Effect of Intrinsic Disorder and Self-Association on the Translational

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The Effect of Intrinsic Disorder and Self-association on the Translational Diffusion of Proteins: the Case of #-Casein. Daria L. Melnikova, Vladimir Dmitrievich Skirda, and Irina V Nesmelova J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b00772 • Publication Date (Web): 27 Mar 2017 Downloaded from http://pubs.acs.org on March 30, 2017

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The Journal of Physical Chemistry

The Effect of Intrinsic Disorder and Self-association on the Translational Diffusion of Proteins: the Case of α-Casein. Daria L. Melnikova†, Vladimir D. Skirda†, Irina V. Nesmelova‡§* †

Department of Physics, Kazan Federal University, Kazan 420011, Russia; ‡Department of

Physics and Optical Sciences, and §Center for Biomedical Engineering and Science, University of North Carolina, Charlotte, NC 28223, USA.

AUTHOR INFORMATION Corresponding Author *To whom correspondence should be addressed: Irina V. Nesmelova, Grigg Hall 306, Department of Physics and Optical Sciences, University of North Carolina, 9201 University City Blvd.,

Charlotte,

NC

28223.

Tele:

704-687-8145;

Fax:

704-687-8197;

Email:

[email protected]

ACS Paragon Plus Environment

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ABSTRACT. Translational diffusion is the major mode of macromolecular transport in leaving organisms and therefore it is vital to many biological and biotechnological processes. Although translational diffusion of proteins has received considerable theoretical and experimental scrutiny, much of that attention has been directed towards the description of globular proteins. The translational diffusion of intrinsically disordered proteins (IDPs), however, is much less studied. Here, we use a pulsed-gradient nuclear magnetic resonance technique (PFG NMR) to investigate the translational diffusion of a disordered protein in a wide range of concentrations using α-casein that belongs to the class of natively disordered proteins as an example.

ABBREVIATIONS: Nuclear Magnetic Resonance (NMR), pulsed-filed gradient (PFG), intrinsically disordered protein (IDP), circular dichroism (CD), Fourier transform infrared (FTIR), stimulated-echo pulse sequence (PGSTE), root-mean square (RMS).


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INTRODUCTION The wealth of protein structural data available in the Protein Data Bank shaped the view of a functional protein as a compact globule with specific, rigid, and well-defined structure1. However, in recent years it became increasingly recognized that the occurrence of unstructured regions of significant size (more than 50 residues) is also common in functional proteins2-3. These disordered regions are characterized by great structural flexibility and plasticity invoking the analogy to flexible synthetic polymers. However, due to the heterogeneous composition of charged, polar, and nonpolar amino acids, proteins are never random coils and always have some residual structure4-5. The degree of compactness of the polypeptide chain depends on the amino acid residue composition of a given protein and on environmental conditions, including the concentration of the protein itself and/or the crowders. Hence, there is a great interest to understand how the intrinsically disordered proteins (IDPs) behave in the wide range of concentrations, from dilute to highly concentrated solutions. In particular, understanding the translational diffusion of IDPs, which is the major mode of macromolecular transport in biological or chemical systems (e.g., the self-diffusion, hereafter denoted simply as diffusion), becomes important. However, thus far only a few diffusion coefficient measurements have been performed for IDPs or proteins unfolded by different denaturants6-11. Although the differences in the diffusion coefficients between folded and unfolded proteins have been reported, it is still not clear whether hydrodynamically the IDP can be pictured as similar to globular proteins, flexible synthetic polymers, or as species with unique features. Previously, master curves have been established for the concentration dependence of the diffusion coefficient of flexible linear polymers12 and globular proteins13. These master curves


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reveal the most common features of the translational diffusion that are independent of specific properties of an individual molecule (i.e., shape, charge, internal dynamics, etc.). In the present study, we sought to compare the concentration dependence of the diffusion coefficient of a disordered protein with the master curves for flexible polymers12 and globular proteins13. We also compare experimental data to the theoretically predicted concentration dependence of the translational diffusion of rigid Brownian particles14. In this study, we have chosen α-casein as a model system. Caseins, comprising the major fraction of proteins in mammalian milk15, were among the first proteins recognized as functional but lacking a well-defined three-dimensional structure16-19. They form a family of four proteins, αs1, αs2, β, and κ-caseins, where αs1- and αs2-caseins represent about 40% and 10% of all caseins and together are referred as α-casein. Different methods of analysis suggest that the amount of random coil conformation in α-casein varies between 40% (Raman spectroscopy)20, 17%-75% (circular dichroism (CD) spectroscopy)21-23, 70-77% (amino acid sequence analysis)16,

21

, and

100% (Fourier transform infrared (FTIR) spectroscopy)24. We use pulsed-field gradient (PFG) NMR to measure the translational diffusion of α-casein in a wide range of protein concentrations and discuss its difference and similarity to globular proteins and flexible synthetic polymers. We also discuss the shape of the diffusion attenuation of spin-echo signal and its dependence on protein concentration, diffusion time, and sample storage time. Moreover, caseins tend to selfassociate25-29. In this study, we observe that α-casein reversibly self-associates in concentrationdependent manner to form labile, three-dimensional, gel-like structures. Thus, the choice of αcasein also allowed us to access the effect of self-association on the concentration dependence of the diffusion coefficient of a disordered protein.


