A “fluid cantilever” to detect amphiphilic biomolecules

Colloids and Surfaces A: Physicochem. Eng. Aspects 343 (2009) 12–19

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Colloids and Surfaces A: Physicochemical and Engineering Aspects journal homepage: www.elsevier.com/locate/colsurfa

A “fluid cantilever” to detect amphiphilic biomolecules Cyril Picard a , Laurent Davoust b,∗ a b

University of Grenoble, UMR LEGI, Microfluidics, Interfaces & Particles Team, BP 53, 38041 Grenoble Cedex 9, France CNRS, LEGI, Microfluidics, Interfaces & Particles Team, BP 53, 38041 Grenoble Cedex 9, France

a r t i c l e

i n f o

Article history: Received 30 September 2008 Received in revised form 5 January 2009 Accepted 30 January 2009 Available online 5 April 2009 Keywords: Label-free Interferometry Capillary waves Meniscus waves Adsorption Surface tension Rheology Surfactants Spectrum Aging

a b s t r a c t Label-free techniques are now identified as relevant tools to detect any biological material which cannot be grafted by a fluorescent tag, for instance. In this growing context, a new detection strategy based on the resonance of micrometric capillary waves is proposed to detect biomolecules. The sensitivity of the surface rheology to the (bio)chemical content of a liquid surface is found to behave as an original transduction means to convert any slight change in the surface composition into a detectable change in the surface geometry. Micrometric deformations are promoted steadily along a functionalised liquid surface by generating linear meniscus waves from a capillary boundary layer which develops all around the outer circular edge. The geometry of the subsequent nearly standing waves net is accurately characterised using refractometry and interferometry techniques. This paper focuses on this last technique which is especially developed to characterise the waves amplitude at the surface centre with a sensitivity of a few hundreds of nanometers. As such, local interferometry allows us to follow in real-time the resonance frequencies of the wave net and finally, to detect any slight change in surface tension induced during the trapping of solubilised biomolecules at the functionalised surface. In order to clearly illustrate the potentialities of a resonant wavy meniscus, use is made of two complementary oligonucleotides. This label-free technique is demonstrated to deliver useful information on the adsorption rate of initially solubilised DNA strands to a lipidic matrix. By following the time-dependent frequency spectrum of the surface waves, it is possible to discriminate between single-stranded DNA strands and double-stranded DNA strands. This new label-free sensor can therefore be considered as a liquid analogy of the well-known cantilever technique. © 2009 Elsevier B.V. All rights reserved.

1. Introduction Since the early works on the enzyme-linked immunosorbent assay (ELISA) in the 1960s, as a first successful attempt to carry out immunoassays without the threat of radioactive labelling, huge efforts have been conducted to facilitate the detection and the characterisation of target molecules (antibodies, antigenes, etc.). High-throughput systems such as microarrays are now available [1]. However, most of them are still based on labelling or on the use of secondary probes even. As such they often strongly complexify the precise understanding of primary bimolecular interactions. Label-free techniques provide new ways to monitor directly the binding between a target analyte and a molecular probe. For instance, use is made of various detection means based on electrical, electromechanical (quartz microbalance, microcantilever), or optical (interferometry [2,3], surface plasmon resonance) transduction. Sensors based on surface plasmon resonance (SPR), probably the most advanced technology, have demonstrated the possibility to precisely measure adsorption rates and kinetics of adsorption

∗ Corresponding author. Tel.: +33 04 76 82 50 38; fax: +33 04 76 82 52 71. E-mail address: [email protected] (L. Davoust). 0927-7757/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfa.2009.01.023

