Dilational Viscoelasticity of Proteins Solutions in Dynamic Conditions

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Dilational Visco-Elasticity of Proteins Solutions in Dynamic Conditions Valentin B Fainerman, Volodymyr I Kovalchuk, Eugene V Aksenenko, Igor I Zinkovych, Alexander V Makievski, Mykola V. Nikolenko, and Reinhard Miller Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b00631 • Publication Date (Web): 21 May 2018 Downloaded from http://pubs.acs.org on May 24, 2018

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Dilational Visco-Elasticity of Proteins Solutions in Dynamic Conditions Valentin B. Fainerman1, Volodymyr I. Kovalchuk2, Eugene V. Aksenenko3, Igor I. Zinkovych4, Alexander V. Makievski1, Mykola V. Nikolenko5 and Reinhard Miller6* 1

SINTERFACE Technologies, Berlin, Germany Institute of Biocolloid Chemistry, Kyiv (Kiev), Ukraine 3 Institute of Colloid Chemistry and Chemistry of Water, Kyiv (Kiev), Ukraine 4 Donetsk National Medical University, Ukraine 5 Ukrainian State University of Chemical Technology, Dnipro, Ukraine 6 MPI Colloids and Interfaces, Potsdam, Germany 2

ACS Paragon Plus Environment

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2 Abstract Drop profile analysis tensiometry used in the oscillating drop mode provides the dilational viscoelasticity of adsorption layers at liquid interfaces. Applied during the progress of adsorption the dynamic surface rheology can be monitored. For β-casein solutions at the same surface pressure values, the dynamic dilational visco-elasticity is the larger, the longer the adsorption time is, i.e. the smaller the studied protein concentration is. For β-lactoglobulin and human serum albumin, the differences in the visco-elasticity values are less or not dependent on the adsorption time at identical surface pressures. The observed effects are caused by the flexibility of BCS while the globular proteins BLG and HSA do not change their conformation significantly within the adsorption layer.

Keywords: Dilational visco-elasticity, Protein adsorption, Drop profile analysis tensiometry, Drop oscillation experiments

* Corresponding author: [email protected]


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3 Introduction Experiments on the surface dilational rheology of proteins solutions provide important information on the adsorption dynamics and on relaxation mechanisms in the adsorption layers. There are quite a number of studies on the dilational visco-elasticity of proteins adsorption layers [1-12], which can be measured as the surface tension response to surface area perturbations. Oscillatory experiments can be performed after having reached the adsorption equilibrium, but also under the dynamic conditions, to obtain the visco-elasticity modulus and the phase angle, both as functions of adsorption time and/or of the dynamic surface pressure [6-13]. Some problems arise when these methods are implemented. If one assumes that certain surface tension value always corresponds to the same state of surface layer irrespective of the duration of layer formation, then the dependencies of the visco-elastic properties on surface pressure, obtained at different bulk concentrations of the adsorbing molecules should also be the same. However, for proteins these dependencies on surface pressure can be different for different protein concentrations [2, 7, 11-13]. At comparatively low surface pressure value ( Π*, the surface pressure is given by [2]:

 1 ΓP − ΓP*  Π = Π * 1 +  n Γp*  a 

(8)

with na being the aggregation number of the protein aggregates. With the set of equations (1) to (8) the evolution of adsorbed states of protein molecules in dependence of bulk concentration c can be well described. As shown in [37], at low protein concentrations a depletion of the initial concentration c0 inside the drop occurs, the amount of which depends of the involved volume V and the surface area S of the drop. The final concentration inside the solution drop, after having reached the adsorption equilibrium, is then given by c = c 0 − (S V )ΓP . Applying harmonic volume oscillations to a drop leads to sinusoidal compressions and expansions of the drop surface. In this way PAT-1 is suitable to measure the dilational viscoelastic characteristics of the protein adsorption layer. Joos [39] derived equations for the surface dilational visco-elasticity applicable for the adsorption at a spherical surface with radius r, using a diffusion mechanism for the adsorption process. The visco-elasticity E is then given by [39,40]:

