Mechanical Properties of Immunoglobulin G and Albumin Monolayers

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Mechanical Properties of Immunoglobulin G and Albumin Monolayers Arti Ahluwalia,*,† Elisa Stussi,† and Claudio Domenici‡ Centro “E. Piaggio”, University of Pisa, Via Diotisalvi 2, 56126 Pisa, Italy, and CNR Institute of Clinical Physiology, Pisa, Italy Received September 22, 1994. In Final Form: August 16, 1995X The mechanical properties of protein films at the gas-water interface are determined by means of a mobile barrier. The films are subjected to extensional and compressional surface stresses and strains as opposed to the commonly used shear ones. Two proteins, immunoglobulin G and albumin, with distinctly different characteristics at the interface are investigated. The results from albumin films demonstrate the validity of this method and indicate that, in certain cases, only one measurement is required to completely characterize the elastic constants of the monolayer. From the viscoelastic properties observed for IgG between surface pressures of 3.5 and 26 mN/m, possible mechanisms to explain the film’s behavior have been deduced.

1. Introduction The growing interest in organized thin organic films arises from their possible applications in fields such as molecular electronics and membrane modeling. Protein films are rapidly becoming a part of this active sphere of research for producing ordered layers of molecules, chiefly because of their potential applications to sensing systems. In particular, IgG (immunoglobulin G) films, which can be employed in immunosensors, have been the object of investigation with attention being paid mainly to their antigen recognition properties.1,2 In spite of the seminal works of authors such as Graham and Phillips3 and MacRitchie4 and the more recent efforts made to organize protein monolayers into two-dimensional domain structures,5,6 there remains a large gap in our knowledge of the behavior and characteristics of protein monolayers.7 In an effort to improve our understanding of the physical processes underlying interfacial phenomena, we have attempted to characterize the mechanical behavior of protein films at the gas-water interface. The rheological behavior of a monolayer can furnish insights into the microscopic interactions between the molecules and also between the molecules and the interface medium. It can also indicate optimum deposition conditions, in terms of deposition speed and pressure, and could thus lead to an improved Langmuir-Blodgett (LB) film. A classical mechanical characterization method, using stress-relaxation and creep measurements, has been applied to interfacial films. In this case, as opposed to the methods commonly found in the literature, which pertain to shear deformations or forces,8-10 the film is subjected to unilateral compressional and extensional step †

University of Pisa. CNR Institute of Clinical Physiology. X Abstract published in Advance ACS Abstracts, November 1, 1995. ‡

(1) Ahluwalia, A.; De Rossi, D.; Ristori, C.; Schirone, A.; Serra, G.; Biosens. Bioelectron. 1992, 7, 207. (2) Turko, I. V.; Yurkevich, I. S.; Chashchin, V. L. Thin Solid Films 1991, 205, 113. (3) Graham, D. E.; Phillips, M. C. J. Colloid Interface Sci. 1979, 70, 403. (4) MacRitchie, F. J. Colloid Sci. 1963, 18, 555. (5) Uzigris, E. E.; Kornberg, R. D. Nature 1983, 301, 125. (6) Ahlers, M.; Blakenburg, R.; Grainger, D. W.; Meller, P.; Ringsdorf, H.; Salesse, C. Thin Solid Films 1989, 180, 93. (7) Andrade, J. D. Thin Solid Films 1987, 152, 335. (8) Graham, D. E.; Phillips, M. C. J. Colloid Interface Sci. 1980, 76, 240. (9) Buhaenko, M. R.; Goodwin, J. W.; Richardson, R. M. Thin Solid Films 1988, 159, 171.

