Local compressibilities in insulin as determined from pressure tuning hole burning experiments and MD simulations

Abstract

We present a hole burning study on insulin in a glycerol–water solvent by using the intrinsic amino acid tyrosine as a photochemical probe. The focus of the experiments is on the comparative pressure response of the spectral holes for insulin in its native state, in its chemically denatured state and for tyrosine in the glycerol–water solvent. From an analysis of the color effect of the pressure response, we can identify two different spectral ranges characterized by a markedly different sensitivity to pressure. We conclude that at least two tyrosines (or two groups of tyrosines) out of the eight in the insulin dimer are photochemically labeled, and that they are characterized by markedly different compressibilities, namely 0.08 and 0.13 GPa⁻¹, respectively. An interesting observation concerns the compressibility in the unfolded state: It is significantly lower and closer to the value measured for the pure tyrosine molecule in a glycerol–water solvent. In contrast to the native state, the response of the various tyrosines in the unfolded state to pressure variations is quite uniform. The experiments are compared with MD simulations of monomeric insulin at ambient temperature. The computational results show that the local compressibilities around the different tyrosines vary significantly and that they strongly depend on whether just the first shell of molecules or the first two shells are included in the local volume.

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1. Introduction

Volume fluctuations of proteins are quite important with respect to protein function and protein stability. The mean square of the volume fluctuations is directly related to the compressibility. Since the compressibility can be measured, the mean square of the volume fluctuations is experimentally accessible. The latter is a measure of protein flexibility. For many proteins, flexibility is directly related to biological function. As to protein stability against temperature, its correlation with the compressibility has recently been pointed out by Dadarlat and Post.¹ However, also the stability of proteins against pressure is largely determined by the difference of the compressibilities in the native and in the denatured state, respectively:² A larger compressibility in the denatured state ensures that its volume falls below that of the native state if pressure becomes sufficiently high so that the denatured state is thermodynamically favored. However, in some proteins there is also a certain temperature range where higher pressure stabilizes the native state. If so, the compressibility in the denatured state must be smaller according to thermodynamic principles.

There has been a lot of activity to determine protein compressibilities, both experimentally and theoretically via computer modeling. Only recently, detailed formulas have been derived to calculate local compressibilities of any arbitrarily chosen volume, say around some amino acid residue in a protein.³

Most of the experiments on the determination of protein compressibilities are focused on measuring the sound velocity of protein solutions.^4–8 The compressibility of the protein itself has to be extracted from the compressibility of the solution by varying the protein concentration. A major problem in these experiments concerns the hydration shell: It is considerably denser than bulk water, but it cannot be measured separately. Its contribution has to be estimated.⁵ However, the empirical rules used seem to guarantee results with reasonable accuracy. Nevertheless, it is impossible to probe compressibility variations within the protein molecule using ultrasound techniques.

A quite different approach in measuring compressibilities is based on site selective spectroscopic experiments.^9,10 These types of experiments exploit the color effect in pressure-tuning of frequency selected optical lines within an inhomogeneous absorption band. One of the outstanding features of these spectroscopic experiments is that the response to pressure is mediated by a probe molecule through its interaction with the environment. Since these interactions are of rather short range,¹¹ the compressibility measured is a local compressibility of a volume around the probe whose size is determined by the average range of the respective interactions. In principle, these techniques have the capability of measuring compressibility variations within a biological macromolecule if the macromolecule contains several probes.

In this study we present pressure-tuning spectral hole burning experiments on the hormone-protein insulin by using its tyrosines as natural optical probes. Our goal was to measure the intrinsic compressibility of this protein, to check whether the various tyrosine sites show significantly different elastic properties and to compare the experimental results with compressibility calculations as obtained from MD simulations. The simulations were carried out with the insulin monomer, which corresponds to the physiologically active form of the protein. In the experiments, insulin most likely prevailed in a dimeric state, because the necessary protein concentrations needed in most biochemical and biophysical studies are in a range where insulin-associations can hardly be eliminated.