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EXPERIMENTAL METHODS Bovine α-casein (C6780) was purchased from Sigma-Aldrich and used without further purification. In our experiments, at small concentrations of protein, a monoexponential diffusion attenuation over more than three orders of magnitude was observed, indicating that the translational diffusion of α-casein is characterized by a single diffusion coefficient, and impurities (if present) or αs1- and αs2-caseins are indistinguishable as far as their translational diffusion coefficient is concerned. Samples were prepared at protein concentrations ranging from 0.5 to 15% (w/v %) by dissolving the lyophilized powder of α-casein in D2O in order to minimize the signal from water protons in NMR spectra. Concentration dependence of the diffusion coefficient is plotted as a function of α-casein volume fraction ϕ. The volume fraction was calculated using the following relation:

ϕ=

1

ρ 2 ⋅ ω1 1+ ρ1 ⋅ (1 − ω1 )

,

(1)

where ω1 is the weight fraction of water, and ρ1 and ρ2 are the densities of water and α-casein, respectively. To calculate the density of α-casein, we used the value of its partial specific volume 0.728 cm3/g, determined previously30. All NMR measurements were performed at 298 K on a 400 MHz Bruker Avance-III TM spectrometer equipped with gradient system that allowed a maximum gradient, g, of 28 T/m (e.g., 2800 G/cm). Self-diffusion coefficients (hereinafter referred to simply as diffusion coefficients) were measured using the stimulated-echo pulse sequence (PGSTE)31. Fourier transformed 1H NMR spectra showed well-separated signals from residual water and protein


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molecules, permitting the selective registration of protein diffusion coefficient (Figure 1A). Representative stacked plot of 1H NMR spectra for the measurement of α-casein diffusion coefficient is shown in Figure 1B. The integrated area of the peak between 0.16 and 3.61 ppm, indicated by bracket, was used to calculate the diffusion coefficient of α-casein. The experiments were carried out using 48 different values of g, the gradient pulse duration δ of 2 and 5 ms, the time between the leading edges of gradient pulses ∆ = 50 and 800 ms, the time interval between the first and the second radiofrequency pulses τ = 16 ms, and the recycle delay of 4400 ms. Dependent on protein concentration, either monoexponential or multi-exponential diffusion attenuations were observed for α-casein solutions. The monoexponential diffusion attenuation of spin echo amplitude, A( g 2 ) , was described by the following equation with a single diffusion coefficient:

(

)

A( g 2 ) = exp − γ 2δ 2 g 2t d D , A(0)

(2)

where A(0) is the spin echo amplitude at g = 0, γ is the gyromagnetic ratio for protons, and

t d = ∆ − δ 3 is the diffusion time. In this case, the diffusion coefficient was determined from the linear slope of the attenuation according to Eq. 1. The multi-exponential diffusion attenuation is described by the spectrum of diffusion coefficients (discrete or continuous, where the integral is taken over the continuous spectrum of diffusion coefficients):

(

)

A( g 2 ) = ∑ pi exp − γ 2 g 2δ 2t d Di . A(0) i

(3)

Here pi is the relaxation weighted fraction of the component with the diffusion coefficient Di. The average diffusion coefficient D is then defined according to the following equation:


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D = ∑ pi Di .

(4)

i

It was shown that the value of D can be determined with high accuracy from the initial slope of the diffusion attenuation, i.e., when g → 0 32. Accordingly, the translational diffusion of αcasein was described by the average diffusion coefficient D determined from the initial slope of the multi-exponential diffusion attenuation. The standard error of diffusion coefficients was below 1-5% (dependent on protein concentration). The net displacement of the molecules accessible by PFG NMR is given by the Einstein relation: r 2 = 6 Dt d .

(5)

Similar to diffusion coefficients, relaxation times Т1 and Т2 for α-casein protons were determined using the integrated area of the peak between 0.16 and 3.61 ppm. Spin-lattice relaxation time T1 was measured using the inversion recovery pulse sequence (180˚ – t – 90˚). The recovery time t was varied from 20 to 30000 ms. Spin-spin relaxation time Т2 was measured using the spin echo pulse sequence (90˚ – τ – 180˚), where τ varied from 2 to 600 ms. RESULTS The diffusion attenuation of spin echo signal We first investigated the shape of the diffusion attenuation of spin-echo signal from α-casein protons, taking the advantage of large pulsed-filed gradients available to us. We were able to distinguish the diffusion attenuation components characterized by diffusion coefficients as small as ~10-15 m2/s. Figure 2 shows semilogarithmic plots of spin-echo intensities recorded at