  D dc E = E0 1 − i [νr ⋅ coth(νr ) − 1] ϖr dΓP  

−1

(9)

E0 = dΠ/d(ln ΓP) is the visco-elasticity at the high frequency limit, ν 2 = i (ϖ D ) , D is the diffusion coefficient of protein molecules in the solution, f is the drop oscillation frequency, and ϖ = 2πf is the circular frequency. The surface dilatational visco-elasticity can be presented as a complex quantity: E = Er + iEi, which can be split into the visco-elasticity modulus |E| and the phase angle φ between stress (dγ) and strain (dA):

E = E 2r + E i2 , φ = arctan(E i E r ) . (10) The measured dilational visco-elasticity components can be compared with values predicted by the theory. Protein adsorption layers at concentrations above the critical point are usually

(

)

considered as composite layers [41], for which E0 can be estimated by E 0 = E*0 ΓP ΓP* , while E *0 is the E0 value in the critical point.


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8 Results and Discussion The dynamic surface tension measured for different aqueous BCS solutions is shown in Fig. 1. Four oscillations cycles at a fixed frequency of 0.1 Hz and 9% area amplitude were performed at adsorption times of 200, 400, 2000 and 5000 s after drop generation. The dashed line at a surface tension of 65 mN/m refers to the visco-elasticity data for BCS analysed further below. Similar dependencies for BLG are summarized in Fig. 2. The bold curve corresponds to the concentration of 10 µmol/l and the oscillation amplitude of 2.5%. The dynamic surface tension measured for different aqueous HSA solutions is shown in Fig. 3. The oscillations with a frequency of 0.1 Hz and area amplitudes of 3% and 9% were applied at adsorption times of about 200, 400, 2000 and 5000 s after drop generation. For all three studied proteins the surface tension at 5000 s was close to the equilibrium. To estimate the equilibrium values, two approaches were employed: (i) the dependence of surface tension on time was measured during up to 10000 s, and the obtained values were replotted vs the inverse time to extrapolate to infinite time, and (ii) dynamic experiment was performed during no less than 40000 s, and final values were taken as a reliable estimate of the equilibrium surface tension. These values are shown in Fig. 4 as dependencies of surface pressure Π on the initial protein concentration in the drop (which was identical to the solution concentration supplied to the drop through the capillary). These results were fitted by a software which implements the model equations (1)-(8) and accounts for the mass balance in the drop (consideration of possible depletion due to adsorption), to evaluate the model parameters listed in Table 1. The values estimated for the same substances by fitting the isotherms obtained by bubble profile analysis tensiometry in [1] and [42], respectively, are also shown in Table 1. The parameter values obtained from these two different experimental methods are rather similar: for example, the values for the minimum and maximum molar areas obtained here are almost identical to those reported in [1, 42]. It should be noted that the difference between the initial (c0) and equilibrium (c) concentrations is very significant: e.g., for the BCS this difference amounts to two orders of magnitude, similarly to that obtained in [42] for the drop and bubble profile methods. Note that the protein concentration decrease within the drop depends on the initial concentration, adsorption activity of the protein and the drop size (volume and surface area). For example, for the critical concentrations of the proteins studied here (0.05, 0.1 and 0.5 µmol/l for BCS, HSA and BLG, respectively) the equilibrium concentration becomes lower than the initial one by a factor of 105, 73 and 8, respectively, due to the depletion caused by adsorption.


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Fig. 1. Dynamic surface tension of BCS solutions measured by PAT-1; curves are labelled by the initial concentrations in µmol/l; shown are also the effect the surface area oscillation amplitude of ±9% and at times of 200, 400, 2000 and 5000 s.


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10

Fig. 2. The same as in Fig. 1 for BLG solutions. The thin curve corresponds to an area oscillation amplitude of 2.5%.