from sensitive real-time monitoring of binding processes. However, while in many biological systems, recognition processes between target and probe molecules are often involved in cell membranes also characterized by a non-negligible degree of intrinsic mobility, it is worthy to note that all the sensors developed until now are based on the immobilisation of molecular probes on solid substrates. A new methodology, which relies on the specific functionalisation of a liquid surface, for instance covered by an appropriate lipidic layer, was recently put forward in the promising framework of the label-free biosensors. Beyond the straightforward advantage that Langmuir mono- or bi-layers can behave as good biomimetics of cell membranes, preserving both the conformation and the integrity of the captured biomolecules (compared to monolayers on solid support [4]), new prospects are offered through the possibility to deform a functionalised fluid interface. For instance, bindinginduced adsorption at a functionalised liquid surface can be speed up expanding the surface area. The detection threshold can be also improved by flow-focusing adsorbed biomolecules within the interface [5,6]. This paper bears on a new label-free sensing technique which takes full benefit of the fluidity of a liquid–gas interface [7]. Based on the sensitivity of resonant capillary waves to the chemical content of a meniscus, our system is the fluid counterpart of the

C. Picard, L. Davoust / Colloids and Surfaces A: Physicochem. Eng. Aspects 343 (2009) 12–19

well-known cantilever technique. More particularly, while cantilevers are designed to detect a frequency shift induced by a change in molecular loading, the “fluid cantilever” as presented in this paper is based on a frequency shift also driven by surface aging. Any slight change in the biochemical content of a liquid meniscus affects durably its (surface) rheology, in particular its surface tension which in turn impacts upon the resonance frequencies of the surface waves. Beyond the need to justify the hydrodynamical peculiarities of the meniscus waves, the purpose of this paper is to give further insights into the interferometric technique developed for the real-time measurement of the waves amplitude. This technique is validated thanks to an optical technique based on refractometry [8]. We demonstrate that the resonance frequencies can be precisely identified from the amplitude spectrum measured by interferometry. As a consequence, it is possible to assess the adsorption kinetics of the biomolecules at the interface as well as the time-dependence of the surface tension. Finally, it is demonstrated that one gains qualitative insights into the time-dependent surface rheology. As an illustration of its sensitivity, our optical technique based on interferometry is finally used to discriminate between single-stranded and double-stranded complementary oligonucleotides when they contribute to surface aging by binding to cationic lipids headgroups spread at the interface.

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Fig. 1. Schematic of the location of the excitation and damping forces for the menis) Gravitational cus waves (on the left) and the Faraday waves (on the right). ( ) viscous damping in the Stokes layers, ( ) damping excitation forces, ( ) damping in the capillary boundary layer due due to the surface forces and ( to the contact line dynamics.

2. Meniscus capillary waves in a small oscillating container The experimental setup under consideration in this paper is basically close to the one involved in previous studies devoted to surface rheology [8,9]. A vibrating cylindrical cell made of glass and filled with water is put forward as a demonstration tool. As such it has been designed at a macroscopic scale for practical reasons (diameter: 50 mm, depth: 45 mm). The main constraint for a potential miniaturisation concerns the meniscus size which necessarily needs to be wider than a few hundreds of ␮m2 so that the meniscus can be populated at least by a couple of capillary cylindrical waves. In this paper, the relevance of meniscus waves as a label-free transductor is demonstrated putting forward the strong dependence of the geometry of the waves induced by the cell vibration to the biochemical content of the interface. The waves of interest here originate from the oscillation of gravity experienced by the liquid surface in the moving frame of the vibrating cell. In such conditions, two types of parametrically induced surface waves can be excited according to the form of the right hand side of the following Eq. (1) written for one particular wave mode, k, in the large depth limit [10]: ∂2 k + ∂t 2



kg +

k3 





k +  (k ) = kg˛zo 1 +

k zo



cos ωt

(1)

where ω is the forcing angular frequency,  is the density of the supporting sub-phase, ˛ is a control parameter of the forcing term, zo is the local altitude,1  k is the local vertical (transversal) displacement of the waves (surface elevation) for a wave number k and ( k ) is a function which accounts for the radial wave damping. If the waves amplitude is large compared to zo , the term on the right hand side (RHS) of (1) simplifies as, kg˛ k cos ωt, and (1) is nothing but the well-known Mathieu equation used to characterize the extensively studied Faraday waves [11,12]. As a result of the spatially uniform forcing term, the Faraday instabilities are fully standing waves (see Fig. 1), whose amplitude is growing exponentially for any excitation

1 The vertical position of the surface center when the meniscus is at rest is taken here as the reference. For (1) to be valid, the altitude zo stands for the profile of the static meniscus whose curvature is supposed negligible compared to the surface curvature induced by the waves.