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2 different α-casein concentrations as a function of parameter k = (γ δ g) (see Eqs. 2, 3). A

monoexponential decrease of the echo signal over three orders of magnitude is observed at protein concentrations of 0.5 to 2% (Figure 2A), and hence the translational diffusion of α-casein is described by a single diffusion coefficient at these concentrations. At protein concentrations greater than 2%, the signal attenuation curves deviate from monoexponential behavior, demonstrating that α-casein solution becomes heterogeneous. The curvature is clearly enhanced at higher concentrations of protein (Figure 2B-D), indicating that the heterogeneity of α-casein solution increases as the protein concentration increases. The deviation of the diffusion attenuation from monoexponential behavior can be caused by several factors. In the simplest case, the nonexponentiality of the diffusion attenuation is associated with the polydispersity of diffusing species due to their molecular weight distribution as it is observed, for example, in solutions of synthetic polymers. Note, that this is not the case, however, with α-casein solutions, because at low (≤ 2%) concentrations of protein the diffusion decays are monoexponential, indicating a very narrow or no molecular weight distribution of αcasein molecules, which is a characteristic feature of proteins. Another potential cause of the polydispersity to consider in α-casein solutions is the crosslinking of α-casein molecules due to the formation of disulfide bonds, because α-casein contains several cysteine residues. This process is irreversible and is expected to be more pronounced at higher protein concentrations. To verify whether the crosslinking of α-casein molecules occurred in the course of our experiments, we carried out the reversibility test. Figures 3A and 3B display diffusion attenuations collected using the 2% and 5% α-casein solutions prepared freshly or by dissolving more concentrated, 10% and 15% samples of α-casein, respectively, used to acquire the


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diffusion attenuation shown in Figure 2D. The 10% and 15% samples were used after the completion of the experiments, e.g., at least after 72 hrs, including sample storage at 277 K. Diffusion attenuations shown in Figures 3A or 3B are identical, unambiguously confirming that the multi-exponential diffusion attenuation results from the reversible process. Consequently, the most likely reason for the heterogeneity in α-casein solutions is the reversible selfassociation of α-casein molecules leading to the formation of supramolecular structures of different sizes. This is further confirmed by the dependence of the degree of diffusion attenuation curvature on time after sample preparation. Figures 4A and 4B show diffusion attenuations for α-casein solutions at protein concentrations of 2% and 10%, respectively, collected over the course of 72 hrs after sample preparation. No changes are observed in the signal attenuations at the concentration of α-casein 2%. However, in 10% solution of α-casein, the curvature of the diffusion attenuation gradually increases with time, and a new component appears in the diffusion attenuation after 2 hrs. The diffusion coefficient of this component, Dmin, is considerably small, 1.4 ± 0.1 × 10-15 m2/s at 298 K. The weight of this component increases with time from about 6-9% at 2 hrs to about 30% at 72 hrs after sample preparation, suggesting a slow kinetics of reversible self-association in the solution of α-casein during storage. The dependence on diffusion time The multi-exponential form of the diffusion attenuation indicates that the solution of αcasein becomes heterogeneous at protein concentrations greater than 2% due to reversible molecular self-association, giving rise to a distribution of diffusion coefficients. To gain further insight into the process of self-association (self-organization) in concentrated solutions of αcasein, NMR diffusion experiments were performed over a wide range of diffusion times32-35.


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The diffusion attenuation of spin-echo signal is a function of two independent experimental variables, the strength of the pulsed-field gradient g and the diffusion time td (Eqs. 1 and 2). Accordingly, when spin-echo amplitudes A(g2) collected at different values of td are plotted using

(

)

coordinates log A( g 2 ) / A( 0 ) vs. (t d ⋅ k ) , where k = (γ ⋅ δ ⋅ g )2 , the dependence of the diffusion attenuation on td indicates that the measured diffusion coefficient is a function of td. Figure 5A shows diffusion attenuations for the 15% α-casein solution, acquired at td values of 200, 400, and 800 ms. As the diffusion time increases, the initial slope of the diffusion attenuation remains unchanged, whereas the slope of the slow-diffusing component of the diffusion attenuation decreases, and, hence, the diffusion coefficient Dmin decreases. Plotting the diffusion attenuation of spin-echo signal as a function of k allows evaluating the dependence of the diffusion coefficient on diffusion time. Figure 5B shows the data, presented in

(

)

Figure 5A, re-plotted using coordinates log A( g 2 ) / A( 0 ) vs. (k ) . The slope of the slowestdiffusing component of the diffusion attenuation remains constant for all values of td as shown by dashed lines in Figure 5B. Accordingly, the diffusion coefficient is inverse proportional to the diffusion time and the RMS displacement of α-casein molecules remains constant, as it follows from Eq. 6A:

Dmin =

r2 6t d

∝ t d −1 .

(6)

Figure 5B shows that at the protein concentration of 15% more than 90% of α-casein molecules undergo anomalous, e.g., the fully restricted diffusion. Similar effects have been observed previously32-36, in particular in gelatin gels33-34 and in cross-linked polybutadiene networks32, 36.