The purpose of the calculations was to verify that tyrosine sites with markedly different properties do exist. Further, in our experiments we focused on the difference of the compressibilities in the folded and in the chemically unfolded state of insulin in order to find out whether site-specific properties remain during unfolding.

Insulin is a globular protein consisting of 51 amino acids organized in two polypeptide chains, usually named A and B, that are linked via two disulfide bridges. Since its discovery it has been subject to intense biochemical and biophysical investigation. It was actually the first protein whose complete amino acid sequence was known.¹² It regulates the glucose transport through cell membranes by binding to specific trans-membrane receptor proteins. The high propensity to form aggregates e.g. dimers, tetramers, hexamers, but also fibril-like structures, depending on the pH, on temperature, concentration, etc. has often been studied.^13–17 Space-filling ball models of monomeric and dimeric insulin together with their tyrosines (four per monomer) are shown in Fig. 1. Our experiments were carried out at pH values of about 2. Such conditions prevent high order association-states while the native fold is largely preserved.¹³ Accordingly, under the conditions of our experiment, insulin most likely prevails in a dimeric form.¹³ In the following we will call this state the folded state in order to distinguish it from the structure under high urea concentration, which we will call the urea unfolded state.

Fig. 1 Space filling models of monomeric (a) and dimeric (b) insulin. Tyrosines are dark shaded and labeled. Note that in (b), not all of the eight tyrosines are labeled. Adopted from refs. 13 and 43.

2. Experimental and computational methods

Spectroscopic determination of the compressibility

Pressure-tuning experiments of spectral holes are solvent shift experiments. The dominant interactions which causes the solvent shift of a probe molecule in a certain environment are the dispersion and the higher order electrostatic interaction (dipole–induced-dipole interaction).^18–20 Both of them fall off with distance as R⁻ⁿ with n = 6. The ordinary dipole–dipole interaction is not expected to add much to the solvent shift due to the fact that the dipoles in the environment of the probe are supposed to be rather randomly oriented, even in a protein. This interaction will contribute mainly to the line broadening under pressure. Application of pressure (in our experiments of order 1 MPa) changes the distances between probe and the molecules in the environment, hence, modifies the solvent shift. The pressure-induced line shift s_p depends on the magnitude of the probe–solvent interaction (i.e. on the solvent shift s) and on how much the distance between probe and solvent molecules can be changed at a given pressure level. This change in distance, in turn, is determined by the compressibility. Hence, we write

s_p = 2κsΔp = 2κ(ν − ν_vac)Δp (1)

where we inserted for the solvent shift s of the selected wavenumber ν, s = (ν − ν_vac), with ν_vac being the so-called vacuum absorption frequency of the probe (for a review see ref. 21). The factor of 2 in eqn. (1) comes from the exponent 6 in the distance dependence of the interaction. The above equation has two parameters, namely ν_vac, which characterizes the probe and κ, the isothermal compressibility, which characterizes the solvent. However, due to the fact that our experiment probes a local compressibility in a small volume around the probe, one has to be aware of the fact that the elastic properties of this volume can be strongly influenced by the probe itself, e.g. through electrostatic or entropic interactions (e.g. hydrophobic ordering). It should be noted as well that ν_vac as measured in a pressure-tuning experiment is not the absorption frequency of the probe in a gas phase experiment. It is the vacuum absorption frequency of a fictive probe molecule including all the interactions with the solvent which cannot be modified by pressure at the pressure level of the experiment. Eqn. (1) is based on a series of approximations²² which have been discussed quite often in the literature.²¹ In the above form it holds for a R⁻ⁿ interaction potential, only.

We have been exploiting eqn. (1) quite often for determining protein compressibilities.^9,11,23–25κ is obtained by plotting s_p/Δp over the selected wavenumber ν in the inhomogeneous long-wavelength band. Following eqn. (1), a straight line is obtained with a slope of 2κ. Despite the many approximations inherent to this formula, the results obtained fit quite well to what is known from other experiments and from simulations.

