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Relative Contributions of Core Protein and Solvatation Shell in the Terahertz Dielectric Properties of Protein Solutions Marianne Grognot, and Guilhem Gallot J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b06442 • Publication Date (Web): 22 Sep 2017 Downloaded from http://pubs.acs.org on September 25, 2017

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The Journal of Physical Chemistry

Relative Contributions of Core Protein and Solvatation Shell in the Terahertz Dielectric Properties of Protein Solutions Marianne Grognot and Guilhem Gallot∗ LOB, Ecole polytechnique, CNRS, INSERM, Université Paris-Saclay, 91128 Palaiseau cedex, France E-mail: [email protected]

Abstract The properties of the solvation shell surrounding biomolecules in solution are fundamental to understand the modifications of the dynamics of the water molecules by peptides and proteins. The dynamics of the hydrogen bonding network typically occurs at the picosecond time scale, then terahertz spectroscopy is a unique tool to investigate the solvation shell. Here, we present terahertz measurements of the refractive index and extinction coefficient of solutions of biomolecules of various molecular weights. We observe a clear correlation between the terahertz dielectric properties and the weight of the molecules. A three-component model is developed and analyzes the relative contributions from the solute and the solvation shell to the total dielectric values. We find that the amino acids and short peptides (small molecules) domain is mainly governed by the solvation shell, while the solute properties are also implied in the protein domain (big molecules).

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Introduction Water plays a major role in the structure and function of biomolecules. 1,2 In particular, the water molecules at the interface between protein and bulk water around the proteins – the protein hydration shell – is fundamental in protein folding and function. Over the past decades, much effort have been made to thoroughly study the dielectric properties of proteins and hydration shell in solution. The proteins in solution alters the dynamics of water molecules in the hydration shell, providing a more structured hydrogen bonding network, changing the coordination number of interfacial water molecules and increasing the relaxation times. Much experimental and theoretical works have been performed to study the perturbation of the water molecules at the proximity of ions, peptides and proteins: numerical simulations 3–10 and experiments such as NMR, 11,12 FTIR, 13 2D infrared spectroscopy, 14 femtosecond polarization resolved pump-probe spectroscopy, 15 femtosecond fluorescence up-conversion, 16 surface sum frequency generation, 17 extended depolarization light scattering. 18 Terahertz spectroscopy has also recently been demonstrated as a powerful tool in biology 19 to probe the water-protein interaction, 6,7,20–31 in dehydrated samples 25,30,31 and most importantly in liquid samples of DNA 28 or proteins. 19–24,32 Terahertz Time Domain Spectroscopy 33 (THz-TDS) has been widely used to record the molar absorption of the solvated ions and proteins. 19,22–24,26–29 However, our understanding is still incomplete and many questions remain about the delicate interplay between water and proteins. The terahertz spectroscopic properties of the solute differs from the size of the molecule. For instance, proteins in solution induce a decrease of absorption 24,34 compared to neat water, whereas ions induce an opposite effect, 35,36 questioning the interaction between water and solutes. Here, we investigate a large number of biomolecules in solution, from big proteins to their elementary blocks, amino acids (75 Da to 250 kDa), by terahertz spectroscopy, to reveal size-dependent trends in both the absorption and refractive index of the solutions.

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Terahertz signal (a.u)

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Time (ps)

Figure 1: Example of recorded data (dots) and parabolic fits (solid lines) for solute (round, green) and reference neat water (square, blue).

Experimental Section The terahertz signal is generated by a classical Terahertz Time-Domain Spectroscopy (THzTDS) setup, 37,38 composed of a GaAs photoconductive transmitter lit by a femtosecond laser that generates a sub-single cycle THz pulse, with frequencies centered around 0.5 THz and extending from 0.2 to 2 THz. The pulse is detected by a low temperature grown GaAs photoconductive detector. A delay line between the emitter and detector terahertz chips allows to measure the amplitude A(t) of the terahertz electric field in the time domain, at controlled delays t. An Attenuated Total Reflection (ATR) prism is added to the THz-TDS setup, and makes use of the interaction of the evanescent wave at the back of the prism with the solutions under study. 39 The THz-ATR device is a very transparent high-resistivity silicon isosceles prism (n ≈ 3.42) with a base angle of 42◦ . The impinging beam is polarized in the plane of incidence (p-polarization), and is altered by both absorption and refractive index of the liquid topping the prism. ATR measurements are independent on the thickness of the sample, and then well adapted to strongly absorbing materials (see Supporting Information for experimental details). The dielectric properties of the solutions are given by the complex dielectric constant



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ˆ = (n − iκ)2 , where n is the refractive index and κ the extinction coefficient. Within our experimental terahertz frequency range, the spectrum of the solutions can be assumed to be homothetic to the reference spectrum of neat water, with a very good approximation for peptide 40 and protein 22,24,41 solutions. Therefore, in the linear regime of concentrations, the variations of n and κ for the solutions are given by     ∆n = nsol − nw = δn C nw