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The size of restrictions, estimated using Eq. 6, is about

r 2 ≈ 50 ± 5 nm. This values

exceeds the dimensions of α-casein molecule, for which the reported values of radius are in the range of 28-32 Å37. The observation of restricted diffusion in the solution of α-casein is in agreement with the observation that several molecules of αS1-casein can interact to form wormlike polymer chains, or flexible filaments, where the hydrophobic regions of the individual chains join end to end38-40. Our results suggest that these α-casein chains can further noncovalently interact (i.e., hydrophobically, electrostatically, or via hydrogen bonds) to form a three-dimensional gel-like structure, leading to a fully restricted mobility of the individual αcasein polymer chain as a whole. The translational diffusion that is characterized by Dmin is then associated with the movement of chain segments between points of inter-chain interactions. While the slope of slow-diffusing component depends on td, the initial slope of the diffusion decay remains constant. Therefore, to analyze the diffusion data for heterogeneous α-casein solutions, two populations of molecules characterized by two different diffusion coefficients should be considered. The fraction of self-associated, slowly diffusing α-casein molecules p g is characterized by the diffusion coefficient Dmin. Another fraction of molecules is characterized by a significantly, e.g., several orders of magnitude, larger diffusion coefficient that essentially determines the initial slope of the diffusion attenuation. The diffusion coefficient of this fast diffusing α-casein species does not depend on diffusion time, indicative of their free, nonrestricted, albeit hindered due to high protein concentration, diffusion. Figure 6B shows that the fraction of self-associated molecules pg decreases with time, indicative of the exchange between the "free" and self-associated α-casein fractions. Solid line in Figure 6B represents the best fit to the equation that allows estimating the lifetime τg of molecules in the self-associated state:


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 t pg ( td ) = pg ( 0 ) ⋅ exp  − d  τ  g

  , 

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(7)

where pg(0) is the steady state fraction of self-associated α-casein species. According to this estimate, τg is about 3.5 s. In summary, the diffusion attenuation in solutions of α-casein at protein concentrations less than 2% is described by a single diffusion coefficient and is independent of storage and diffusion time, indicating that no association of α-casein molecules occurs at these protein concentrations. At protein concentrations greater than 2%, we observe several peculiar features: (1) the nonexponentiality of the diffusion attenuation that becomes more pronounced as the concentration of α-casein increases; (2) the dependence of the diffusion attenuation on storage time; (3) the dependence of the diffusion attenuation on diffusion time, indicating that the diffusion of about 90% of α-casein molecules is fully restricted, and the size of restrictions is much greater than the size of the molecule of α-casein; (4) the reversibility of the process leading to the deviation of the diffusion attenuation from monoexponential behavior. Taken together, these observations can be explained by the reversible self-association of α-casein molecules to form supramolecular three-dimensional gel-like structure. Concentration dependence of the diffusion coefficient of α-casein

Experimental data presented in Figures 2 and 4 show that diffusion attenuations become increasingly multi-exponential when the concentration of protein or sample storage time increase, and hence the diffusion attenuations can be described by Eq. 3. Thus, an average diffusion coefficient D , given by Eq. 4 and determined from the initial slope of the diffusion attenuation as exemplified by dashed lines in Figure 2, was used to quantitatively describe the


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translational diffusion of α-casein in solution. We note that

D

не зависит от времени

диффузии, так как predominantly reflects the behavior of non-associated α-casein molecules, для которых значение КСД существенно больше Dmin . Кроме того, мы установили, между свободными молекулами альфа-казеина и молекулами, образующими гель, существует молекулярный обмен. Это есть дополнительная причина независимости среднего КСД от времени диффузии. Таким образом мы имеем все основания рассмотреть зависимость среднего КСД молекул альфа-казеина от концентарции. The dependence of α-casein diffusion coefficient D on protein concentration, expressed as a volume fraction ϕ , is shown in Figure 7A (black diamonds). The logarithmic scale reveals two qualitatively different diffusion regimes in solutions of α-casein. In the first regime, the diffusion coefficient does not significantly depend on protein concentration and displays the asymptotic 0 behavior (ϕ ) . This regime corresponds to dilute solutions, where the distance between protein

molecules is sufficiently large to neglect their interactions. In α-casein solutions, this regime occurs at protein concentrations less than 2%. In the second regime, the diffusion coefficient of α-casein demonstrates a very strong dependence on protein concentration, indicating that the

interactions between α-casein molecules are not negligible. When the concentration of α-casein is greater than 5%, the concentration dependence of α-casein diffusion coefficient can be −12 approximated by the straight line with the slope of (ϕ ) (dotted line).