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Fig. 3. Dynamic surface tension of HSA solutions measured by PAT-1; curves are labelled by the initial concentrations in µmol/l; also shown is the effect the surface area oscillation amplitude of ±9% and ±3% at times of about 200, 400, 2000 and 5000 s.


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12

Fig. 4. Adsorption isotherms for BCS (), HSA () and BLG () solutions plotted vs the initial concentrations in the drop c0. Points are experimental data; curves were calculated using the model equations. Table 1. Parameters of Eqs. (1)-(8) for proteins adsorbed at the solution/air surface. Parameters

BLG [42]

aP α ω0 (105 m2/mol)

0.2 2.0 4.5

0.75 2.1 3.1

1.2 0.0 2.0

0.28 1.9 3.0

1.0 0.0 2.5

0.0 0.0 3.5

ωmin (106 m2/mol)

6.5

6.0

4.5

4.0

25

36

ωmax (10 m /mol) na Π* (mN/m) b1 (103 m3/mol) bX (m3/mol) L

1.4

1.5

4.0

6.5

7.5

7.5

5 25.5 2.2 1.0 2

4 21 0.68 16.0 2

13 20.5 2.0 9.0 2

10 16.5 3.0 15 2

17 100 50 2

3 18.4 37.0 95 2

7

2

BLG

BCS [42]


BCS

HSA [1]

HSA

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13 In literature, the dynamic visco-elasticity data are plotted in a number of ways: as dependencies on time at fixed surfactant concentration and surface oscillation frequency [12, 13, 31]; as dependencies of complex visco-elasticity components (modulus, phase angle or, alternatively, as real and imaginary parts) as functions of the surfactant concentration at fixed oscillation frequency [2, 9]; as dependencies of the modulus on surface pressure at fixed surface oscillation frequencies, surfactant concentrations or time [7, 11, 43]. In Figs. 5 and 6 the dependencies of the visco-elasticity modulus for solutions of the three proteins studied here on the surfactant concentration at fixed times (400 and 5000 s) and at a fixed surface area oscillation frequency 0.1 Hz are shown. In these figures, in addition to the values for different concentrations plotted in Figs. 1-3, the data for other concentrations are shown (8 or 9 concentrations for each protein, with two points corresponding to two time intervals). These data are very complicated to analyze, because the dependencies for different proteins are essentially un-similar. For BCS and HSA the curves exhibit maxima; however, for the BSC the location of this maximum is independent of time, while for HSA the maximum becomes shifted towards lower concentrations with increasing time. For BLG, the dependence is absolutely different and even more complicated. The surface pressure is a parameter which in a way ‘generalises’ or ‘accumulates’ various characteristics of the surface layer. It follows from the data reported in [7, 11, 41] that the surface visco-elasticity modulus, if expressed as dependency on surface pressure, is virtually independent of the surfactant concentration. Therefore, in our studies we use the dependence of the visco-elasticity modulus on surface pressure at different concentrations and fixed values of the oscillation frequency.


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Fig. 5. Dependencies of the visco-elasticity modulus of HSA and BLG solutions on initial concentration at different adsorption times labelled in seconds; dotted lines are guides for the eye.


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Fig. 6. Dependencies of the visco-elasticity modulus of BLG solutions on initial concentration at different adsorption times and surface oscillation amplitudes. , adsorption time 400 s, amplitude 9%; , adsorption time 5000 s, amplitude 9%; , amplitude 3%, time 400 s and above; dotted lines are guides for the eye.

In Figs. 7 and 8 the dependencies of |E| on Π are presented as measured at different adsorption times. The surface area oscillation experiments were made at one fixed frequency (0.1 Hz) and one oscillation amplitude (9%). To plot these dependencies, the data obtained from Figs. 1 and 2, and also similar values measured for other concentrations were used. For example, it is seen from Fig. 1 that at 2000 s the oscillations were applied to the solutions at surface pressure values of 2, 7, 13 and 16 mN/m. The values of the visco-elasticity modulus at these Π values at 2000 s are presented in Fig. 7; it is seen that the curve exhibits a maximum at about 9 mN/m. Similar dependencies for a number of systems were reported by Noskov in [12, 13]. However, in these publications, in contrast to the present study, the dynamic dependencies of the visco-elastic modulus on time were analysed.