0743-7463/96/2412-0416$12.00/0

deformations and forces. An advantage of this particular method is its simplicity, as it can be used with any moving barrier-type computer-controlled film balance without requiring new apparatus. Although a few measurements of this type on lipid and polymer films have been described (see, for example, refs 11 and 12), as far as we know they have not been applied to protein films. The major difference in the approach described here is that the measurements were performed by applying small step changes to a system at (or near) equilibrium rather than compressing the film over a large area and then measuring relaxations. In the latter approach, the relaxation behavior of the film will depend to a large extent on the rate and magnitude of compression, whereas the response of a system at equilibrium to small perturbations is generally independent of its history prior to equilibrium. This paper describes the method employed to investigate the rheological properties of a film at the gas-water interface with reference to studies performed on human serum albumin (HSA) and IgG. Albumin is one of the most commonly used proteins in interfacial work, and the results obtained may be compared with those in the literature. It also provides a comparison with IgG, which was studied to characterize and better understand its behavior at the interface. The experimental results obtained from the mechanical characterization of the two protein films have allowed us to evaluate the elastic constants of the films at low surface pressures. A simple generalized picture of the viscoelastic behavior of the proteins at the gas-water interface has also been composed from the measurements. 2. Materials and Methods A thermostated Lauda FW2 film balance (Lauda, Ko¨nigshofen, Germany), equipped with a Langmuir float and with a usable trough area of 46 cm × 20 cm, was employed for the studies. The entire system is housed in a laminar flow hood with appropriate prefilters and filters. The film balance is interfaced to a PC via a GPIB bus, and BASIC software was written to provide the desired barrier movements and data acquisition modes. The maximum possible sampling frequency for pressure and area data was 26 Hz, but this high a rate was unnecessary for the measurements which were carried out over an hour. A standard rate of 1 Hz was thus imposed. The proteins used were human (10) Abrahams, B. M.; Ketterson, J. B.; Miyano, K.; Kueny, A. J. Chem. Phys. 1981, 75, 3137. (11) O’Brien, K. C.; Lando, J. B. Langmuir 1985, 1, 453. (12) Biddle, M. B.; Rickert, S. E.; Lando, J. B. Thin Solid Films 1985, 134, 121.

© 1996 American Chemical Society

IgG and Albumin Monolayers serum albumin of g99% purity (MW 65 000; Fluka, Buchs, Switzerland) and purified IgG pooled from normal rabbit serum (MW 150 000; Sigma, St. Louis, MO). 2.1. Isotherms. Isotherms of the two proteins were formed at 20 °C. This was done as a preliminary characterization. Human serum albumin (HSA) films were formed by spreading 0.2 mL of a 0.5 mg/mL water solution onto a phthalate-buffered subphase of pH 4.9, which is the isoelectric point of this protein.13 The films were compressed immediately upon spreading at a barrier speed of 0.75 cm/min. 0.3 mL of a 0.5 mg/mL IgG solution, which had been previously dialyzed against water to remove any salts present, was spread onto a phosphate-buffered subphase at its measured modal isoelectric point (pH 7.1 ( 0.5) and compressed in the same manner. The same subphases and spreading solutions were used for the rheological measurements. Milli-Q water and reagent grade salts were used in all preparations. Prior to each measurement the surface of the subphase was cleaned by repeated compression and aspiration, until no increase in pressure was observed upon compression to the minimum working area (about 20 cm2). The possibility of pressure measurements being affected by the presence of dissolved protein or impurities in the clean part of the subphase was checked by measuring the surface pressure in that region with a Wilhelmy plate (MDT, Moscow, Russia). While a monolayer of IgG was slowly compressed and expanded over a period of about 3 h, the pressure reading of the Wilhelmy plate remained within 0 ( 0.1 mN/m. 2.2. Stress-Relaxation and Creep Measurements. The modality for the measurements was as follows: measurements referred to as stress-relaxations were performed by applying a step change in area to the film. In most cases the protein film was first compressed, at a speed of 0.75 cm/min, to a given pressure. The barrier was then halted and the pressure allowed to reach an equilibrium value, which, for the purpose of the experiments, was defined as one that did not change by more than 0.1 mN/m in 20-30 min. The repeatability of the equilibrium pressure was (0.2 mN/m. At this point the barrier was moved forward at its maximum speed (18.5 cm/min) until the pressure rose by about 2 mN/m from the equilibrium value. The barrier was then stopped, and the pressure data were acquired for an hour. The strains imposed ranged from 2% to 6%, depending on the steepness of the isotherm, except in the case of HSA at high pressures where higher strains were required. For the purpose of preparing LB films, the monolayer properties under compression are of particular interest. To determine whether the response of the film to small perturbations was analogous under both compression and expansion, in some cases, after the compression step, an expansion step was also executed. Measurements referred to as creeps were executed in the same manner as the stress-relaxations in the initial stages. After an equilibrium pressure was reached, the barrier was moved at its maximum speed to a pressure about 2 mN/m higher than the equilibrium one. Once this pressure was attained, the film balance entered its closed-loop operation mode to maintain constant pressure. The area and pressure data were acquired over 1 h. Creep measurements were inherently more difficult to obtain than stress ones, especially in the case of the more condensed IgG films. This was due to the large degree of overshoot, arising from the inertia of the barrier. The problem was slightly ameliorated by modifying the software and by attempting to compensate for it by estimating the amount of overshoot from previous creeps and stresses. All stress and creep measurements were performed at a temperature of 20 ( 0.2 °C, and each measurement was repeated, starting from a clean surface, at least four times.