We next compare the concentration dependence of the diffusion coefficient of α-casein with master curves obtained for diffusion coefficients of globular proteins13 (blue experimental points) and flexible linear synthetic polymers12 (solid red line) shown in Figure 7B as a function of normalized volume fraction (top axis) as well as with the theoretical concentration


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dependence for the diffusion coefficient of rigid Brownian spheres14 (solid cyan line) shown as a function of volume fraction (bottom axis). For easier comparison, the theoretical concentration dependence for Brownian spheres is shown shifted along the log(ϕ ) axis (dashed cyan line). The key difference between concentration dependences of polymer and globular proteins or rigid Brownian spheres diffusion coefficients is in a more gradual increase during the transition from dilute to concentrated solution. In order to perform the comparison with globular proteins and synthetic polymers, we carried out the same normalizing procedure for the diffusion coefficients that was used to build master curves12-13. Initially, the diffusion coefficient of α-casein at each concentration was normalized by the value of the diffusion coefficient at infinite dilution, D0 = 1.0 × 10-10 m2/s (at 298 K), obtained by extrapolating the experimental data points to zero α-casein concentration. The value of D0 is in good agreement with the value of 7.11 × 10-11 m2/s determined previously at 293 K by analytical ultracentrifugation41. This normalization excludes the dependence of the diffusion coefficient on temperature from consideration12-13 and makes possible the comparison of diffusion data collected at different temperatures. In addition, because α-casein does not form a stable and well-folded structure16-19, the influence of internal dynamics on its diffusion coefficient could be expected. Previously, it has been shown that this contribution is not significant for the construction of master curves for the concentration dependence of diffusion coefficients of globular proteins13 and poly(ethylene glycol) homopolymers42, but becomes important in the case flexible polymers12 and poly(allylcarbosilane) dendrimers43. Based on experimental data obtained for 17 different polymer-solvent systems, it was shown that the contribution of internal dynamics to the diffusion coefficient can be excluded by dividing the polymer diffusion coefficient by the dimensionless


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normalizing function L(ϕ ) obtained from the concentration dependences of the polymer T1 and T2 relaxation times12. Therefore, we carried out T1 and T2 relaxation time measurements for all studied concentrations of α-casein. It was found that T1 and T2 relaxation times did not have significant concentration dependence (data not shown), and hence the influence of the internal dynamics of α-casein on its diffusion coefficient could be neglected and normalizing the diffusion coefficient by L(ϕ ) was not necessary. Finally, the values of volume fractions were normalized by the critical concentration ϕˆ . During the construction of master curves for globular proteins and synthetic polymers, ϕˆ was determined from the intersection of two asymptotes, with zero slope (dilute solutions) and with −3 the slope (ϕ ) (concentrated solutions). These asymptotes are indicated by dashed lines in −3 Figure 7A. Note that the asymptotic behavior (ϕ ) was theoretically predicted for the diffusion

coefficient of synthetic polymers44-47 and empirically determined for globular proteins13. Similarly, ϕˆ for α-casein solution was determined from these asymptote intersection of the 0 −3 asymptote (ϕ ) and the tangent (ϕ ) drawn to the experimental concentration dependence of

the diffusion coefficient (dashed lines) as shown in Figure 7A. It was found to be equal 0.02 ± 0.001. The concentration ϕˆ is also indicated by a cross sign in Figure 7B. Although the choice of −3 tangent (ϕ ) seems arbitrary, we note that the division of each value of the volume fraction by

the factor 0.02 ± 0.001 is merely equivalent to a shift of the whole curve along the log(ϕ ) axis as indicated by black arrows in Figure 7B. The concentration dependence of the normalized α-casein diffusion coefficients is shown by magenta diamonds (Figure 7B). The diffusion coefficient of α-casein shows the same trend as


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globular proteins up to the concentration of protein of about 2-5%. Furthermore, because the experimental data and the theoretical curve show the same trend, one can say that qualitatively α-casein behaves similar to rigid Brownian particles in the range of concentrations form 0.5 to

2%. In concentrated solutions, the concentration dependences of diffusion coefficients of −3 globular proteins and flexible linear polymers have the slope of (ϕ ) . In contrast, the −12 . concentration dependence of the diffusion coefficient of α-casein is much stronger, i.e. (ϕ )

Given that even in the highly concentrated solution of entangled polymer chains such a strong dependence is not observed, the most plausible explanation, which is also supported by the observation of multi-exponential diffusion attenuations (Figures 2, 3, and 4), is that the molecules of α-casein self-assemble into supramolecular structures. The formation of supramolecular structures results in the increase of the hydrodynamic radius of the diffusing species that leads to the arbitrary large decrease of the diffusion coefficient dependent on the number of molecules joining this structure. DISCUSSION In recent years, intrinsically disordered proteins gained significant attention as these proteins are abundant in eukaryotes and conduct basic functions48-50. A few studies highlighted the difference of the translational diffusion of disordered and globular proteins6-11. However, whether there is a common trend in the translational diffusion of different IDPs, as for example found for globular proteins13, remains to be discovered when sufficient amount of experimental data becomes available. α-Casein is a milk protein that binds large amounts of calcium while remaining largely disordered19. In this study, we investigated the translational diffusion of αcasein over a wide range of concentrations. The following three important observations should


