On the thermodynamics of biomolecule surface transformations

Journal of Colloid and Interface Science 375 (2012) 1–11

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Feature Article

On the thermodynamics of biomolecule surface transformations Stefania Federici a, Giulio Oliviero a, Daniele Maiolo a, Laura E. Depero a, Italo Colombo b, Paolo Bergese a,⇑ a b

Chemistry for Technologies Laboratory and INSTM, University of Brescia, Via Branze, 38, I-25123 Brescia, Italy Department of Industrial Engineering and Information Technology, University of Trieste, Via Valerio, 6/a, I-34127 Trieste, Italy

a r t i c l e

i n f o

Article history: Received 22 November 2011 Accepted 4 February 2012 Available online 24 February 2012 Keywords: Thermodynamics Biomolecules Surfaces Molecular-recognition Molecular machines Nanoparticles self-assembly Biosensors

a b s t r a c t Biological surface science is receiving great and renewed attention owing the rising interest in applications of nanoscience and nanotechnology to biological systems, with horizons that range from nanomedicine and biomimetic photosynthesis to the unexpected effects of nanomaterials on health and environment. Biomolecule surface transformations are among the fundamental aspects of the field that remain elusive so far and urgently need to be understood to further the field. Our recent findings indicate that surface thermodynamics can give a substantial contribution toward this challenging goal. In the first part of the article, we show that biomolecule surface transformations can be framed by a general and simple thermodynamic model. Then, we explore its effectiveness by addressing some typical cases, including ligand–receptor surface binding, protein thin film machines, nanomechanical aspects of the biomolecule–nanoparticle interface and nanomechanical biosensors. Ó 2012 Elsevier Inc. All rights reserved.

1. Introduction Topics that seem very distant biologically are next door neighbors in physical chemistry of surfaces. This was hinted 15 years ago by Bengt Kasemo, when he stated: ‘‘It is likely that the symbiosis with biology/medicine will be as important for surface science for the coming thirty years as the symbiosis with semiconductor technology, catalysis and materials science have been in the past thirty years’’ [1]. His vision appears more prophetic than ever today, when it is without question that life science is among the most lively and promising emerging fields of surface science (and vice versa). One may name this area biological surface science and think about it as the branch that deals with ‘‘pure’’ biological surface systems as well as ‘‘hybrid’’ biological–inorganic interfaces, on the typical length scales of molecules, membranes, and cells. Colloidal and interfacial aspects of biological systems have been investigated to some extent in the past years up to date (see for example Refs. [2–10]), but it is fair to say that they were relegated in a sort of niche if compared to biochemical and molecular biology aspects. In the last years, however, they have been brought inexorably to the fore by the advent of the application of nanoscience concepts, nanomaterials, and nanotechnologies to life science. For example, it is emerging the view of the cell as a collection of biomolecule nanomachines, from the protein assemblies featuring the highly coordinated moving machines that supervise cell reactions [11] to bacterial flagellar motors [12]. The nanoscale biolog⇑ Corresponding author. E-mail address: [email protected] (P. Bergese). 0021-9797/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2012.02.013

ical–inorganic interface is another hot subject [13,14] that begun on the investigation of DNA manipulation and machinery at inorganic nanoparticle surfaces [15] and soft interfaces [16] and today comprises a myriad of challenging issues ranging from the fundamental understanding of biological activity of nanoparticles to toxicological and environmental side-effects of nanomaterials [17–22]. Also, several nanotechnological tools are to date widely employed to characterize biological systems. We limit here to recall scanning probe microscopy (SPM), which is probably the most representative of the category, that is currently being used to investigate single biomolecules [23] as well as cells [24,25]. The list of examples would be endless. Therefore, implementing the first scheme proposed by Kasemo [1], we attempted to frame the basic and the applied subjects that orbit biological surface science with the help of the ‘‘galaxy’’ reported in Fig. 1. The subjects directly related to biological surface science lie on the inner orbit and comprise biomolecular machines [11,26,27], nanomaterial– biological interface [13,14], smart surfaces [28] and nanomaterials [29], biomolecule, bio-inspired surfactants and bionanoconjugate self-assembly [11,16,30], and biomolecule-lipid membranes [8,31,32]. The outer orbit features the subjects to which molecular surface science is among the critical aspects. It includes the areas of drug technologies [33,34], bioelectronics [35,36], nanomaterials versus health and environment [21,37,38], cell biology [39,40], cell-surface interaction [3,9,41], synthetic biology [42], biomaterials [43,44], and solid-phase bioassays [45–47,50]. Indeed, within the limits of the authors’ taste in subdividing and naming these subjects and the fact that most of them are intertwined, the galaxy is impressive for the number and relevance of the components.