3. Experimental Results 3.1. Mechanical Measurements on Human Serum Albumin. As shown in Figure 1, the HSA isotherm consists of three zones. At large areas per molecule the pressure rises smoothly; this is followed by a flatter region and then a steeply rising zone at small areas per molecule. Stress and creep measurements were performed in each (13) Mariani, G.; Bianchi, R. An Overview on the Biology and Pathophysiology of Human Albumin; Immuno S.p.A.: Pisa, 1982; p 20.

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Figure 1. Surface pressure-area per protein molecule isotherm of HSA at 20 °C (s) and a smoothed version of the isothermal compressional modulus derived from the isotherm (- - -).

of the first two zones. Pressures in the last zone cannot be maintained as they tend spontaneously to fall to values in the plateau zone. The film is therefore unstable at small areas per molecule, and it was not possible to perform the rheological measurements described here. The mechanical behavior of albumin has been quite thoroughly studied at the gas-water interface, and the mechanical responses at only two representative pressures of about 8 and 19 mN/m were considered here. It is well-known that albumin molecules unfold upon spreading.14 At large areas per molecule, the surface pressure continues to rise until it reaches a steady state value after a few hours. This phenomenon has been ascribed to the conformational rearrangements of segments of the albumin molecules.3 It was observed that by simply spreading the HSA solution and waiting 3 h without moving the barrier, a steady state pressure of 8.3 ( 0.2 mN/m was reached. Stress and creep measurements were performed using this as the equilibrium starting pressure. Figure 2a shows a stress-relaxation, with both compression and expansion steps, and Figure 2b a creep. In Figure 2c the pressure maintained during the creep measurement is reported. The step responses at low pressures show no relaxation. Measurements in the plateau region were performed by first compressing the film immediately upon deposition to 20 mN/m. The pressure then dropped sharply in the first few seconds, and after 30 min an equilibrium pressure of about 19 mN/m was attained. The responses of typical creep and stress measurements are given in Figure 3. Because of its “flatness”, there was little pressure overshoot in this region and the pressure input for the creeps was a fairly good representation of a step. 3.2. Mechanical Measurements on Immunoglobulin G. IgG films underwent the same treatment as HSA at 19 mN/m. As is evident from the isotherms (Figures 1 and 4), there are several differences between IgG and HSA films. IgG forms more condensed films than HSA, and its apparent area per molecule, calculated from the initial quantity of IgG spread, is much lower than that of HSA. The isotherms are fairly monotonic, and at all pressures the films attained an equilibrium pressure after 40 min. (14) MacRitchie, F. J. Colloid Interface Sci. 1977, 61, 223.

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a

a

b

b

c

c

Figure 2. (a) Compression-expansion stress-relaxation (strain ) 4.2%) and (b) creep measurements on HSA at 8.3 mN/m. (c) The pressure maintained by the control loop during the creep measurement.

