has been observed before when changing the temperatures (Ronne et al. 1997). Whereas for a 100 μm layer of water at 97 °C, 40% of the radiation at 1.5 THz is absorbed, at the freezing point only 0.4% of the radiation will be absorbed. The change is much larger than in any other spectral region because this frequency range probes directly the mobility of the water network motions. This example suggests that a precise determination of the THz absorption coefficient is therefore a sensitive tool to detect solute induced changes in the fast water dipole fluctuations around solutes.

In order to be able to record very small changes we have set up a spectrometer, which directly measures the variation in the THz absorption with respect to a reference. Whereas the absorption coefficient α of bulk water and the solvated biomolecule are both large (on the order of 400 cm⁻¹), the solute induced change is relatively small (Δα is on the order of 10–20 cm⁻¹), but carries the essential information. Our experimental set-up is shown in detail in Fig. 3.

Figure 3. Setup for THz measurements.

Displayed is the radiation path of the THz radiation. The mirror-chopper splits the radiation into two distinct beams. One part is passing through the bulk water, the other through the biomolecule solution. Both are then focussed onto the detector.

As discussed in the theory section, the THz spectrum of the solvated biomolecules to a first approximation increases smoothly with frequency, similar to what was found for bulk water. Over a narrow range (e.g., 2.1–2.8 THz) the spectra can be fitted linearly, as observed in Fig. 4. However, the important information is not contained in the variation of THz absorption with frequency, but instead in the variation of the THz absorption with increasing biomolecule concentration. In general, we observe both a THz excess when the concentration of the protein is still low, and a THz defect when the concentration of the proteins is relatively high. This happens because the hydration water absorbs more than either protein or bulk water. When increasing the concentration the solvation shells begin to overlap and at high concentration the water displacement effect dominates.

Figure 4. THz spectra of ${\mathbf{\lambda }}_{\mathbf{6}-\mathbf{85}}^{*}$ .

THz spectra are shown for the buffer and the solvated five helix bundle protein ${\lambda }_{6-85}^{*}$ for different protein concentrations. The frequency dependence of the THz absorption coefficient is linear between 2.25 and 2.55 THz (15 °C, buffer and two protein concentrations). We observed a THz excess for concentrations of 0.47 mM and a THz defect for concentrations of 0.86 and 1.14 mM.

If the biomolecule did not affect the water in its surroundings, we would expect a linear change from the large THz absorption coefficient of bulk water to the very small absorption coefficient expected for a biomolecule when raising the biomolecular concentration from zero to 100%. In that case, the following model would fit the absorption coefficient as a function of concentration:

$$\alpha ={\alpha }_{\text{Protein}}\frac{V_{\text{Protein}}}{V}+{\alpha }_{\text{Buffer}}\frac{V-V_{\text{Protein}}}{V}\approx {\alpha }_{\text{Buffer}}(1-{\rho }_{\text{Protein}}{c}_{\text{Protein}}).$$ (2)

In this equation, the protein has a concentration c_Protein in the total volume V and ρ_Protein is the protein density. This so-called two component model corresponds to the red curve as shown in Fig. 5. However, when each solute is surrounded by a dynamical hydration shell which has a THz absorption different from bulk water—due to changes in the water dynamics—then we expect a deviation from this linear behavior.

Figure 5. Concentration dependence of the THz absorbance of a biomolecule solution.

The boxes show how hydration water volumes simply add up at low concentration (left), but crowding eventually leads to overlap, until most of the volume is occupied by the biomolecules. The plot shows absorbance expected for biomolecule+bulk water only (red curve), biomolecule+bulk+hydration water [blue curve, Eq. 3], and experimental data (black circles) for lactose, the latter exhibiting the THz excess.

Note that the total volume of hydration shells increases linearly with protein concentration at low concentrations. If the absorbance of a given hydration shell exceeds the absorbance of the bulk water displaced by the shell and protein, the overall absorption will at first increase linearly with protein concentration. Eventually, the hydration shells overlap, and their total volume then actually decreases relative to the increasing volume of protein. If the biomolecules absorb less than water at high concentration we expect a turnover in the absorption coefficient with increasing biomolecule concentration. This deviation from linearity for the case of hydration shells is displayed schematically in Fig. 5, in particular for w_lactose∕w_solution>0.2 (w=p⋅V).

If we assume that the absorption coefficient within a certain distance from the biomolecule is changed compared to bulk water, the minimum fitting model required to describe the solute-solvate system must incorporate a third component, attributed to water in the dynamical hydration shell around the solute

$$\alpha ={\alpha }_{\text{Protein}}\frac{V_{\text{Protein}}}{V}+{\alpha }_{\text{Shell}}\frac{V_{\text{Shell}}}{V}+{\alpha }_{\text{Buffer}}\frac{V-V_{\text{Protein}}-V_{\text{Shell}}}{V}.$$ (3)

In a first proof of principle experiment we measured the solute induced change in the THz absorption for a disaccharide, lactose (Heugen et al., 2006). For disaccharides, the three-component model provides an excellent description of the measured data, which is shown in Fig. 5 by black dots along with Eq. 3 (blue curve). The model allowed us to fit the size of the solvation shell because the solvation around sugars is rather homogeneous. The induced THz absorption changes for disaccharides can be systematically correlated with the number of sugar-water contacts (Heyden et al., 2008).