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be emphasized: (i) in dilute solutions, similarly to globular proteins and rigid Brownian particles, the concentration dependence of the diffusion coefficient of α-casein is weak, (ii) in concentrated solutions, the dependence of α-casein diffusion coefficient on concentration is much stronger than that of globular proteins or flexible polymers, and (iii) the shape of the diffusion attenuation of spin-echo signal depends on protein concentration, diffusion time, and sample storage time, and changes from monoexponential to multi-exponential at protein concentrations greater than 2%. Our results show that in the concentration range from 0.5 to 2% the molecule of α-casein remains compact, and hydrodynamically it can be described by the model of a rigid Brownian particle. Further confirmation of the compactness of α-casein molecule (23 kDa) in dilute solution comes from the comparison of its diffusion coefficient (1.0 × 10-10 m2/s at 298 K) to the diffusion coefficient of globular proteins of comparable or larger molecular mass. For example, the diffusion coefficient is reported to be equal to 1.34 ± 0.5 × 10-10 m2/s at 303 K13, 51, 1.01 × 1010

m2/s at 293 K52, and 1.13 × 10-10 m2/s at 298 K53 for lysozyme (14.6 kDa); 0.87 ± 0.4 ×10-10

m2/s at 297 K13 for myoglobin (17 kDa); 0.54 ± 0.4 × 10-10 m2/s at 297 K13, 0.58 × 10-10 m2/s at 298K54, 0.6 × 10–10 m2/s at 294 K55, and 0.4 × 10–10 m2/s at 294 K56 for BSA (bovine serum albumin, 66.5 kDa). The estimate of the radius of α-casein molecule using its diffusion coefficient of 1.0 × 10-10 m2/s at 298 K at infinite dilution yields the value of about 20 Å. This value is somewhat smaller than reported radii of 28-32 Å for α-casein monomers determined at different pH values by gel chromatography37, where the difference can be due to the variance in experimental conditions and method differences. Furthermore, the conclusion on the compactness of the molecule α-casein that follows from our diffusion data in dilute solutions is in agreement with fluorescence data showing the presence of some structural organization in α-


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Page 18 of 40

casein, as shown by red shifts of Trp fluorescence spectra upon the addition of urea57. The compactness of α-casein molecule can be also expected because it falls under the category "weak polyampholyte" based on the content and distribution of charged residues58. In dilute solutions (i.e., intermolecular interactions of α-casein are negligible), the diffusion coefficient of α-casein follows the same trend as the concentration dependence of the diffusion coefficients of globular proteins13 and rigid Brownian spheres14. The normalization procedure, performed to enable the comparison of these concentration dependences, results in a mere translation of the curve along vertical and horizontal axes when the logarithmic scale is used. Therefore, the shape of the curve remains unchanged. This result suggests that the molecule of α-casein remains in the compact state, which is hydrodynamically comparable to that of the rigid

Brownian particle, though the molecule of α-casein does not form a stable structure even at crowded conditions57. In concentrated solutions (protein concentrations greater than 2%), both the strong dependence of the diffusion coefficient on protein concentration and the deviation of the diffusion attenuation from the monoexponential dependence indicate that the α-casein selfassociates. The smallest diffusion coefficient determined in our study is equal to 1.4 ± 0.1 × 10-15 m2/s. This value is much smaller than the value of 4 × 10-13 m2/s reported previously for casein micelles59. However, the authors emphasize that their reported diffusion coefficient did not account for all the slow diffusing species because 33% of the total signal remained nonattenuated59. Applying a significantly higher pulsed-field gradient (25 T/m vs. 5 T/m) allowed increasing the dynamic range of the diffusion attenuation and detecting slower diffusing species in our study. The dependence of the diffusion attenuation and Dmin on diffusion time suggests that the diffusion of slowly diffusing α-casein species is restricted, and, hence, the diffusion


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coefficient of 1.4 ± 0.1 × 10-15 m2/s cannot be attributed to an α-casein aggregate moving as a whole as proposed previously59, because in this case it would undergo unrestricted diffusion. Thus, Dmin is attributed to the molecules of α-casein confined to the aggregate structure. This possibility seems more plausible in line with the observation that molecules of αS1-casein can interact to form worm-like polymer chains where the hydrophobic regions of the individual chains join end to end38-40. It is also suggested that based on amino acid sequence similarity αS2casein forms similar structures38, 40. We propose that worm-like α-casein polymer chains interact with each other forming a three-dimensional gel network structures that are maintained by a balance of electrostatic repulsion and attractive hydrophobic interactions38, 60. We note that these structures are labile and the self-assembly of α-casein is reversible, because both the exponential form of the diffusion attenuation and the diffusion coefficient of α-casein were reproducible upon the dilution of the concentrated solution. Previously, we have suggested that the shift of critical concentration ϕˆ towards smaller values indicates the tendency of protein molecules to aggregate13. For example, ϕˆ is equal to 0.16 and 0.15 in solutions of myoglobin and lysozyme at pH 2.9-3.0, respectively, where no aggregation is observed, whereas it is equal to 0.08 in the solution of lysozyme with pH 7.4-7.8 where lysozyme molecules form aggregates51,