Stress measurements were performed at five different pressures ranging from 3.5 to 26 mN/m. Pressures above 26 mN/m could not be maintained due to the instability of the film. Because of the steepness of the isotherms, acceptable creep measurements on IgG were very difficult to obtain, and creeps were only performed at 8 mN/m. At pressures above this, the overshoot was unacceptable, and as the stress-relaxations were qualitatively similar at all pressures, 8 mN/m was considered to be fairly representative of the general behavior of the film. Figure 5 shows an IgG compression-expansion stressrelaxation and a creep at about 8 mN/m (8 ( 0.2 mN/m), as well as the pressure maintained by the control loop during the creep measurement.

d

Figure 3. (a) Compression-expansion stress-relaxation (strain ) 21%) and (b) creep measurements on HSA at 19.2 mN/m. (c) The pressure maintained by the control loop during the creep measurement and (d) a typical residual (fitted function minus experimental data).

4. Analysis of Results 4.1. Albumin. Figures 2 and 3 show the surface pressure and area data (expressed as surface strains) obtained from the stress and creep measurements on HSA. Parts a and b of Figure 2 show no relaxation of pressure or area, and the response to compression and subsequent extension indicates completely reversible behavior. In mechanical terms the response of the film can thus be said to be purely elastic. At low pressures, the HSA film can therefore be represented by a “spring” whose unilateral surface elastic modulus, K′, is given by

K′ ) -∆π/(∆A/A)

(1)

where π is the surface pressure and A is the area. The surface elastic modulus from both stress and creep measurements at this pressure was 44 ( 5 mN/m, which is in the same range as the values given in Blank et al.15 for sinusoidal deformations applied to “aged” albumin films. (15) Blank, M.; Lucaessen, J.; Van den Tempel, M. J. Colloid Interface Sci. 1970, 33, 94.

Figure 4. Surface pressure-area per protein molecule isotherm of IgG at 20 °C (s) and a smoothed version of the isothermal compressional modulus derived from the isotherm (- - -). The area per molecule of IgG is estimated from the initial quantity of IgG spread.

In the plateau region at intermediate pressures, the responses, as shown in Figure 3, are more complicated. As observed in the compression and expansion stress-

IgG and Albumin Monolayers

a

b

c

Figure 5. (a) Compression-expansion stress-relaxation (strain ) 2%) and (b) creep measurements on IgG at about 8 mN/m. (c) The pressure maintained by the control loop during the creep measurement.

relaxation studies, the behavior of the film is not completely reversible and this is most likely due to a viscous component, which is not evident at lower pressures. A detailed analysis of the curves of 1 h duration shows that both stresses and creeps are composed of at least three decaying exponentials, which indicates that there are at least three distinct phenomena occurring in the film. The curves were fitted to a general equation of the form

f(t) ) A exp(-t/τA) + B exp(-t/τB) + C exp(-t/τC) (2) using a Nelder-Mead simplex algorithm to minimize the error between the fitted functions and the data.16 A, B, and C are related to the elastic parameters of the film whereas τA, τB, and τC are linked to its viscous properties, and t is time. In all cases the fits have a χ2 value of less than 0.07. A typical residual for a stress-relaxation experiment is shown in Figure 3d. As illustrated, the fit is fairly uniform except in the first few seconds of the data because the sharp pressure gradient in this region makes the fitting process less precise. Hence the term associated with the shortest time constant is the least accurate. Using an equation with more than three exponentials to fit the data does not reduce the error appreciably and has no effect on the residual at t close to zero, while an equation with two exponentials has unacceptably high residuals, with χ2 of the order of 1. Residuals for the creeps were similar to those of the stress-relaxations. The first exponential has a time constant, say τA, typically of the order of tens of seconds, the second, τB, of a few minutes, and the longest, τC, of over 19 h. The extension part of the compression-expansion stress-relaxation measurements was also fitted to the same function. The amplitudes of all three exponentials as well as the values of the two shorter time constants were, within the limits of experimental error, equal to those under compression, (16) MATLAB, Optimization Toolbox; The Mathworks Inc.: Natick, MA.