In addition to its importance as energy currency for living systems, solvated mono- and disaccharides are found to have a significant stabilization effect on proteins and membranes in a dehydrated or frozen state. (Block, 2003; Crowe et al., 1984). Plants which can survive extreme conditions are known to produce oligosaccharides for protection. This effect is also widely used in industry for food protection. It was speculated that slowing of the hydration dynamics might lead to a reduced biological activity of the proteins, though a measurement had not been previously possible. By a fit of the measured THz absorption coefficients we were able to determine the size of the dynamical hydration shell for various sugars. An overview of our results is given in Fig. 6. These results support the hypothesis that the bioprotection mechanism of sugars is caused by its long range retardation of hydration dynamics.

Figure 6. Dynamical hydration shell around a saccharide.

Comparison of the size of the dynamical hydration shell of sugars as probed by THz spectroscopy according to reference (Heyden et al., 2008) are illustrated.

A further example showing the power of this new experimental approach was the study of the five helix bundle protein ${\lambda }_{6–85}^{*}$ which also yielded an unexpected nonmonotonic trend in the measured terahertz absorbance as a function of the protein: water molar ratio (Ebbinghaus et al., 2007). The trend could be explained by overlapping solvation layers of an unexpectedly long range around the proteins, more than 20 Å, which is greater than the pure structural correlation length usually observed. The measurements showed that about 1000 water molecules are directly influenced in its flow, a dramatic effect. The protein with its dynamical hydration shell is shown in Fig. 7.

Figure 7. Dynamical hydration shell around a protein.

The five helix bundle protein ${\lambda }_{6-85}^{*}$ is shown surrounded by water in the dynamical hydration shell.

The change of the water network dynamics was found to be most pronounced for the wild type and much less for the partially unfolded protein. The THz absorbance for the partially unfolded protein essentially resembles that of a transparent ball of the size of the radius of gyration (Ebbinghaus et al., 2008). This could imply that upon unfolding, the protein is losing the ability to influence the fast water network oscillations, raising new speculation about the biological significance of the long range influence on the water dynamics for protein dynamics and protein function (Ebbinghaus et al., 2007). Perhaps protein surfaces have evolved to dynamically restructure their solvent.

This leads to the question: what property of the surface is responsible? Point mutations on the surface or in the interior can be correlated with changes in the THz absorption to investigate this question. We therefore studied distinct site-specific mutants of the small lambda repressor fragment and ubiquitin, and have observed large changes in the THz absorbance as a result (Ebbinghaus et al., 2008). We investigated the distinct THz response when varying the surface charge as well as when increasing the flexibility of the protein.

The first important result was that any mutation of the proteins causes a decrease in the THz excess; i.e., the effect of influencing the fast water network oscillations seems to be optimized for the wildtype. More specifically we made the following observations for λ repressor:

(1) When replacing a single polar glutamine sidechain with aromatic residues the nonlinear concentration dependence is already less pronounced, regardless of whether we introduce an additional mutation that enhances or decreases helix stability. Thus surface charge affects the THz response.

(2) When coupled with Ala-Gly mutations (A37, 49 G) that greatly destabilize the protein (Yang and Gruebele, 2004), the Tyr mutant shows a concentration dependence similar to the low pH proteins. Thus, we conclude that protein flexibility is a second important influence on hydration dynamics as probed by THz spectroscopy.

(3) To test the question of flexibility further, we truncated aliphatic sidechains in the core of ubiquitin, affecting overall protein flexibility, but not surface polarity (Ervin et al., 2002). Indeed, we found that such mutations greatly decrease the THz excess of ubiquitin (Born et al., 2008). In general, any destabilization of the protein by core truncation or by an unfolding transition leads to a decrease in the THz excess and might even lead to a THz defect at low concentrations.

Very recently, we have used such changes in THz absorbance to monitor the hydration layer around a protein while the protein folds. Although the protein ubiquitin requires about 1 s to fold to the fully native state under our conditions, as determined by transient fluorescence spectroscopy, it turns out that the THz response at 0.2–1 THz is about 100 times faster, indicating that the solvent has undergone major rearrangements in response to protein folding long before the protein has settled into the native structure (Kim et al., 2008).

SUMMARY

Terahertz absorption is a new sensitive tool to probe the interaction of protein surfaces with their solvent shells. Local perturbation by surface site-specific mutation, as well as global perturbations resulting from increasing protein flexibility both produce significant changes in the terahertz absorbance of aqueous proteins. Such changes can be used in the future as sensitive probes of protein-solvent dynamics and are opening up the possibility of using THz absorption as a probe for protein folding kinetics and for functional dynamics measurements. The development of quantitative models for the THz spectra will make it possible to understand solvation dynamics of proteins at the molecular level. This will shed new light on how far out proteins influence their solvent shells, whether this influence has functional advantages that could have evolved, and pinpoint which protein properties cause dynamical reordering of the solvation shell.