Fig. 2. The organisation of the viscous and capillary boundary layers along the cylindrical side wall of the vibrated cell and their respective thicknesses lv and lc with the surface tension , the bulk molecular viscosity , the bulk density  and g the gravity constant. The spatial dependence of the vertical surface displacement is described with the zero-order Bessel function of the first kind J0 and the complex wave number k.

frequency close to the discrete eigen frequencies associated to the radially limited cell. On the other hand, for a forcing parameter much smaller than a critical value ˛c which depends on the excitation frequency (see e.g. [13] for further details), the excitation term becomes negligible compared to the damping term.2 In that case, the excitation term writes according to, kgzo cos ωt, and (1) simplifies to a linear ordinary differential equation. Hence, those linear capillary waves, referred to as meniscus waves, are oscillating at the forcing angular frequency ω, and are generated from the capillary boundary layer staying around the outer edge of the cylindrical side wall (Fig. 2). Since the excitation source is localised and controlled to yield cylindrical waves (2D axisymmetry), a spatially uniform viscous damping applies radially along the liquid surface (see Fig. 1). Also, the meniscus waves can be considered as the superposition of two travelling capillary waves. First, a radially inwards travelling wave (centrifugal component) is excited from the outer edge where its wave vector is necessarily normal to the side wall [9,14]. Due to a radial focusing and a reflection of this centrifugal component at the surface centre, a second radially outwards travelling wave is excited (centripetal component). As a result, meniscus waves are truly standing only at the surface centre while they can be considered as nearly standing elsewhere all along the liquid surface.

2 If the local altitude zo is much larger than the amplitude  k , this is no longer true near a capillary boundary layer which develops along the circular edge at the top of the cell (Fig. 2).

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Fig. 3. Optical scheme for the interferometry technique with the typical optical paths followed by the reflected laser beams whether the surface center was virtually tilted.

Due to the finite radial extent of the interface and the linear damping of the waves, the system exhibits a series of linearly damped resonance modes. As a result, for each resonance frequency, the meniscus waves are still excited in linear regime while they fulfill the boundary conditions imposed by the oscillating cylindrical cell (boundary value problem). Beyond the meniscus waves, Faraday waves stand as a second kind of parametrically induced surface waves and they can be excited as well in our experiments. But as a matter of fact, our experiments confirm the statement established by Henderson et al. [15] that the stationary regime of the Faraday waves seems to be not enough sensitive to the molecular content of the wavy surface. This is one of the main reasons why the transient regime due to the decay of Faraday waves induced by the excitation shutdown has been extensively investigated, in particular as a means to characterise the rheology of a liquid surface covered by a layer of surfactants [15–20]. The frequency shift associated to the Faraday waves decay depends indeed on dissipation sources such as viscous surface and bulk forces as well as other various damping phenomena, especially the energy dissipation due to the contact line dynamics [18–20]. Unlike Faraday instabilities which are growing or decaying exponentially, meniscus waves can be sustained in linear stationary regime at a tunable frequency and with an amplitude as small as required to avoid breakup of chemical bonds within (or between) the molecular complexes adsorbed to the Langmuir film. Surprisingly, those meniscus waves have been seldom considered for a surface rheology characterisation although they are much more suitable than decaying waves for such a purpose. Unlike the time damping of the decaying wave which depends on various dissipative phenomena, the spatial damping of the meniscus waves depends solely on the viscosity of the sub-phase and the surface forces (if the contact line is pinned at the outer edge). Moreover, when being generated in a stationary regime, the meniscus waves are particularly convenient to investigate kinetics of the (transient) surface aging associated with the capture of biomolecules [21]. The meniscus waves of interest here are supplied with an amplitude as small as a few hundreds of nm. Such a small deformation of the liquid surface is transmitted from the cell vibrations which are precisely monitored from three electrodynamical sources distributed all around the cell under a supporting plate [7,9]. The vibration frequency is tuned within the rheological frequency range (10–100 Hz).