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whereas the longest time constant was slightly higher. In addition, it was observed that compression of an HSA film at a speed of 2.5 cm/min (rather than 0.75 cm/min) prior to equilibrium produced practically the same stressrelaxation response, with only τC being slightly higher. τC is several times greater than the duration of a typical compression experiment, and therefore the associated exponential can be taken as a constant over the time scales considered in our experiments. The response of the HSA film is thus equivalent for expansion and compression over small areas, and our definition of equilibrium is adequate for the length of our experiments. The time constant τC is generally thought to represent solubilization or desorption of the film17 and indicates that under the time scales of our experiments the molecules can be considered practically insoluble. The values for coefficients and time constants of the fitted data are given in Table 1. The coefficients were normalized in terms of stress and strain, and for the purpose of comparison between creeps and stresses, the reciprocals of the coefficients of the creep functions are presented. The errors given in Table 1 are the standard deviations between the values obtained from (at least four) different trials. Strictly speaking, only the instantaneous response (A + B + C for stress or 1/(A + B + C) for creeps) and the responses at t f ∞ (C or 1/C) can be directly compared. The other parameters are related to each other through a complex implicit analytical expression. That the responses at t ) 0 and t f ∞ are equivalent confirms that the two experiments are analogous. 4.2. Immunoglobulin G. All of the IgG stressrelaxations were viscoelastic in nature, similar to those of Figure 5a and not unlike those of HSA at 19 mN/m. At all pressures investigated, the film underwent irreversible changes during the deformation process. As mentioned previously, creep measurements were very difficult to obtain and were only made at 8 mN/m. These too were viscoelastic in nature (see Figure 5b). As in the case of HSA, the creep and stress data for IgG were fitted to a three decaying exponential function (eq 2). The χ2 test gave a value of 0.05 for the goodness of fit, slightly less than that for HSA, indicating a better correlation. For stress-relaxations, the first time constant is of the order of 30 s, the second of about 8-10 min, and the longest varies from about 30 h for a pressure of 3.5 mN/m to 20 h for a pressure of 26 mN/m. The normalized coefficients of the fitted function (A, B, and C) versus surface pressure are shown in Figure 6. The two shorter time constants τA and τB are shown in Figure 7. Fitting the extension part of the compression-expansion stress-relaxation curves to a three decaying exponential function revealed that all three amplitudes and the two shorter time constants were equal for both compression and extension while the long time constant was greater for extension. As in the case of HSA, for small deformations and in the time scales of our experiments, IgG’s reponse to expansion and compression is identical. The normalized values obtained for the coefficients and time constants at 8 mN/m are given in Table 1. 5. Evaluation of Surface Elastic Constants The results of the stress-relaxation and creep experiments were applied to a simplified model based on the theory of elasticity. The model is able to describe the elastic behavior of a film and allows its surface elastic constants to be determined. In particular, the surface (17) Loglio, G.; Rillaerts, E.; Joos, P. Colloid Polym. Sci. 1981, 259, 1221.

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Table 1. Values of the Parameters of the Fitted Function f(t) ) A exp(-t/τA) + B exp (-t/τB) + C exp(-t/τC) for HSA at 19 mN/m and for IgG at 8 mN/ma elastic coefficients (mN/m) surface pressure π (mN/m) (A + B + C) or 1/(A + B + C) A or 1/A B or 1/B HSA stress creep IgG

stress creep

19 19 8 8

11.7 ( 1.5 11 ( 3 93 ( 7 98 ( 14

3.3 ( 0.6 -30 ( 6 25 ( 4 -206 ( 23

2.5 ( 0.8 -40 ( 5 21 ( 1 -174 ( 12

time constants C or 1/C

τA (s)

τB (s)

τC (h)

5.9 ( 0.6 3.3 ( 0.6 13 ( 2 7(1 46 ( 2 303 ( 27 47 ( 6 48 ( 3

37 ( 2 58 ( 6

19 ( 4 22 ( 4

498 ( 32 24 ( 3 792 ( 112 84 ( 13

a In the case of creep measurements, the reciprocals of the coefficients A, B, and C have been given. The errors are the standard deviations between at least four measurements.