(1)

   ∆κ = κsol − κw = δκ C κw where nsol and nw are the refractive indices for the solution and neat water, respectively, C is the concentration and δn is the mass relative refractive index. Equivalent notations apply to the extinction coefficient κ. Therefore, ∆n and ∆κ are the averaged variations of n and κ from solution to neat water over the 0.2-1.6 THz range. The dielectric parameters ∆n and ∆κ are finally obtained from ∆A and ∆t by calibration with known ionic solutions 24,40 (see Supporting Information for further details). The solutions are deposited on the THz-ATR prism in a 1.9 cm2 -area delimiting cell with a volume of about 500 µl. A measurement consists of recording the maximum amplitude of A(t) and its corresponding time delay t (Figure 1). In order to improve the precision of our data, several acquisitions are performed around the maximum, then a parabolic fit provides the amplitude and time delay. The variations of amplitude ∆A and delay ∆t for solute, compared to the reference ones for ultra pure water (Milli-Q, Millipore) are defined as ∆A = (Asol − Aw )/Aw and ∆t = tsol − tw . A minimum of 30 acquisitions are averaged for improved precision. A wide range of molecule size was investigated, from the smallest amino acid (glycine, 75 Da) to big proteins such as catalase (250 kDa). Several criteria were considered: a good solubility to explore a large range of concentrations ; the highest grade of powders and saltfree (Sigma-Aldrich, Taufkirchen, Germany). All experiments were performed at 21±0.3◦ C


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Table 1: Name and molecular weight of the biomolecules analyzed by THz-ATR measurements. Molecule Glycine Serine Lysine Tricine Gluthatione LSKL-NH2 peptide Lysozyme Myoglobin Ovalbumin Hemoglobin Albumin Catalase

Molecular weight (kDa) 0.075 0.105 0.146 0.179 0.307 0.458 14.3 17.1 44.3 64.5 66 ≈ 250

temperature. The molecules were weighted, dissolved in ultra pure water by slow agitation. They were filtered with 0.2-µm pore filters and their final concentration was controlled by UV spectrophotometry (NanodropTM 2000c) when reference molar extinction data were available. This guarantees clear solutions at high concentrations. The molecules investigated here are found in Table 1 with their molecular weight.

Results and Discussion The experimental terahertz dielectric parameters ∆n/nw and ∆κ/κw were measured versus concentration C, for the 12 molecules listed in Table 1. Figure 2 shows the results for 6 representative molecules. Other molecules can be found in Supporting Information. In the concentration range considered here, we observe a linear evolution of ∆n/nw and ∆κ/κw with respect to C, in agreement with the assumption of the linear regime in Eq. 1. At higher concentrations we would encounter nonlinear dependence on concentration. 13,40 It has also been reported nonlinear effects in dilute systems 7 but we do not observe this behavior with our molecules. For the relative extinction coefficient ∆κ/κw (Fig. 2b), we observe that the



1,04 1,03 Glycine Serine Glutathione Peptide Albumin Catalase

n/nw

1,02 1,01 1,00 0,99

(a)

0,98 0

50

100

150

200

250

300

Concentration C (g/l) 1,00

Glycine Serine Glutathione Peptide Albumin Catalase

0,98 0,96

w

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0,94 0,92 0,90 0,88

(b)

0,86 0

50

100

150

200

250

300

Concentration C (g/l)

Figure 2: Variations of ∆n/nw (a) and ∆κ/κw (b) versus solute concentration C for 6 representative biomolecules. The dotted lines are linear fits. overall modification by adding the biomolecules to pure water is a decrease of extinction, in agreement with previous results. 23,24 Furthermore, κ strongly depends on the size of the molecules, larger variations being obtained for the bigger molecules. As for the refractive index (Fig. 2a), values of ∆n/nw are larger than 1 for small molecules (Glycine or Serine for instance), corresponding to an increase of n compared to pure water. However, the behavior is opposite for the bigger molecules, with an observed relative decrease of n. Therefore, both n and κ are strongly affected by the size of the dissolved molecules. To further analyze this observation, the mass relative dielectric parameters δn and δκ (Eq. 1) are extracted versus the molecular weight M of the molecules, and can be found in Fig. 3. Overall, the trend of


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(a)

3x10-4

n

2x10-4

1x10-4

0

-1x10-4 0,1

1

10

100

1000

Molecular Weight M (kDa)

(b)

0

-2x10-4



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-4x10-4

-6x10-4

-8x10-4 0,1

1

10

100

1000

Molecular Weight M (kDa)