3. Materials and methods 3.1. Relevance of local interferometry Many optical techniques are available to investigate surface waves dynamics [22–24]. For a simple and accurate characterisation of the meniscus waves, two complementary optical techniques have been developed. Refractometry permits to measure the slope of the interface while interferometry allows us to measure the amplitude of the waves at the surface centre. Our goal here is to describe the interferometric technique specifically designed for our application and to illustrate its capabilities, the refractometric technique already presented in the literature is mainly used here as a calibration tool. 3.1.1. Optical setup Interferometry is a simple technique of high sensitivity particularly suitable to quantify the amplitude and the spectral changes induced by surface aging. A small time response, and a good spatial resolution as well, are among the main advantages of this technique whose signal to noise ratio is fairly good. The very point chosen to carry out the interferometric measurements is the surface center for two major reasons. • First, the amplitude of the axisymmetrical waves is maximal at the surface center (around 1 ␮m) where an anti-node is standing; this is exactly at the surface center where the travelling components of the meniscus waves are vanishing. • As a result, the surface center is the only point where the surface is expected to remain theoretically horizontal during oscillatory surface elevation. The apex of the anti-node, localised at the centre of the liquid surface, can therefore be used as a mirror translating vertically while staying parallel to the cell bottom. The interferometric signal is built from the phase lag between two successive reflections of the incoming laser beam: a first laser reflection on the transparent cell bottom and a second reflection of the transmitted part of the laser beam on the center of the liquid surface where the best sensitivity is achieved. From the time-dependence of the phase lag between the two optical paths, it is therefore possible to identify the vertical displacement of the surface center in the cell frame. The initially horizontal incoming laser beam is redirected vertically towards the interface through the transparent cell bottom thanks to a tilted

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mirror M (Fig. 3). Both reflected beams keep exactly the same optical path as the beam issued from the laser source until they reach a beam splitter BS introduced here to separate the beams of interest from the incoming beam and to drive them up to the avalanche photodiode detector (APD). This APD sensor (Hamamatsu 5C5460-01) delivers a signal proportional to the time-dependent light intensity resulting from the interference of the two reflected beams. The light intensity I is thus formed by a succession of Doppler bursts whose instantaneous frequency is directly proportional to the surface displacement amplitude [25,26]:

I=

c 4









n εe Ac 2 + A 2 + 2Ac A cos 4 o sin(ωt) e

(2)

where εe and e are the electrical and magnetic permitivities, c is the light celerity in the vacuum, Ac and A are the amplitudes of the electric fields respectively reflected on the cell bottom and on the fluid interface, n is the optical index of the water, = 633 nm is the laser wave length and  o is the amplitude of the surface elevation at the surface centre. It is worthy to note from Eq. (2) that  o is independent on the magnitude of the light intensity and as such it can be identified regardless of the gain of the APD sensor. This constitutes one of the major advantage of the interferometry which does not require calibration. Although the surface center is supposed to stay horizontal during its vertical oscillatory elevation, it can be sporadically disrupted by small angular artifacts. To minimized their impact on the length of the optical path followed by the beam reflected at the fluid interface, two convex lenses L and LAPD are inserted at a distance one focal length apart from the fluid interface and from the APD, respectively. The first function of the lens L , is to focus the collimated incoming beam on the interface so that capillary wavelength as small as 100 ␮m can be investigated. The second function of L is to deflect the beam reflected on the interface whatever its potential angular deviation, so that it becomes parallel to the incoming beam once it has passed through L . The collimated incoming beam precisely adjusted to pass through the center of L is just slightly uncollimated on its way back after it has been reflected on the cell bottom. The lens LAPD is then used to focus the beams delivering the Doppler signal from the APD. The increase of the optical path due to the potential angular deviation of the liquid surface is then confined between the lens L and the interface and between the lens LAPD and the APD. In these two regions, the erroneous increases of the optical path write according to the small angular artifact,  , and the focal length, f and fAPD : x =