Table 2. Values of the Instantaneous Response of the 2-D Hydrostatic Deformation (IER), the Isothermal Compressional Modulus (ICM), and the Steady State Elastic Response (C) of the Stress-Relaxation Measurements for IgG π (mN/m)

IER (mN/m)

ICM (mN/m)

C (mN/m)

3.5 8 15 18 22 26.5

29 ( 3 46 ( 2 44 ( 3

27 42 47 43 42 41

30 ( 2 47 ( 6 65 ( 3 72 ( 4 62 ( 3 41 ( 3

hydrostatic compression or expansion (or the hydrostatic surface elastic modulus) is given by

K)λ+µ Figure 6. Surface elastic coefficients of IgG as a function of pressure. The qualitative behavior of the coefficients, A (- - -), B (‚‚‚), and C (s) has been drawn.

(4)

The elastic modulus in a laterally confined 2-D system (or the unilateral surface elastic modulus), as is the one described here, is

K′ ) λ + 2µ

(5)

The two-dimensional (2-D) analogue of the coefficient of

Similar expressions for the Young’s modulus, E, and the Poisson ratio, ν, can also be derived.10,19 In the present case then, K′ is the instantaneous elastic response of the films and can be obtained directly from the experimental data (initial stress ÷ initial strain) or is given by the sum A + B + C in the case of stress-relaxations or 1/(A + B + C) in the case of creeps. To estimate the hydrostatic surface elastic modulus K, additional measurements to simulate a two-dimensional hydrostatic deformation were also carried out on IgG films. A clean glass slide was immersed into the subphase prior to spreading. After the attainment of equilibrium pressure, the film was expanded by moving the barrier for a small distance at its maximum velocity and simultaneously the slide was lifted up at the same strain rate using the standard Lauda dipper mechanism. Data acquisition was performed as for the stress experiments. This experiment was performed at 3.5 and 8 mN/m using 0.3 mL of spreading solution (as for the stress and creep experiments) and at 15 mN/m using 0.6 mL. The position of the dipping well (about two-thirds of the way down the trough) prohibited measurements at higher pressures. This measurement was considered to be the simplest way of approximating the 2-D hydrostatic elastic modulus with our present trough. The results of the instantaneous elastic response (IER) in these experiments are given in Table 2. According to Abrahams et al.,19 the 2-D hydrostatic modulus K can also be obtained from the isothermal compressional modulus (ICM) derived from an isotherm, provided that the film does not have a residual shear modulus and that the compression time is much longer than the viscous relaxation times (in the present case τA and τB). This is true for complex systems such as protein

(18) Landau, L. D.; Lifshitz, E. M. Theory of Elasticity, 2nd ed.; Pergamon Press: Oxford, 1970.

(19) Abrahams, B. M.; Ketterson, J. B.; Behroozi, F. Langmuir 1986, 2, 602.

Figure 7. The relaxation times, τA and τB, of IgG and their approximate behavior as a function of pressure.

elastic moduli obtained for albumin films can be compared with those reported in the literature. We consider a protein film at the gas-water interface, which can be approximated to a two-dimensional system. The elastic constants which characterize the system can be derived from the expression for the energy per unit area in a manner analogous to that of an isotopic threedimensional material.18 The free energy, F, due to an elastic deformation can be written in terms of the Lame´ constants, λ and µ, and the tensors of deformation, u as

1 F ) λuii2 + µuij2 2

(3)

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Table 3. Elastic Constants Calculated from the Stress-Relaxation Measurements on HSA and IgG at Low Pressuresa π (mN/m)

K′ (A + B + C) (mN/m)

K (mN/m)

µ (mN/m)

λ (mN/m)

ν

E (mN/m)

HSA

19 8.3

11.7 44

5.9 32

5.8, (3-5),8 (6-8),22 12

0.1 20

0.009 0.45

11.7 35

IgG

3.5 8

54.8 93

30 47

24.8 46

5.2 1

0.09 0.01

54.3 93

a

The values for the shear modulus obtained by Graham and Phillips8 and Boyd and Sherman22 for HSA are also given.