Note that the holes not only shift but also broaden. In a perfectly homogeneous sample a simple R⁻ⁿ potential does not give rise to any broadening. However, a protein is rather heterogeneous. The simplest way to take this into account is to consider a dispersion of κ-values. As a consequence the pressure-induced displacement for some atoms is larger than for others. This gives rise to a broadening. Of course, the same result is obtained if more complex potentials are considered.²²

It should further be noted that in a spectroscopic experiment it is the isothermal compressibility that is measured, rather than the adiabatic compressibility which results fom ultrasound studies. The latter is significantly smaller since additional compression work against thermal expansion has to be performed.⁴

Temperature dependence of protein compressibilities

An important question concerns the temperature dependence of protein compressibilities, especially if low temperature experiments are compared with MD simulations at ambient temperature. We stress that wherever low temperature data can be compared with results obtained at room temperature, the coincidence is usually rather good. The physical basis for the obviously weak temperature dependence of κ seems to have its origin in the low thermal expansion coefficient of proteins. As an example we can take myoglobin. The linear thermal expansion coefficient has been determined to about 100 × 10⁻⁶ K⁻¹.²⁶ From this number we calculate that the average relative interatomic distance between a pair of atoms changes only by about 3% in a temperature intervall of 300 K. In absolute numbers this means a change in distance of about 5 × 10⁻² Å. Changes in distances of this order of magnitude simply seem to be too small to induce significant changes in the curvature of the atom–atom potentials. As a consequence the interatomic forces do not seem to change significantly and, hence, it is justified and reasonable to compare low temperature compressibilities of proteins with MD simulations obtained at room temperature.

Experimental details

Our hole burning laser system consists of an argon ion laser (Coherent Sabre) which pumps a dye ring laser (Coherent 822) whose output (about 1 W) is fed into an external ring resonator for frequency doubling. The UV-output of the ring resonator was a few milliwatts. It is transferred via a light fiber to the sample. Measured is the OD against air. In the present experiments, the fundamental was generated in the Rhodamine 6G-range covering a UV-range from 34 600–35 300 cm⁻¹. All the optical components in the external resonator are computer-controlled so that a continuous tuning through the accessible UV-range was possible. The respective resolution was of the order of a few tens of MHz.

Typical hole burning times were of the order of minutes. The power for reading the holes was reduced by four orders of magnitudes.

The sample was immersed in a He-cryostat and kept at a temperature of about 2 K. Pressure was transmitted via He-gas and was detected with a piezo crystal. It could be varied continously up to a maximum level of 10 MPa. In the present experiment, however, a level of 1.5 MPa was sufficient. Note that at temperatures around 2 K, liquid helium solidifies around 2.4 MPa. The accuracy of the pressure level was about 0.02 MPa. Holes were burnt over a broad range of the inhomogeneous absorption. The depth of the holes varied between approximately 0.5–5% of the OD. Accordingly, the signal to noise ratio varied tremendously.

The so-called quasi-homogeneous linewidth was obtained from an extrapolation of the hole width to zero burning fluence and by dividing the respective value by a factor of 2 (for reviews on hole burning see refs. 21, 27–30).

Sample preparation and CD-spectroscopy

Insulin and L-tyrosine were purchased from Sigma-Aldrich (Product No. 57590, 93830, respectively). For the low-temperature experiments the samples were dissolved in a 0.1 M Tris/HCl solution, which was subsequently mixed with glycerol in a volume ratio 2 : 3. The final concentration of insulin was about 1 mM, that of tyrosine around 3 mM. To avoid aggregate formation in insulin the pH was adjusted to a value of 2, as recommended by the product information sheet. The pH value of the tyrosine samples was 1.6.

The protein concentration in the room-temperature CD-spectra was 20 μM.