f 2 − f  2  f , cos(2 )

xAPD =



2

2

fAPD + f tan(2  ) − fAPD  2 

2

2

f . fAPD

The error can thus be minimized decreasing f and increasing fAPD . In order to keep a good focalisation on the small APD sensor, one prefers to keep a limited distance fAPD and to place L as close as possible of the cell bottom to reduce f as much as possible. Finally, the focal lengths that have been chosen are fAPD = 250 mm and f = 75 mm as a fairly good compromise between available space, the need of a good focalisation of the beams on the APD and a measurement accuracy as high as possible. To avoid any interference with the laser beam coming from the laser source, the lens L and the beam splitter BS are very slightly tilted in order to prevent any parasitic reflections to reach the APD. In this way the light power received by the APD depends solely on the phase lag between the laser beams coming respectively from the cell bottom and the liquid surface.

Fig. 4. Absolute value of the time derivative of a typical signal given by the APD (dash line with markers) and visual guide (solid line –). The agitation frequency is identified from the time derivative as 45.3 Hz.

3.1.2. Identification of the waves amplitude The fast interferometric measurements at the surface centre are analysed with a three-step procedure to identify the waves amplitude. First the interferometric signal is used to calculate the waves frequency. Checking it is equal to the vibrations frequency, one confirms the linearity of the exciting meniscus waves. To this purpose, a fast Fourier transform (FFT) of the time derivative of the interferometric signal is performed. The time derivative is based indeed on a combination of frequency modulation according to the interface vertical velocity and on an amplitude modulation according to the vibration frequency (Fig. 4). This vibration frequency is initially hidden within the original signal which is purely frequency modulated (Fig. 6). Its instantaneous frequency depends only on the instantaneous velocity of the fluid interface in the cell frame. This step is particularly useful as well to eliminate any signal that would be too noisy to be compatible with an accurate determination of the wave amplitude. To identify the wave amplitude with good accuracy, the interferometric signal is acquired during 10 agitation time periods. The time dependence of the interferometric signal can be expressed only according to the agitation frequency previously determined and to the waves amplitude as shown by Eq. (2). Rather than performing a time consuming sliding Fourier transform to get the instantaneous frequency, a direct identification process of the waves amplitude is implemented under Matlab software making use of Eq. (2). The amplitude,  o , is sought within an initial range of values defined from a rough assessment of the maximal frequency,3 fm = 2ω o n/ , deduced from the FFT of the whole APD signal (Fig. 5). Identification is performed independently of each of the ten acquisition periods in order to be less sensitive to any change in the signal amplitude from one period to another one. The wave amplitude is finally calculated as the averaged value over the ten acquisition periods. The standard deviation gives an uncertainty of the order of 10%, which takes both into account the experimental fluctuations of the amplitude and the uncertainty attached to the identification process. A typical experimental signal and model fit are shown in Fig. 6.

3 The maximal frequency fm of a signal cos (˝(t)) is the maximal value of the instantaneous frequency fi defined as fi = 1/2 ∂˝/∂t.

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Fig. 7. (o) Time dependence of the waves frequency for a frequency window (45–55 Hz) swept continuously. (䊉) The corresponding waves amplitude when the DOGS monolayer is deposited on a water sub-phase (see Section 3.2). Fig. 5. FFT of the APD signal. The agitation frequency is 45.3 Hz. The wave amplitude is 1.53 ␮m, this corresponds to a maximum instantaneous frequency of the burst of 1.4 kHz, while the direct FFT delivers an approximate frequency of 1.8 kHz.