or polymeric films in which the boundary conditions, and hence mechanical properties, may vary during the course of a stress-relaxation or creep experiment, as in the case of hydrogels. In these latter biphasic systems, the variation of water content of the polymeric matrix can change the characteristics of the material, allowing different coefficients to be obtained from a single experiment.20 Similar behavior can be expected for Langmuir films of proteins which have been shown to possess at least two distinct phases.21 Given these considerations, the normalized coefficient C (or 1/C in the case of creep) should also be equal to K, the hydrostatic surface elastic modulus, because it represents the elastic response of the film at time t f ∞, when the system is completely relaxed and not subject to lateral constraints. Table 2 shows the values of the instantaneous elastic response of the experiments simulating a hydrostatic deformation as well as the values of ICM from the isotherm in Figure 4 and the corresponding values of C for stressrelaxation measurements. The instantaneous response of the hydrostatic deformation experiments on IgG at low pressures coincides well with values of C and ICM. Thus, at low pressures, the 2-D hydrostatic elastic modulus as obtained from the above experiments is equivalent to the response at t f ∞ of the stress-relaxation and creep experiments, as well as to the isothermal compressional modulus. This demonstrates that in this particular case, λ and µ can be obtained from a single stress-relaxation or creep experiment. At pressures beyond 8 mN/m, when the IgG film becomes more rigid, additional mechanical measurements are required to characterize an IgG monolayer. As suggested in ref 10, nonuniform shear stresses may not be easily relieved in a rigid film, and so neither the 1 h isothermal compression nor the steady state response of the measurements described here necessarily reflects the conditions of a true hydrostatic deformation and hence the hypothesis that the ICM and K (and hence C) are equivalent does not hold. Moreover, above about 8 mN/ m, the experiment using the slide is probably unsuitable for measuring the 2-D hydrostatic modulus because the relatively rigid film probably fractures while the slide is extracted. The same assumptions regarding the equivalence of C, the ICM, and K can also be extended to HSA, given that, at 8.3 and 19 mN/m, the films are less rigid than those of IgG at 8 mN/m. Using the coefficients obtained from the fitting, the Lame´ constants λ and µ, as well as the Poisson ratio and the Young’s modulus have been calculated for HSA and for IgG at low surface pressures. The results are summarized in Table 3. The shear modulus µ of HSA at 19 mN/m compares favorably with the shear moduli given in refs 22 (shear measurements on spread films) and 8 (shear measurements on adsorbed films), for equivalent albumin concentrations. These data are also presented in Table 3. (20) Chiarelli, P.; Basser, P. J.; De Rossi, D.; Goldstein, S. Biorheology 1992, 29, 383. (21) Ahluwalia, A.; De Rossi, D.; Monici, M.; Schirone, A. Biosens. Bioelectron. 1991, 6, 133. (22) Boyd, J.; Sherman, P. J. Colloid Interface Sci. 1970, 34, 76.

6. Discussion 6.1. Behavior of Albumin at the Interface. Albumin has been extensively studied at the gas-water interface, and its mechanical behavior at different surface pressures can be fairly well explained by McRitchie’s segments, trains, loops, and tails model of an extended polymer.23 By comparing the dimensions of native albumin ((13 × 3 × 3) nm3), to those at the interface, it can be seen that albumin unfolds to occupy an area of about 7 times its native area. At low pressures, the albumin molecules, once spread, unfold and the surface pressure slowly increases while the molecules undergo conformational changes.3 When the molecules have reached an equilibrium state, they are far apart and do not exhibit strong cohesive interactions. In the low-pressure region, the molecules can be likened to springs, and their behavior, on the time scales of these measurements, can be described as purely elastic (Figure 2). In the plateau region the molecules form trains and loops at the interface whereby segments are expelled into the subphase as a consequence of the decreasing area available per molecule. Due to the expulsion of segments, the pressure does not increase significantly with decreasing area. In this region, the molecules are close together, and movements may be hindered by interactions between loops, tails, and side chains, and may also give rise to irreversible deformations. In this region then, the HSA film exhibits viscoelastic properties (Figure 3). At higher pressures, in the steepest zone, entire molecules begin to desorb irreversibly, and the film may even form multilayers. This very simplistic, but generally accepted, picture of albumin explains in broad terms the rheological behavior of the film in the three zones of the isotherm. The three time constants that are observed can be related to relaxation processes within the film. As already mentioned, the longest time can be attributed to the slow dissolution of the molecules into the subphase. The other time constants may represent refolding or internal rearrangement mechanisms.8 6.2. Viscoelastic Properties of Immunoglobulin G. IgG is a very stable Y-shaped molecule consisting of four polypeptide chains which are linked to each other via disulfide bonds. The total number of disulfide bonds is 16-24 and is similar to the number of S-S bonds (17) in native albumin. An important feature of IgG is its hinge region, which permits the angle and the relative orientation between the arms of the Y to vary greatly. The molecule thus possesses a large degree of flexibility in this region. Unfortunately literature on the basic physical properties of IgG at the interface is rather scarce despite its increasing use in thin films for fabricating sensing surfaces. The molecules behave in a manner which has yet to be described and explained completely. Ellipsometric, X-ray scattering, and deposition studies have shown that the IgG molecule maintains its native structure on deposition (23) MacRitchie, F. Chemistry at Interfaces; Academic Press: San Diego, 1990; p 146.