A high molar (>8 M) stock solution with urea was prepared for unfolding experiments. Measurements were carried out at various urea concentrations.³¹

Circular dichroism spectra were measured with a J-810 spectral polarimeter. The path length of the quartz cuvette used was 2 mm. Temperature was kept at 20 °C.

Data evaluation

The evaluation of the pressure-tuning experiments were done in the following way: The low-temperature hole spectra were fitted to a Voigtian profile, and the assigned position of the hole center was plotted as a function of pressure. It always showed a perfect linear dependence on pressure (see Fig. 4, below). Subsequently, the spectral shift per pressure s_p/Δp was plotted as a function of burn frequency to determine ν_vac and κ.

For the determination of the quasi-homogeneous linewidth, the behaviour of the holewidths was measured as a function of hole area. The quasi-homogeneous linewidth was obtained from the value of the holewidth extrapolated to zero area (i.e. to zero fluence) by dividing it by 2.

Molecular dynamics

The MD simulation was performed using the CHARMM program package (version c28b1,³²). Atomic interactions were modeled using the all-atom force field CHARMM22 (for the protein see ref. 33, for glycerol see ref. 34) and the TIP3P water model.³⁵ Monomeric insulin (PDB ID 9INS) was studied in a cubic glycerol–water box (3 : 2 v/v) of a side length of 56 Å containing 788 glycerol and 2232 water molecules. The system was studied at neutral pH. The simulation was done at constant temperature and pressure (p = 0.1 MPa, T = 298 K). After a 1.5 ns equilibration, the subsequent production run of 1 ns in the NpT-ensemble was used for analysis, structures were saved every 200 fs. Further details of the simulation and the analysis are the same as used in our recent study of cytochrome c.³⁶

The MD generated configurations were used to calculate the Voronoi volumes³⁷ for all heavy atoms in the system. The volume of any part of the system was obtained by adding the contributions from the constituent atoms. The simulation system was divided into three parts: the protein, the solvation layer sharing at least one Voronoi face with the protein, and the solvent outside the first solvent shell and the protein (bulk). In order to investigate local properties around the tyrosine sites, we investigated fluctuations of the volume of the tyrosine residue and all atoms sharing at least one Voronoi face with the tyrosine. For comparison, we investigated also the region containing the first and second solvation layer around each tyrosine. The Voronoi polyhedra of atoms in the second layer have at least one common face with the first layer atoms.

The isothermal compressibility κ_i of any sub-part i of the protein–solvent system was obtained by averages of the statistical NpT ensemble:³

The symbol δ stands for the deviation from the mean, e.g. δV_i = V_i − 〈V_i〉, k_B is the Boltzmann constant and T is the absolute temperature. V is the volume of the whole simulation system. The symbol 〈…〉 stands for the average over the statistical ensemble.

The solvent radial distribution function g(r) around the protein (perpendicular to the protein surface) was obtained by determining for each solvent molecule the closest distance r of the hydrogen atoms of the OH-groups from the protein atoms (including hydrogens).

3. Results

In Fig. 2, we compare the broad band absorption spectra at 4.2 K of tyrosine, insulin in its folded state and in its chemically unfolded state (see the CD-spectra in Fig. 6, later). The three samples were all prepared from stock solutions of the respective solute in glycerol–water (3 : 2, v/v). In all spectra the long-wavelength peak is scaled to the same height. The spectra look rather similar with their two peak structure. The insulin spectrum is red-shifted by 250 cm⁻¹. The difference between folded insulin and urea-unfolded insulin is marginal. The range where hole burning was performed in the various samples, is indicated.

Fig. 2 Broad band absorption spectra of tyrosine, folded insulin and urea-unfolded insulin in glycerol–water at 4.2 K. The range where hole burning experiments were performed is marked by the bar.