3.1.3. Waves vibration frequency To investigate the frequency dependence of the wave amplitude, the frequency at which the cell is vibrated is gradually modified according to time. This frequency modulation is monitored so that the frequency change is smaller than 0.3% over 10 periods of oscillations (which is the typical acquisition time used for one surface elevation measurement). Unlike a Heaviside variation which might be imposed to study decaying waves [15], a strategy based on a continuous frequency sweeping does not induce any parasitic perturbations on the wavy surface and allow us to work in quasi-stationary regime. The time dependence of the waves amplitude can thus be monitored during a linear increase of the frequency over a frequency window centered around a natural frequency of the system (see Fig. 7). As illustrated in the central graph of Fig. 8, the waves amplitude spectrum as obtained from local interferometry during frequency scanning is fully validated by the refractometric technique developed for a discrete number of frequencies during stationary regime. The radial dependence of the amplitude of the surface slope measured by scanning the liquid surface with refractometry is plot around the central graph (8). The waves amplitudes at the surface center identified from each of the slope profiles are plot in the central graph with square markers. The fairly good agreement between both measurement techniques allow us to continue in all confidence with interferometry only.

judiciously chosen to present a strong affinity with the biomolecular probes to be trapped to the interface. Unlike common biochips whose solid substrate requires to be functionalised by a matrix of molecular probes before adding on it any target liquid sample, a liquid surface is easily accessible from above and therefore can be covered by a lipidic monolayer at any time [5]. This gives as well the possibility to inject simultaneously the probe and target molecules within the sub-phase and to collect them after binding to the lipidic monolayer. On the other hand if the purpose of the measurement is to study the kinetics of the probe/target recognition process (hybridization if DNAs strands for instance), then the interface can be initially covered with the lipidic monolayer and functionalised with the probes before adding target molecules within the sub-phase. Our aim here is to exemplify the first approach which constitutes a specific feature of a fluid (label-free) biochip. For this purpose, two complementary single-stranded oligonucleotides, (dT)22 and (dA)22 (sequences of 22 thymine and 22 adenosine bases, provided by Eurogentec) are diluted in ultrapure water (resistivity: 18.2 M m). Two sub-phase compositions are considered: • A first sub-phase is enriched with (dT)22 and (dA)22 , both of them at a bulk concentration of 3.9 × 10−8 mol L−1 . To let the complementary sequences to hybridize, the resulting buffer is systematically prepared 24 h before starting the experiment. All buffers are stored at a temperature of 4 ◦ C. • The second sub-phase is enriched with (dT)22 . For comparison purposes, twice the amount of (dT)22 is diluted so that a final buffer concentration of 7.8 × 10−8 mol L−1 is finally obtained.

3.2. Biochemical samples Most of the biomolecules of interest are not spontaneously amphiphilic. To be functionalised the interface needs to be covered by an appropriate layer of amphiphilic molecules, typically lipids

To capture the oligonucleotides at the liquid surface, a Langmuir monolayer made of dioctadecylamidogly-cylspermine (DOGS) (>98% purity, Promega) is deposited on the water sub-phase. The DNA strands exhibit indeed a strong affinity for the DOGS (cationic)

Fig. 6. (䊉) Typical example of an APD signal. (—) Corresponding curve fit deduced from Eq. (2) for the excitation frequency, ω/2 = 45.3 Hz, and a wave amplitude,  o = 1.53 ␮m.

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Fig. 8. Central figure: the amplitude versus frequency around one resonant frequency of 49.2 Hz for a pure water surface with data ( ) measured from interferometry and seven discrete data () deduced from the slope curves. Series of seven inserts: ( ) slope curves along the liquid surface for a discrete series of frequencies (f = 47, . . ., 51 Hz), as measured from refractometry.

lipid whose spermine headgroup is able to anchor in the minor groove of DNA [27]. Note also that the respective affinities of (dT)22 and (dA)22 for the DOGS lipids are similar [28,27]. The DOGS lipids are solubilised in pure chloroform ([DOGS] = 0.5 mM). Because of the high volatility of this solvent, the concentration of the DOGS solution changes rapidly each time the solution is used. As a result, the precision one gets for the surface concentration is fairly poor and the uncertainty is estimated to be of the order of 15%. 4. Results The mechanical properties of the interface depend on the interactions between the different molecules trapped at the interface. The DOGS monolayer on its own has a noticeable impact on the surface properties and as such, it is worthy to investigate its impact upon the resonant modes of the meniscus capillary waves. As illustrated in Figs. 9 and 10, one notices a drastic damping of the resonance amplitude associated with a clear shift of the natural frequencies. For larger and larger amounts of DOGS, the resonance frequencies shift to lower and lower values while the vertical amplitude of the resonant modes first decreases and finally