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Drug discovery Drug delivery

Biosensors

Bioelectronics Biomimetic photosynthesis

Biomoleculelipid membranes

Solid-phase Biomolecular immunoassays Biomolecule and machines bionanoconjugate Biological self-assembly surface science Biomimetic and bioinspired Nanomaterialmaterials biological Biomaterials and medical implants

Smart surfaces and nanomaterials

Tissue engineering

interface

Nanomaterial toxicology Nanomaterial and the environment

Cell biology Synthetic biology

Cell-surface interaction

Fig. 1. Tentative layout of the galaxy of the fundamental and applied subjects that orbit biological surface science.

As often happens, technological application and the exploitation run faster than fundamental understanding, but, as the history of science teaches us, advancing technology as well as conceiving and concretizing revolutionary visions are rooted in the basic research. Among these basics, biomolecule surface transformations at the biological–inorganic interface have been an elusive open challenge so far. Up to date, the efforts to unravel it have been primarily focused on natural and synthetic DNA hybridization, thanks to the high level of knowledge of the phenomenon in solution [48] and driven by the need for implementing DNA microarray and biosensor technology [49,50]. Interest is also growing around more revolutionary applications, as exploiting DNA ability to spontaneously form specific duplex and quadruplex structures for bottomup synthesis of materials [51,52] and nanomachines [53]. What has now being established is that DNA surface hybridization displays peculiar physicochemical features missed in bulk solution. Such features originate from a subtle co-operative action of electrostatic, steric (hydration), and thermal fluctuation (entropic) forces [54] which are modulated by the specific solid–solution interfacial environment, that is, by the solution ionic strength, the surface and its modification chemistry, the surface density of the immobilized ssDNA, the strand lengths of the ssDNA partners, and, eventually, the presence of a reporter label (see and merge Refs. [55–63]). In synthesis, this is a complex molecular scenario that is hard to disentangle and varies interface by interface, often in a mystifying way. The molecular approach proposed by the literature up to date has the merit to offer detailed insights into case by case, but it is inherently complex and far from setting up a unified model. Therefore, an alternative general approach allowing for systematic interpretation and measurement of these interfacial effects would highly contribute to bring basic understanding as well as applications to the next level. By following Gibbs’s suggestion: ‘‘One of the principal objects of research in any department of knowledge is to find the point of view from which the subject appears in the greatest simplicity’’ [64], we addressed this need by showing that a simple and effective route toward a general description of biomolecule surface transformations is offered by vintage thermodynamics of colloids and interfaces [65].

In the next two sections, we will draw the theoretical framework of this approach (elaborated in a general and unified formalism for the first time), while in the following sections, we will exemplify its effectiveness by putting it in action on some key examples from our recent activity: DNA surface hybridization [66], protein thin film machines [67], biomolecule directed selfassembly of nanoparticles [68], and microcantilever and contact angle nanomechanical biosensors [69–71]. 2. Theoretical 2.1. Biomolecule surface-bulk transformation cycle In this section, we will show by a simple thermodynamic argument that a biomolecular transformation in bulk (free) solution is inherently different from the analogous transformation confined at a solid–solution interface and that this difference can be rightly described in terms of the energy spent by the system for ‘‘accommodating’’ the transformation at the interface. We shall restrict the discussion to ligand–receptor monovalent binding in saline solution in order to focus on the thermodynamics rather than on the mathematics. So, consider the chemical equilibrium of the recognition [72] of a single L molecule by a single R molecule modulated by the presence of electrolytes to form the non-covalent complex LR. This equilibrium can be described by the equation:

L þ R þ jC¡LR

ð1Þ

where j represents the difference between the number of electrolytes C, initially free in solution, strongly associated with the non-covalent LR complex. In writing Eq. (1), we adopted the formal approach historically known as counterion condensation. It was first introduced in the fifties by Scatchard to incorporate the Debye–Hückel theory of ionic solutions into his analysis of the binding properties of proteins [73], was assessed in the late seventies by Record et al. [74], and recently brushed up for addressing surface DNA hybridization [59,63]. Now, consider the case in which the recognition (1) is forced to occur at solid–solution interface because one of the binding partners is immobilized onto the solid.