Fig. 3 shows the zero-fluence extrapolated hole widths (the so-called quasi-homogeneous hole widths) across the inhomogeneous absorption for both, the folded and the urea-denatured protein. For comparison, we also present data for tyrosine in solution. The data sets show only moderate color effects, if at all: In the denatured protein there is a narrowing tendency towards the red edge. In the native protein as well as for tyrosine in solution there is no significant dependence on wavenumber. Their absolute values are rather close as well and are, on average, by roughly a factor of 0.6 smaller as compared to unfolded insuline. From the absence of a significant color effect in insulin we conclude that T₁-processes like wavenumber-dependent fluorescence lifetimes due to complex formation with water molecules,³⁸ or fast energy transfer between the various tyrosines, do not seem to play an important role. The time associated with the measured quasi-homogeneous linewidth of insulin is around 0.23 ns and is most probably determined by dephasing and/or spectral diffusion processes.

Fig. 3 Zero-fluence extrapolated hole width of folded (open squares) and urea-unfolded (black circles) insulin. For comparison data on tyrosine in solution are shown as well. Note that the quasi-homogeneous linewidth is obtained by dividing the respective hole width γ_H by a factor of 2. Solvent: Glycerol–water at 2 K.

In Fig. 4 we present pressure-tuning experiments of spectral holes for two selected frequencies. The data are for folded insulin.

Fig. 4 Behavior of hole profiles under pressure variation at two different wavenumbers. The shift s_p of the central wavenumber is perfectly linear with pressure. Sample: folded insulin in glycerol–water at 2 K.

Figs. 5 and 6 summarize the pressure shift data: Plotted is the shift per pressure s_p/Δp over the wavenumber for three different samples, namely insulin in its folded state (Fig. 5), free tyrosine in solution and urea-unfolded insulin (Fig. 6). According to eqn. (1), a straight line is expected. Within reasonable accuracy, this is the case for tyrosine in solution and for urea-denatured insulin (correlation factors of 0.99). However, for folded insulin it is not the case: The data set definitely bends over to a markedly steeper slope in the red edge of the band. Despite the scattering of the data points due to the fact that some of the holes are rather shallow, the two ranges (34 600–34 850 and 34 900–35 300 cm⁻¹) can be fitted to straight lines reasonably well (correlation factors of 0.84 and 0.92). The respective slopes yield two drastically different compressibilities, namely 0.08 and 0.13 GPa⁻¹. The two straight lines cut the zero pressure shift abscissa at 35 156 and 35 408 cm⁻¹. According to eqn. (1), these wavenumbers correspond to two different vacuum absorption frequencies ν_vac1 and ν_vac2, respectively. We assign these two different ranges to two different tyrosine species which most likely differ in their complexation-state with solvent molecules. The data point at 35 273 cm⁻¹ is very close to ν_vac2. The respective hole spectra, as it responds to pressure variations, is shown in the insert. It is evident that a pressure shift is nearly absent, in agreement with theory. However, broadening is there and it is comparable to all the other holes in the whole data set (see Fig. 4). Fig. 6 is similar to Fig. 5, but the data refer to urea-unfolded insulin and to unbound tyrosine in glycerol–water. There are two interesting observations: First, the whole data series of the unfolded insulin follows quite nicely a straight line rather similar to the respective behavior of sole tyrosine in solution. It is not anymore possible to distinguish different probe sites. The various photochemically labeled tyrosines obviously behave very much the same way under pressure variations. Second, the compressibility is reduced as compared to the folded state. This reduction is dramatic with respect to the highly compressible component and comprises almost a factor of 2. It is within 25% of the respective value of free tyrosine in solution.

Fig. 5 The shift of holes per pressure s_p/Δp, as a function of burn wavenumber. The straight lines are linear fits to the data in the blue and red range of the spectrum. These lines extrapolate to the so called vacuum absorption wavenumbers, ν_vac1 and ν_vac2, respectively. At these frequencies, the pressure shift vanishes. The profile of one of the blue most holes (insert) shows that this is indeed the case. From the slopes of the straight lines the two compressibilities κ₁ and κ₂ could be determined. Note, that for the calculation of κ₁ and κ₂ we did not take into account data points in the overlap region (unfilled circles).