Fig. 10. Natural frequencies and their dependence on the DOGS surface concentration for two radial modes: ( ) 9 nodes and ( ) 10 nodes.

slightly increases. From Fig. 11, one notices that the resonance wave numbers,4 kr , do not depend on the molecular content of the surface. Consequently, as suggested by [7], once the resonance waves numbers are known, they can be used to calculate the surface tension from the dependence of the natural frequencies to the surface concentration via the simplified dispersion relation which follows:



iωr

kr + m kr





2

= −ωr 2 1 −

m kr

2

kr g ωr + i(kr + m) + − ωr ωr kr



2 (3)

with , the viscosity of the sub-phase, , the density of the subphase, kr , the wave number at the resonance and where m = 2

kr + iωr /. Fig. 12 compares the surface tension, as obtained from Eq. (3) and the resonance frequencies (Fig. 10), to the surface tension at ther-

Fig. 9. Resonance amplitudes and their dependence on the DOGS surface concentration for two radial modes: () 9 nodes and (o) 10 nodes.

4 This figure has been plot combining interferometry and refractometry in order to obtain the frequency dependence of the wave number for each surface concentration.

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Fig. 11. Impact of the DOGS surface concentration upon the dimensionless surface elevation against the wave number ([molecules, nm2 ] = () 0; () 0.5; () 0.84; () 0.92; (♦) 1.07; () 1.23).

modynamical equilibrium, as measured with a Wilhelmy plate in a Langmuir trough. The significant agreement between both surface tension suggests that a local measurement based on interferometry can be used to perform surface tension measurement. It can also be used to follow the kinetics of surface aging. While the variations of the resonance frequencies are easily interpreted as surface tension-dependent, the variations of the resonant amplitudes are more complicated to interpret. Since the meniscus waves originates from the dynamical deformation of the curved surface in the capillary boundary layer, there is a combination of the vertical and horizontal displacements in this boundary region nearby the surface. These displacements have to match the displacements observed in the core region of the surface. These displacements are controlled by the wave number k and the complex horizontal and vertical waves amplitudes,  o and  o , respectively, whose ratio writes according to the surface viscoelastic modulus ε [10]:



1

i2 ε o − 1− 1 2 1 3 o 3  3 2 ω2

−1 (4)

From Eq. (4), it appears that any changes of the viscoelastic parameter ε can contribute to a phase lag between the horizontal and vertical displacements and also to a change in their relative amplitudes. These changes are potentially combined with an increase of both the radially inwards traveling component and the spatial damping of the waves. It appears clearly that the variation of the resonance amplitudes cannot be expressed from one single parameter.

Fig. 12. Dependence of the surface tension on the DOGS concentration as measured by interferometry (markers) and with a Langmuir trough (line).

Fig. 13. Succession of resonance frequencies during surface aging. The axisymmetry of the meniscus waves gives rise to radial eigenmodes with circular wrinkles radially distributed along the liquid surface. Except for the situation of a pure water system (8 radial eigenmodes), the number n of radial eigenmodes starts from 9 and is incremented by 1 for each new curve rising from the bottom to the top of the figure. (♦) Pure water system, () pure water sub-phase covered by a DOGS monolayer, () sub-phase enriched with dA22 –dT22 and covered by a DOGS monolayer, () sub-phase enriched with dT22 and covered by a DOGS monolayer.