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and have indicated that at high surface pressures the molecules are vertically oriented in a random up-down manner at the gas-water interface.24 It has also been demonstrated that IgG retains its antigen binding properties after transfer from the gas-water interface to a glass slide.1 These results indicate that IgG does not undergo the large conformational modifications that albumin does at the gas-water interface. Figure 6 shows that the elastic parameters A, B, and C increase with pressure, until about 17 mN/m, indicating that the film is becoming more rigid due to increased close packing. There is only a slight increase in the values of the time constants (Figure 7) until about 16 mN/m, at which point they begin to decrease sharply. It is likely that in this zone the molecules are at their most closely packed, thus limiting any additional increase in the processes that give rise to viscous phenomena such as intermolecular friction. A further increase in pressure possibly initiates some desorption phenomena, and the elastic moduli begin to decrease while the time constants have a slight inflection. Above about 18 mN/m, the mechanical behavior of the film becomes more complicated. The behavior of the elastic and viscous parameters at pressures above 18 mN/m could be attributed to the deformation of the hinge region. As the hinge is strained, the system becomes more rigid, and the time constants decrease and correspondingly the elastic parameters, A and B, increase again. This phenomenon is limited to short time scales and does not influence the term associated with C. Higher pressures probably cause molecular desorption to predominate thus rendering the film unstable and prone to collapse. Anomalus behavior of IgG films at high pressures has also been noted in ref 24 in (24) Ahluwalia, A.; De Rossi, D.; Schirone, A. Thin Solid Films 1992, 211, 726.

Ahluwalia et al.

which an isopiestic point, between two zones with fluidlike and solid-like mechanical properties, is observed. 7. Conclusion A method of determining the rheological properties of protein monolayers using small uniaxial step deformations and forces is presented. For films at low surface pressures, it provides the same information as the torsional methods normally used to study floating monolayers, with the advantage that no instrumentation in addition to a computer-controlled film balance is required. The results on albumin films are in good agreement with both shear and translational measurements in the literature. It is shown that for HSA and for IgG at low pressures, the measurements described are sufficient to completely characterize the elastic constants of the monolayer. By applying the classical equations of elasticity for a twodimensional system to the results, it is possible to obtain the values of the Lame´ constants, Poisson ratio, Young’s modulus, 2-D hydrostatic modulus, and the uniaxial surface elastic modulus of the monolayers. The mechanical properties of IgG reveal a rather complex behavior at high pressures, which has not been observed in other protein films. This behavior may be attributed to the flexible hinge region of the molecule. The conclusions on IgG are limited because of the lack of information available on this protein at the interface and can only be extended by a more complete understanding of the physical processes governing IgG and other proteic films. This can be achieved after several different aspects of the monolayer have been investigated, for example, using molecular and fine structure analysis techniques, as well as more traditional ones such as surface potential measurements. LA940753X