Fig. 6 This figure is similar to Fig. 5. (a) Data for the urea-unfolded insulin. The straight line yields a compressibility of 0.076 GPa⁻¹. The insert shows the CD-spectra without, with 4 M and with 8 M urea. Θ is given in millidegrees [mdeg]. The loss of secondary structure is obvious from the decreasing far-UV signal (around 45 000 cm⁻¹). See also ref. 31.

The tyrosines in insulin have different microenvironments and their exposition to the water/glycerol solvent varies significantly. Just to get an impression how the various tyrosine probes respond to the different microenvironments and to what extent this variation may influence the local elastic properties, we performed molecular dynamics simulation of monomeric insulin. We calculated the respective radial distribution functions for water and glycerol for the four tyrosine sites as well as for the whole protein, the coordination numbers, residence times and volume fluctuations. From the volume fluctuations, we determined the various local compressibilities. The respective numbers for the solvent, the whole protein, the first shell and the first two shells of the four tyrosines are listed in Table 1. As characteristic examples we show in Figs. 7–10 the radial distribution functions of solvent and cosolvent molecules around the protein as well as around the hydroxyl groups of Y14A, Y19A and Y26B. Note that these functions are normalized in a way that their respective value for the bulk is unity.

Fig. 7 Radial distribution function around the insulin molecule (monomer) for water (a) and glycerol (b). Solvent: glycerol–water 3 : 2 (v/v).

Fig. 8 Radial distribution function around Y14A for water (a) and glycerol (b). Solvent: glycerol–water 3 : 2 (v/v).

Fig. 9 Radial distribution function around Y19A for water (a) and glycerol (b). Solvent: glycerol–water 3 : 2 (v/v).

Fig. 10 Radial distribution function around Y26B for water (a) and glycerol (b). Solvent: glycerol–water 3 : 2 (v/v).

Table 1 Local compressibilities from MD simulations of monomeric insulin in a 3 : 2(v/v) glycerol–water solvent

Local sites	κ[GPa^−1]		Mean error [GPa^−1]
a Only the first solvent shell taken into account. b First two solvent shells taken into account.
Solvent shell	0.321^a	0.411^b	0.012^a	0.017^b
Y14A	0.278^a	0.364^b	0.026^a	0.013^b
Y19A	0.183^a	0.296^b	0.047^a	0.015^b
Y16B	−0.014^a	0.030^b	0.049^a	0.034^b
Y26B	0.187^a	0.193^b	0.006^a	0.007^b
Protein	0.181		0.005
Bulk	0.381		0.002

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4. Discussion

Simulations: General features

We stress that the numbers obtained for the compressibilities are reasonable wherever they can be compared with experiments or theoretical studies. Some of the (local) compressibilities which are relevant to the present discussion, are shown in Table 1. The experimental value for the compressibility of water at ambient conditions is 0.45 GPa⁻¹.³⁹ For the glycerol–water mixture the simulations yield a value of about 0.38 GPa⁻¹. Looking at the compressibilities of just the first and the first two shells around the protein, we observe significant variations. We interpret this as an indication that water hydrogen bonding exerts a strong influence on the compressibilities: In the first shell, the partial compressibility of the water molecules is high, obviously due to the fact that water–hydrogen bonding is only one-sided. In the second shell, just the opposite occurs. This shell is significantly less compressible due to a stiffer hydrogen network which is now two-sided. The partial compressibility of the glycerol molecules in the two shells varies also quite significantly, although in a different way as compared to water. We also stress that the value obtained for the whole protein (0.18 GPa⁻¹) is in a reasonable range (see ref. 4).

Interestingly, the local compressibilities around the four tyrosines are subject to strong variations. Considering just the compressibility of the first shell, the strongest variation occurs between Y14A, the most exposed residue, and Y19A and Y26B, residues which are strongly shielded from the solvent. The respective ratios of the compressibilities comprise a factor of about 1.5. The compressibility of Y16B is subject to very large errors due to the high volume fluctuations of this residue. Again we find that the packing density of environmental molecules in the first shell can be significantly different from the second shell resulting in significant variations of the associated compressibilities. This is especially pronounced in the case of Y19A.