53, 61-62

. Our present data for α-casein firmly

support this conclusion. The critical concentration ϕˆ in α-casein solution is equal to 0.02, which is smaller than the critical concentration for lysozyme at pH 7.4-7.8. A significant decrease of the diffusion coefficient of α-casein at protein concentrations above 2-5 % is observed. The concentration dependence of the diffusion coefficient of α-casein becomes significantly stronger than the concentration dependence of flexible linear polymers or


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−12 −3 globular proteins (the slope of (ϕ ) vs. (ϕ ) ). Consequently, the diffusion in the solution of

α-casein at high concentration is qualitatively different. At high concentrations, globular proteins

become densely packed, however they remain structurally distinct and separated units. In contrast, flexible linear polymer coils become overlapped and entangled.

Because of the

entanglement two types of motion exist, the cooperative diffusion of segments in the network of polymer chains and a diffusion of individual polymer chains through the network associated with the movement of the center of mass of a polymer molecule44-47. The concentration dependence of the diffusion coefficient also deviates from rigid Brownian particles14, where the slope becomes infinitely large as the concentration of particles tends to the concentration of dense packing. Taken all together, our data suggest a different mechanism for the diffusion of α-casein in concentrated solution. We attribute a strong dependence of α-casein diffusion coefficient on concentrations to continuous self-assembly of α-casein molecules into labile supramolecular structures, forming the three-dimensional gel-like network. CONCLUSIONS We carried out a detailed investigation of the translational diffusion in solutions of α-casein and discovered several interesting features. Despite the lack of well-defined three-dimensional structure, the molecule of α-casein remains compact in dilute solution. As the concentration of α-casein increases, it reversibly self-assembles into labile supramolecular gel networks. The self-

assembly of α-casein manifests itself through the non-exponential, time-dependent diffusion −12 attenuation, and strong (e.g., (ϕ ) ) dependence of the diffusion coefficient of α-casein on

concentration. This dependence is much stronger than the previously observed concentration dependence of the diffusion coefficient of globular proteins or linear flexible polymers12-13.


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Whether similar structures are formed in concentrated solutions of other disordered proteins remains to be elucidated by further PFG NMR diffusion studies. It is possible that such behavior only reflects the specific interactions between α-casein molecules.


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FIGURE LEGENDS Figure 1. Example of NMR spectra for diffusion coefficient determination. (A) 1D spectrum of α-casein recorded at 298 K for a 7% protein solution prepared in 100% D2O. The spectral region

used for diffusion analysis is indicated shown by a bracket. (B) A representative stack plot of 1D NMR spectra for diffusion coefficient measurement. Figure 2. Diffusion attenuations of spin-echo signal in solutions of α-casein. Diffusion attenuations are shown for protein concentrations of 0.5%, 1%, 2% (A), 5% and 7% (B), 10% and 11% (C), and 15% (D), prepared in 100% D2O. Different scales were used for clearer presentation of data. The deviation from a monoexponential attenuation is observed at protein concentrations above 2%. All measurements were done at 298 K. Figure 3. Reversibility test. Diffusion attenuations are shown for protein concentrations of 2% (A) and 5% (B). Open triangles in panel (A) and half-filled squares in panel (B) are used to show diffusion attenuations collected for freshly prepared α-casein solutions, also displayed in Figures 2A and 2B. Solid triangles in panel (A) and open circles in panel (B) indicate diffusion attenuations collected for 2% and 5% α-casein solutions prepared by dilution of 10 and 15% αcasein samples, respectively, after all measurements using these samples have been completed. Solid lines show a monoexponential diffusion attenuation calculated using Eqs. 2 and 4 for the average diffusion coefficient

D

(corresponds to the initial slope drawn to experimental

curves). Samples were prepared in 100% D2O. The measurements were done at 298 K. Figure 4. The dependence of the diffusion attenuation of spin-echo signal in solutions of αcasein on the time after sample preparation. Diffusion attenuations are shown for protein