To investigate the sensitivity of the resonance frequencies during the capture of the oligonucleotides to the interface, interferometry measurements are performed by scanning repeatedly a frequency window ranging between 45 and 55 Hz (Fig. 7). The size of this window is chosen as small as possible to be scanned as many times as possible during a given time period while being large enough to contain at least one resonance frequency. In Fig. 7 there are initially two resonance frequencies, approximately 46 and 54 Hz. Because of the chemical aging of the interface, one observes an increase of the resonance frequencies and progressively the second resonance point goes out of the frequency window. As shown in Fig. 13, for a pure water surface, the resonance frequency of about 50 Hz is remarkably stable (standard deviation less than 0.1 Hz). When a DOGS monolayer is spread over the surface, the frequency spectrum shifts immediately followed by a slow transient regime over 50 min. We believe that thermodynamical equilibrium is achieved after a quick Marangoni-induced spreading followed by a 2D diffusionlimited regime associated to a much longer time scale. We consider now a water sub-phase enriched with oligonucleotides. As soon as DOGS are spread over the surface, a strong shift of the natural frequencies down to much smaller values is clearly made evident with the succession of three resonance modes observed within the frequency window. This global trend is also confirmed when the sub-phase is enriched with non-hybridized oligonucleotides. This time, up to four different resonance modes cross the frequency window. Hence, during surface aging, because of the gradual shift of the resonance frequency, several eigenmodes can resonate at a same frequency but at different times essentially controlled by the kinetics of the oligonucleotide capture to the lipidic matrix. One notices that the succession of the resonance modes is faster in the case of single-stranded DNAs than in the case of double-stranded DNAs. The growing number of radial modes during DNA adsorption at the lipidic monolayer can be connected to the arising of additional circular wrinkles along the waves net. Clearly, this finding is fully consistent with a liquid surface more and more rigid as long as the molecular densification increases. A growing importance of the radially inwards travelling component is also expected.From Fig. 13, one can built the dependence of the dynamical surface tension as shown in Fig. 14. The surface tension curves calculated from the successive resonance wave numbers are perfectly superimposed which further confirm the reliability of the method. Use is made of a log scale for the time axis to clearly show the early times of the

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ing with us valuable knowledges about the model system based on DOGS and DNA strands. This research was financially supported by a grant from the French ministry of research. References

Fig. 14. Dynamic surface tension for several system compositions. () Pure water sub-phase covered by a DOGS monolayer, (䊉) sub-phase enriched with dA22 –dT22 and covered by a DOGS monolayer, () sub-phase enriched with dT22 and covered by a DOGS monolayer. The dashed lines are a visual guides.

capture process. As expected, the surface tension is initially poorly affected by the sub-phase content. It is only after 2 min approximately that the curves start to deviate one from each other. The first 2 min of the transient regime reflect only the establishment of the DOGS monolayer all along the surface; after roughly 2 min, the sub-phase contents fully contributes to the dynamical surface tension. 5. Conclusion The resonance behaviour of an air/water interface populated by capillary meniscus waves is used as a label-free detection method to investigate the capture of biomolecules at the interface. This technique is applied to a monolayer composed of DOGS lipids spread over an aqueous sub-phase. Due to electrostatic interactions, DNA strands, previously solubilised in water sub-phase, are known to bind to DOGS at the upper surface [28,27]. The investigation of the kinetics due to DNA immobilization at the lipidic monolayer demonstrates a strong sensitivity of our technique to the sub-phase composition. In particular, a shift of the resonance frequencies is clearly made evident during DNA-lipid binding. An evidence is given that the technique based on the resonant spectrum of the meniscus waves clearly discriminates between single-stranded DNAs and double-stranded DNAs. Nevertheless, at the time being, the technique does not pretend to give detailed insight into the chemical kinetics within the underlying sub-phase. For instance, a possible denaturation of the double-stranded DNA complexes dA22 –dT22 followed by individual adsorption of the subsequent single-stranded oligonucleotides dA22 and dT22 to the lipids is also possible. We believe that this new label-free technique is somewhat the fluid analog of the well-known cantilever technique. In the same way, the specificity of the biochemical capture is essentially dependent on the relevance of the surface functionalisation. Acknowledgements The authors are grateful to Dr. Agnès Girard-Egrot, Dr. Daphné Thomas and Prof. Loïc Blum (LGEB, University of Lyon) for shar-

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