The composition of the molecular environment around a certain center in terms of solvent and cosolvent molecules is reflected in the various radial distribution functions. The radial distribution function around the protein molecule is interesting because it shows a preferential binding of glycerol to the protein: The glycerol number density in the first layer is twice as high as in the bulk, whereas the density of the water molecules in the first layer is only by a factor of 1.5 higher than the respective bulk density. This finding is worthwhile to be noted because it is well known that glycerol as a cosolvent has a significant influence on volume and compressibility of a protein:⁴⁰ It reduces both, volume as well as compressibility, most probably by exerting osmotic stress on the protein through sucking internal water molecules from the protein thereby reducing the inter-atomic distances.⁴¹

The radial distribution functions around the OH-group of the tyrosines demonstrate a significantly different structuring of the solvent and cosolvent molecules in the neighborhood of this group. This structuring, for instance, the formation of hydrogen-bonded complexes with one or several water molecules⁴² or the formation of an ordered hydrogen-bonded network around the aromatic part of tyrosine through hydrophobic interaction, may have a significant influence on optical properties of the probe (absorption energies, etc.) as well as on the local elastic properties of the molecular environment. All tyrosines have a preferential interaction with water molecules in their first shell: In Y14A, the respective density is twice as high as in the bulk, in Y26B it is even three times as high. For Y19A the water density is even higher and prevails also in the second shell. Note that Y26B and Y19A are strongly shielded from the solvent through the protein scaffold. The glycerol density prevails in the second shell (except for Y19A). For Y14A, the glycerol density at 5 Å is four times as high as the respective water density and twice has high as the glycerol bulk density. For Y26B, the glycerol density at 5 Å is twice the water density, but is only marginally higher than in the bulk.

In summary, the calculations for the insulin monomer clearly demonstrate that there are tyrosine sites which can, in principle, be distinguished by high resolution spectroscopic techniques via their elastic properties and the molecular constitution of their environments. We assume that site structures with similar properties do also exist in dimeric insulin.

Spectroscopic experiments

Our goal with this pressure-tuning experiment was to test the pressure response of the insulin protein by using its tyrosines as local sensors. Our expectation was that the local environments are sufficiently different so that characteristic responses could be detected which would eventually reflect the local elastic properties. In other words we wanted to know whether spatial variations in the compressibility of the protein could be measured. This goal was triggered by recent theoretical work by Marchi³ who developed an algorithm for calculating local compressibilities. Recently we applied this algorithm to a modified cytochrome c and we could show how the compressibility of the protein pocket is fed by volume fluctuations of the hydration shell and how these fluctuations are reduced by using glycerol as a cosolvent.³⁶ Measuring spatial variations in the compressibility is only possible with optical techniques by exploiting the short range interactions of molecular probes, and, as a rule, UV-hole burning is needed. Otherwise it would be largely impossible to address spectroscopically different, yet spatially well defined sites in the protein.

As our data (Fig. 5) show, the pressure-tuning hole burning experiments indeed reflect significant variations in local compressibilities. Despite the scattering of the data points, the whole series clearly shows two ranges with largely different slopes which can be associated with different compressibilities of the local environments around two tyrosine probes. The fact that we can identify two ranges only, despite the fact that the protein carries several probes, may either be due to the possibility that only two of them are photoreactive, or that only two (or two groups) of them show sufficiently different changes in the elastic properties of their environment so that they can be identified within the signal to noise ratio of our experiment. We favor the first possibility, simply because the depth to which the holes can be burnt, is rather low (Fig. 4), suggesting that the absorption band stems from an appreciable amount of rather photostable molecules. It is even possible to compare our experimental data with results from ultrasound experiments: Gekko and Hasegawa⁴ determined the isothermal compressibility of insulin to about 0.13 GPa⁻¹, a result which corresponds extremely well with the higher compressibility component of our spectroscopic experiments. We stressed the narrow coincidence of low temperature and room temperature compressibility values above. Accordingly, insulin represents another example that this coincidence may have rather general roots.