Figure 3: Variations of δn (a) and δκ (b) versus molecular weight M . Dots are experimental data. The solid lines are obtained from the three-component model with es = 1 nm, and the dotted lines with es = 0.8 and 1.2 nm for the same remaining parameters. δn appears to decrease monotonously with respect to M , within experimental uncertainties (solid circles, Fig. 3a). δn is positive for small molecules but negative for the larger ones, including all the proteins. The inversion of sign is located around M = 300 Da. For the proteins (above 14 kDa here), δn reaches a plateau around the value δn0 = −10−4 L/g. A similar evolution is found for δκ , which also decreases monotonously with respect to M (solid circles, Fig. 3b). All the values of δκ are negative, with a plateau for the proteins around δκ0 = −7 × 10−4 L/g. We developed a dielectric model of the solvated molecules to explain the evolution of the terahertz dielectric properties with respect to the molecular weight of the molecules. We



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bulk water , , , , solute 2R solvation shell , ,

Figure 4: Three-component terahertz dielectric model for biological molecules in solution. The round solute is surrounded by a solvatation shell bathing in pure bulk water. consider a three-component model (Fig. 4): the solute, a solvation shell around the solute, and bulk water. Assuming a total solution volume V , as well as the volumes Vp , Vs , and Vw for the solute, solvation shell, and bulk water components, respectively, the effective dielectric values are given by 7

xeff =

Vp Vs Vw xp + xs + xw V V V

(2)

where x stands for either n or κ, and xp , xs , and xw refer to the solute, solvation shell, and bulk water components, respectively. The solvated molecule is described as a sphere of radius R which is a good approximation for the highly soluble molecules used in this study. 42 The density of the molecules ρ is found to be almost constant from amino acids to big proteins; 43 a value ρ = 1.37 × 103 g/L was taken in the following. The last parameter is the solvation shell thickness es , which in the literature is considered to remain in a limited range, usually between 0.8 and 1.2 nm. 7,44 From these data, we express the volumes of the molecule as well as of the solvation shell, and obtain after straightforward calculation 1 ∆x 1 = δx = C xw ρ

xp xs 2/3 2 1/3 3 NA − 1 + A1 es M + A2 es M + A3 es −1 xw M xw


(3)

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where NA is Avogadro’s number, A1 = 4π

3 4πρNA

2/3

, A2 = 4π

3 4πρNA

1/3 , and A3 =

4π . First, the right side of Eq. 3 do not depend on C, which is consistent with the linear 3 hypothesis considered in Eq. 1. Second, the left part of the right side is related to the contribution of the solute itself to n and κ. This term do not depend on M , but only on ρ and on the dielectric properties of the solute. It is therefore constant. On the contrary, the right part is related to the solvation shell, and depends on a series of powers of M as well as on the dielectric constants of the solvation shell. The results from this model are superimposed to the experimental data in Fig 3. The solid lines are obtained with es = 1 nm and the dotted lines with es = 0.8 nm and es = 1.2 nm. The remaining parameters (np,s − nw )/nw and (κp,s − κw )/κw for the solute and solvation shell are found in Table 2 and are obtained from the best fit of the data. Uncertainties take into account both the experimental data precision and the uncertainty on the es on a 20% variation. We observe a very good agreement between experimental data and the three-component model. Both δn and δκ exhibit a rapid decrease with M in the small molecular weight domain below 2 kDa, followed by a plateau in the protein domain above 2 kDa. The model values obtained for the extreme values of es (dotted lines) still remain in the limit of the uncertainty of the measurements. Analyzing more closely the signs of the terahertz dielectric parameters in Table 2, we first notice that xs > xw > xp for both x = n and x = κ. Considering a constant concentration C, which corresponds to the case of Fig. 3, an increase of M leads to the replacement of a large number of small molecules by a smaller number of bigger molecules, since ρ is constant. Therefore, both cases have the same solute volume Vp , and then the same weight, but the solvation volume Vs is smaller for large M . Since Vp remains constant, the decrease of Vs for large M is compensated by an increase of the bulk water volume Vw . To summarize, when M increases, the relative contribution of xp remains constant, the one of xs decreases and the one of xw increases. Since xs > xw , the effective values for both neff and κeff decreases when M increases. neff and κeff are larger for small molecules due to the major contribution of the solvation shell. For the bigger molecules, the contribution of the solvation shell becomes 9 ACS Paragon Plus Environment


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Table 2: Terahertz dielectric constants for molecules and solvatation shell. Solute (p) Solvation shell (s)

(n − nw )/nw -0.14 ± 0.02 0.004 ± 0.001

(κ − κw )/κw -0.99 ± 0.05 0.007 ± 0.002

negligible compared to the contribution of the solute, leading to a plateau. Since xp < xw , this plateau has a negative value for both neff and κeff , in agreement with experimental data. For absorption, it reads from Table 2 that κp nw and κs > κw . On the contrary, the solute dielectric properties (np and κp ) are mostly responsible for the the solution properties and the observed plateau for the proteins above 2 kDa, with np < nw and κp < κw . The relative variations from the solute are much larger than the ones from the solvation shell, with an estimated factor of 35 for the refractive index, and 140 for the extinction coefficient. This brings new insights on the underlying relative contributions of the solute and solvation shell in solution.

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TOC Graphic

Bulk water

Solute

Solvation shell


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Relative Contributions of Core Protein and ... - ACS Publications

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