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Fig. 7. Visco-elasticity modulus of BCS solutions as a function of surface pressure at different adsorption times: , 200 s; , 400 s; , 2000 s; , 5000 s; solid curve is calculated from the theoretical model with the parameters listed in Table 1 and a diffusion coefficient of 10−12 m2/s; dashed curve illustrates the maximum (limiting) visco-elasticity E0. Dotted lines are guides for the eye.


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Fig. 8. Dependencies of the visco-elasticity modulus of BLG solutions on surface pressure at different adsorption times labelled in seconds. The dotted lines are guides for the eye. We can see that for Π > 8 mN m−1 and long adsorption times the |E| values for BCS are much larger than those at short adsorption times. We observe a maximum difference for |E| at the same surface pressure of about 30 % for all studied concentrations. The reason for this phenomenon could probably be a different adsorption layer structure under non-equilibrium conditions as compared to that in the equilibrium state, caused by the molecular aggregation, reorientation, change of conformation, or other processes which occur at the solution surface. The solid curve in Fig. 7 was calculated from the theoretical model, Eqs. (1)-(9) with the parameters listed in the Table 1 and a diffusion coefficient of 10−12 m2/s. This curve almost coincides with the theoretical curve and the experimental data reported in [7]. In [2] the time dependencies of the modulus at different protein concentrations and also their concentration dependencies at different times were presented, and the results demonstrated that for the same surface pressure higher visco-elasticity moduli were measured at lower concentrations. The dashed curve shown in Fig. 1 corresponds to a surface pressure of 7 mN/m and it is seen that the lower is the concentration, the higher is the time necessary to attain this surface pressure value, in agreement with the results obtained in this ACS Paragon Plus Environment

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18 work. Moreover, these dependencies, if plotted vs the surface pressure at 2000 and 70000 s, in the surface pressure range above 10 mN/m differ from each other by 30% (for larger times the modulus values are higher). The phase angle values for the BCS solutions are within the range of 5 to 15°, while for the BLG solutions this range is 2 to 8°. The maximum values of this parameter correspond to the maximum values of surface pressure; thus, the imaginary component of the visco-elasticity modulus does not exceed 10% of its absolute value. For HSA solutions the observed phase angle values were even smaller. Fig. 7 also illustrates the dependence of the maximum (limiting) visco-elasticity E0 on surface pressure Π, see Eq. (9). In physical terms, this value corresponds to the infinitely high frequency response to the drop or bubble surface area oscillations when the protein exchange between the solution bulk and adsorption layer is negligible, i.e. the amount of adsorbed protein is constant, and the structure of the surface layer remains unchanged. Another limiting case is when the visco-elasticity is zero, which in physical terms refers to extremely slow oscillations accompanied by a complete exchange of the protein between the bulk and the surface, i.e. when the adsorbed amount per unit interface area remains constant. The E0 values depend on the model parameters and can vary within a quite wide range. The calculations with the model equations show that the increase of b1, ωmin, a and α increases the E0 values, while increasing values of ω0, ωmax and bX decrease the limiting visco-elasticity modulus. It is seen from Fig. 8 that for BLG the differences between the curves for the times of 200 and 5000 s are much lower, and do not exceed 10%. The curves for 400 and 2000 s (omitted in the figure) are located between the two shown curves. The fact that the variations of the visco-elastic modulus with time for BLG are much less significant than those for the BCS is attributable to the difference between the structural characteristics of these proteins. In contrast to the flexible random coil BCS molecules, the BLG molecules possess a globular structure, which remains mostly unchanged in the adsorbed state. This is quite evident also from the values of the model parameters listed in Table 1: the ratio ωmax / ωmin for BCS is about 16, while for BLG it is only 2.5. Consequently, for BCS the surface area oscillations can lead to more significant variations of the average molar area than for BLG; therefore, the relaxation related to the variation of the structure of the protein molecules influences much more significantly the visco-elastic modulus of BCS than that of BLG. The same conclusions regarding the difference between the flexible and globular proteins were made in [12], where a detailed analysis of the dynamic properties of various proteins with different molecular structure was presented. It should be noted that the results obtained at a time of 5000 s (closest to the equilibrium) shown in Fig. 8 are by 15 to 20 mN/m lower than those obtained in [7,11]. In his thesis, Benjamins studied the influence of the oscillation amplitude within the range of 1 to 15% on the viscoACS Paragon Plus Environment