The observation of two spectral ranges due to two different complexes with water is also reflected in the radial distribution function. For instance, Y19A shows a very characteristic pattern in the density distribution for water: It is the only probe residue where the first layer shows a double peak structure in the water density. The respective density is extremely high. Even in the second shell, the density is dominated by water, quite in contrast to the other tyrosines. Such a behavior strongly supports the idea of a special tyrosine–water complex.

Along these lines of reasoning, let us assume that we indeed have two different (groups of) tyrosine probes. Then, the most interesting question is whether we can reasonably safely correlate the observed spectral features with specific tyrosine molecules.

To come to a reasonable conclusion, the behavior of the urea-unfolded sample (Fig. 6) may be of help. These data deviate in two respects from the respective one of folded insulin: First, the slope of the data is rather uniform pointing to a uniform behavior of the tyrosine probes involved. Second, the slope is significantly smaller than in the folded insulin, especially as compared to the data in the red range, and it is within 25% of the respective value of tyrosine in the pure solvent.

Chemically unfolding most probably leads to a random coil structure which is an open structure so that we can expect that the tyrosines become exposed to the solvent. In this case it is straightforward to expect that the tyrosines lose their site specific features and become more alike, in agreement with the experiment. Although the solvent is heavily doped with urea, solvent molecules are still abundant. Hence, the fact that the slope of the data series in Fig. 6 approaches the value of unbound tyrosine in glycerol–water is in the expected trend.

Along these lines of reasoning one would conclude that the low compressibility component in the native insulin stems from tyrosine probes which are strongly exposed to the solvent because the respective κ value comes closer to the value of the free probe in the solvent. On the other hand, the high compressibility component is likely to stem from tyrosines which are less exposed. In the simulations of the monomer, the most exposed tyrosine is Y14A. This is true even for the insulin dimer (Fig. 1) so that we believe that this residue is the most likely candidate for the low compressibility component. As to the high compressibility component, the situation is unclear. In the monomer, the least exposed tyrosine is Y19A. It is also the only one which does not directly contact glycerol, hence it is a good candidate for complex formation with several water molecules. In addition, its local compressibility at room temperature is significantly different from Y14A. However, in the dimer the situation may be different because Y19A appears to be somewhat more solvent accessible, while other tyrosines like Y16B and Y26B of one of the insulin molecules become almost completly buried within the dimer contact interface (see Fig. 1b). So, at present, an assignment of the high compressibility component to a certain site in the dimer is open, but the general argument, namely that it is associated with a more strongly shielded residue, is still valid, because such residues do exist in the dimer as well.

5. Summary

We performed pressure-tuning hole burning experiments with insulin in its folded state, with urea-unfolded insulin and with tyrosine in a glycerol water solvent. In addition we measured the zero-fluence extrapolated hole widths across a large range of the long-wavelength inhomogeneous band. The experiments show two categories of local sites, namely a low compressibility site which we associated with the strongly solvent exposed tyrosines and a high compressibility site which we associated with tyrosine sites shielded from the solvent. The specific site structure gets lost if insulin becomes chemically unfolded. The compressibility in the unfolded state comes close to the respective value of the free residue in the solvent. The experiments were backed up through MD simulations on the insulin monomer. We calculated a series of radial distribution functions in order to get an impression of the molecular compositions of the various sites as well as of the protein solvent shell. From the volume fluctuations as obtained from an MD trajectory, we determined the local compressibilities of the first and the first two shells of molecules around the residues.

Acknowledgements

We acknowledge support from the DFG (SFB533, B5, C2 and FOR358/2, A1) and from the Fonds der Chemischen Industrie.

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