22

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concentrations of 0.5% at times 0 and 72 hrs (panel A) and for protein concentration of 10% at times 0, 2, 48, and 72 hrs after the sample has been prepared. Samples were prepared in 100% D2O. The measurements were done at 298 K. The weight of the component with the diffusion coefficient 1.4 ± 0.1 ×10-15 m2/s (shown by dashed lines) increases over time. Figure 5. The dependence of the diffusion attenuation of spin-echo signal in solutions of αcasein on diffusion time. Same diffusion attenuations are plotted using different coordinates32-35: (A) as a function of t d ⋅ k and (B) as a function of k, where k = (γ ⋅ δ ⋅ g )2 . Diffusion attenatuations are shown for 15% α-casein solution. Curves 1-3 correspond to diffusion attenuations collected at diffusion times 200, 400, and 800 ms, respectively. Curve 4 is a control experiment. The diffusion attenuation shown by curve 4 was collected at 200 ms after the completion of the experiments carried out at different values of td. Figure 6. The dependence of Dmin and pg on diffusion time td. (A) The dependence of the diffusion coefficient of slowly diffusing α-casein species (Dmin) on td in 15% α-casein solution. Solid line has the slope of t d−1 and shows that experimental values of Dmin are inversely proportional to td. Hence, slowly diffusing α-casein species undergo fully restricted diffusion. (B) The dependence of the fraction of slowly diffusing α-casein species on td in 15% α-casein solution. The best fit of experimental data to the Eq. 6 shown by the solid line. The fit yields the steady state fraction of self-associated α-casein species pg(0) of 0.93 and the lifetime in the associated, gel state of about 3.5 s. Figure 7. (A) The concentration dependence of the diffusion coefficient of α-casein. Two linear 0 −12 segments with the slopes of (ϕ ) (dashed line, dilute solution) and (ϕ ) (dotted line,


23


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Page 24 of 40

−3 concentrated solution) are observed. The asymptote with the slope of (ϕ ) is also shown. The

average diffusion coefficient /D0, determined from the initial slope of the diffusion attenuation according to Eq. 4 is shown by black diamonds. (B) Concentration dependence of the diffusion coefficients of α-casein, globular proteins13, linear flexible polymers12, and the theoretical dependence for Brownian rigid spheres14. The master curves for globular proteins (blue experimental points), flexible linear polymers (red solid line), and the theoretical dependence for rigid Brownian spheres (cyan solid line) are shown. In addition, the theoretical dependence for rigid Brownian spheres shifted along the horizontal axis is shown by a cyan 0 −3 dashed line. The asymptotes with the slopes of (ϕ ) and (ϕ ) are indicated. Solid magenta

diamonds represent the concentration dependence of the concentration dependence of the diffusion coefficient of α-casein /D0 normalized by ϕˆ . The normalization procedure merely leads to a shift of the concentration dependence along the horizontal axis.


24

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Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes The authors declare no competing financial interests. Acknowledgments This work was supported by the Faculty Research Grant from the University of North Carolina to I.V.N. NMR measurement were carried out on the equipment of the Federal Centre of Shared Facilities at Kazan Federal University. REFERENCES 1.

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TOC GRAPHICS


33


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 Figure 57 58

A

casein

H2O

8

6

4 1H

chemical shift, ppm

B

H2O

1H

chemical shift, ppm ACS Paragon Plus Environment

1

Page 34 of 40

2

Page 35 of 40

1

1

A

C

A(k)/A(0)

7% 0.1

0.1

2%

0.01

5% 0.01

0.5% 1% 0.0

2.0x1010

4.0x1010

6.0x1010

1

2.0x1011

0.0

4.0x1011

6.0x1011

1

D

B A(k)/A(0)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42


0.9

11%

0.8

15%

10% 0.1 0.7 0

1x1013

2x1013

3x1013

4x1013

0.0

7.0x1013

k·td, s·m-2

k·td, s·m-2 ACS Paragon Plus Environment

Figure 2

1.4x1014

2.1x1014

2.8x1014


1

1

A A(k)/A(0)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

Page 36 of 40

0.1

B 0.1

0.01 0.01

2% 1E-3 0.0

3.0x1010

6.0x1010

9.0x1010

1E-3

0

1x1011 2x1011 3x1011 4x1011 5x1011 6x1011

k·td, s·m-2

k·td, s·m-2

Figure 3 ACS Paragon Plus Environment

Page 37 of 40

100

A(k)/A(0)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58


A

10-1

1 hr 72 hrs

10-2 0.0

2.0x1010

4.0x1010

6.0x1010

B

k·td, s·m-2

Figure 4



1 0.9

A(k)/A(0)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

A

1 0.9

0.8

0.8

0.7

0.7

0.6

B 1, 4

0.6

1 4

0.5

2

0.5

3

2

3

0.4 0.0

Page 38 of 40

0.4 3.0x1014

6.0x1014

9.0x1014

1.2x1015

0.0

3.0x1014

k·td, s·m-2

6.0x1014

k, m-2


9.0x1014

1.2x1015

Page 39 of 40

2.1x10-15

A

1.8x10-15

1.000

B

1.5x10-15

τg = 3500 ± 400 ms ln(pg)

log(Dmin)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42


-15

1.2x10

pg = 0.93

9.0x10-16

6.0x10-16

(

pg ⋅ exp − td τ g

0.368

200

400

600

800

0

log(td)

1000

)

2000

td, ms


3000


log (ϕ / ϕˆ )

log (/D0), log (Dmin/D0)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

Page 40 of 40

ϕ0

ϕ-3

ϕ-12

A

B log (ϕ)

Figure 7

ϕ-3

ϕ0

log (ϕ)


Effect of Intrinsic Disorder and Self-Association on the Translational

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