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19 elasticity modulus [43]. It was shown that for proteins adsorbed at interfaces with a modulus larger than 40 mN/m the values decrease with the increase of the oscillations amplitude. Therefore, in [7, 11] the drop area oscillation amplitudes were kept small, with a minimum value of about ±1%. The effects of the oscillation amplitude on the values measured in [11] were similar to those reported in [19]. It can be supposed that the differences between the results of Fig. 8 and those obtained in [11] are due to the fact that in the present study the oscillation amplitudes were larger. From Fig. 2 we see that for an area oscillation amplitude of 9% the surface tension oscillation amplitudes are ±8 mN/m; this could lead to a non-linear response caused by structural changes in the adsorbed layer at the surface. Fig. 9 illustrates for BLG solutions the amplitude of surface tension oscillations caused by different amplitudes of drop area oscillations, while in Fig. 2 the dynamic curve for the area oscillation amplitude of 2.5% is shown. We can see that for low area oscillation amplitudes the amplitude of surface tension oscillations becomes much smaller, which can possibly be related to a smaller contribution of non-linear effects to the surface deformation response.

Fig. 9. Surface tension oscillations of a 10 µmol/l BLG solution at drop area oscillations amplitudes of 3, 6, 9 and 12%.


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20 The visco-elastic modulus as a function of the drop area oscillation amplitudes is shown in Fig. 10. Here the protein concentrations are roughly one order of magnitude higher than the corresponding critical values. It is seen that for the BLG solutions the modulus becomes higher with the decreasing area oscillation amplitude. For amplitudes below 4% the modulus is virtually independent of the amplitude, while for the amplitude of 12% the modulus is 20 mN/m smaller. On the contrary, for the BCS solutions no dependency of the visco-elastic modulus on the oscillations amplitude is observed. This could possibly be explained by the fact that the value of the modulus for BCS is four times lower than those for BLG. The response of flexible BCS molecules to the surface pressure and surface area oscillations is much higher than that of the globular BLG molecules, which show a weaker response (smaller changes of the surface layer structure) to surface pressure changes and surface deformations. In Fig. 10 also data for HSA are shown. We see that the dependence of the visco-elasticity modulus on the surface area oscillation amplitude is less pronounced than that for BLG, but they are still significantly higher at small amplitudes as compared to those at higher amplitudes. Thus, HSA and BLG as globular proteins behave in a similar way.


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Fig. 10. Visco-elasticity modulus of two BLG solutions (5 and 10 µmol/l, filled and open points, respectively), BCS solution (0.1 µmol/l) and HSA solution (0.2 µmol/l) as a function of the area oscillation amplitude at 5000 s adsorption time.

Fig. 11 illustrates the dependence of the visco-elastic modulus on the surface pressure for BLG solutions for the drop area oscillation amplitude of 3%. Here, the values shown in Fig. 8 (corresponding to an amplitude of 9%) were remapped to an amplitude of 3% using the dependence shown in Fig. 10. Also, the results shown in Fig. 10 for the adsorption time of 5000 s and data obtained for some other concentrations similar to those presented in Fig. 2 for the amplitude 3% are included. The thin dashed curve is reproduced from [7] and gives a good description of the results obtained therein. The curve is also in good agreement with the data shown in Fig. 11 for the adsorption time of 5000 s and an area oscillation amplitude of 3%. The consistency between the experimental data obtained at increasing adsorption times, and the theoretical predictions is rather obvious, suggesting the validity of the applied model.


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Fig. 11. Visco-elasticity modulus for the area oscillation amplitude of 3% for BLG solutions as a function of the surface pressure for adsorption times of 200 s () and 5000 s (); the solid curve was calculated with model equations (1) to (9), the diffusion coefficient 10−12 m2/s and the model parameters listed in Table 1; the dashed curve represents the values for E0; the dash-dotted curve is reproduced from [7]; dotted lines are guides for the eye.

The experimental and theoretical results obtained for solutions of HSA at an area oscillation amplitude of 3% are shown in Fig. 12. We can see that the visco-elasticity modulus measured at different adsorption times are almost the same, which implies that the structure of the adsorbed layer of the globular HSA, similarly to that of BLG, does not depend significantly on the adsorption time. It is seen from Table 1 that the maximum area of the HSA molecules is only two times higher than its minimum value, in agreement with the ellipsoidal shape of the globules and their two possible orientations in the surface layer [1]. At the same time, for flexible BCS molecules the maximum area is 16 times larger than its minimum value. Thus, the hypothesis that the visco-elastic modulus of protein solutions at different concentrations depends only on the surface pressure is valid for globular proteins, while for flexible proteins this hypothesis comes into conflict with the presented data for BCS. Also, the modulus of the HSA solutions depends on the area oscillation amplitude: for an amplitude of 9% the visco-elasticity modulus is by 15 to 20% smaller than that for an amplitude of 3%. Therefore, to obtain consistent rheological results


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23 the oscillation amplitude should be decreased; this is especially true for large values of the viscoelastic modulus.

Fig. 12. Visco-elasticity modulus for the area oscillations amplitude of 3% for HSA solutions as a function of surface pressure for adsorption time 200 s (), 400 s (), 2000 s () and 5000 s (). The solid curve was calculated with model equations (1)-(8), the diffusion coefficient 10−12 m2/s and the model parameters listed in the Table. Dotted lines are guides for eye. Conclusions The drop profile analysis tensiometry with harmonic surface area oscillations (at a fixed frequency of 0.1 Hz) was used to measure the dilational visco-elasticity of aqueous solutions of the proteins BCS, BLG and HSA during the process of adsorption layer formation at adsorption times between 200 and 5000 s. For solutions of BCS we found a visco-elasticity modulus at short times which was about 30 % lower than at the same surface pressure but at longer adsorption times or in the equilibrium state of adsorption. For BLG solutions this phenomenon is much less pronounced. It was found that the differences between the values obtained at various adsorption times do not exceed 10% and for HSA solutions such difference is even practically absent. This


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24 phenomenon is ascribed to the differences in the structure of the adsorbing protein molecules. The structure of the adsorption layers formed by the flexible BCS molecules is quite susceptible to variations of surface pressure and surface area. On the contrary, the structures formed by adsorbed globular molecules, such as BLG and HSA, exhibit a much weaker response to these factors. The discussion is supported by the visco-elasticity modulus calculated with the presented model which considers a mass balance of protein in single drops, i.e. consideration of depletion of proteins due to their adsorption at the surface of the single drop.


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25 Acknowledgements The work was supported by the ESA MAP Soft Matter Dynamics, ICCCW NASU project III-616:20, USUCT State R&D project 24/170290, and the European Training Network CoWet.


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26 References [1]

[2]

[3] [4]

[5]

[6] [7]

[8]

[9]

[10]

[11]

[12] [13] [14]

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Dilational visco-elasticity as a function of surface pressure for BCS solutions measured by drop profile analysis tensiometry at different surface ages


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Dilational Viscoelasticity of Proteins Solutions in Dynamic Conditions

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