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The overall surface effect on the equilibrium can be understood if we consider the thermodynamic cycle reported in Fig. 2. The cycle goes from the free state (state I) to the surface recognition state (state V), broken down into four hypothetical steps, each of them being characterized by a standard molar Gibbs free energy. The first step describes the release of the receptor from the surface into the solution (I to II, Dr Grel 0 ), the second step the ligand–receptor recognition in solution (II to III, Dr Gb;rec ), the third step the association 0 of the electrolytes to the complex in the solution (III to IV, Dr Gb;el 0 ), and the fourth step the immobilization of the ligand–receptor complex to the surface, including eventual condensation of other ions and displacement of surfacial water [7] (IV to V, Dr Gimm Þ. 0 It follows that the surface standard molar Gibbs free energy, Dr Gr0 , is given by b;rec imm Dr Gr0 ¼ Dr Grel þ Dr Gb;el 0 þ Dr G 0 0 þ Dr G 0

ð2Þ

By rearranging and collapsing the terms related to homogeneous steps in the cycle, Eq. (2) can be rewritten as

Dr Gr0 ¼ Dr Gb0 þ W r

ð3Þ

r

where W gathers the surface work terms: imm W r ¼ ðDr Grel Þ 0 þ Dr G 0

ð4Þ

Dr Gb0

and accounts for the energy of the overall ligand–receptor recognition free in solution:

Dr Gb0 ¼ Dr Gb;rec þ Dr G0b;el 0

ð5Þ

From Eq. (3), we learn that the Gibbs free energy of the ligand– receptor surface recognition, Dr Gr0 , is split in a molecular interaction contribution, Dr Gb0 , and a surface work contribution, Wr. The first is the energy related to the ligand–receptor complex formation in solution, including recognition between ligand and receptor, conformational changes and electrolyte condensation. The latter describes the work spent in accommodating the ligand on the surface, including additional electrolyte condensation and nanoscale rearrangements. This simple relation yet brings interesting quantitative insights on debated themes in biomolecule surface recognition. For example, it unequivocally states that surface and solution recognition energies are always different, except in the cases in which Wr ffi 0, that can occur if the energies involved in confining the imm molecules on the surface Dr Grel are very small or, alter0 and Dr G0 natively, equal and of opposite sign. This vision may conciliate a wealth of contradicting experimental observations that from one side report of insane differences between solution and surface

Fig. 2. Thermodynamic cycle describing the surface effect in the recognition between a receptor molecule tethered onto a surface and a ligand molecule free in the surrounding electrolyte solution.

3

molecular recognition [55,59,63], and on the other side state the existence of any difference is a ‘‘myth to be busted’’ [75,76]. Also, we may note that Wr can be either positive or negative. In the case it is positive and comparable or exceeding the solution binding energy, it can reduce or fully inhibit surface binding (from Eq. (3), if W r P Dr Gb0 , then Dr Gr0 > 0). This gives a clear physicochemical justification to the experimental difference in yield of binding between solution and surface that remains an open subject [63] and is often cursorily attributed to lack of experimental control and good-practice [47]. 2.2. Le Châtelier and biomolecule surface transformations Further insight can be gained by translating the terms of Eq. (3) in the related specific type of work [77]. This will bring to a modified general thermodynamic model for biomolecule surface transformations (van’t Hoff isotherm) for surfaces, allowing for quantitative discussion of biomolecule surface behaviors by a Le Chatelier’s principle perspective. Let us start by directly considering the total change of the Gibbs free energy between state I and state V of the cycle reported in Fig. 2 that for clarity are reproduced in Fig. 3 with higher magnification and details regarding the interfacial parameters. In state I (Fig. 3a), the R coated surface and the solvent are in equilibrium, and they form an interfacial phase of mechanical interfacial tension rR, surface charge density and electrostatic potential qR and /R, and thickness sR. In state V (Fig. 3b), the ligand and receptor molecules form at the solid surface complexes stabilized by the condensed electrolytes. This surface excess of molecules and electrolytes with respect to state I triggers a novel interfacial phase with different physicochemical properties. That is the core concept: the fact that the transformation occurs provided the substitution of the state I interfacial phase with the state V interfacial phase, which is characterized by a novel interfacial tension, rLR,

Fig. 3. Ligand–receptor molecular recognition at a solid–liquid interface. (a) Free state (state I of the cycle of Fig. 2), and (b) surface recognition (state V of the cycle in Fig. 2).

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surface charge density and electrostatic potential qLR and /LR, and thickness, sLR (Fig. 3b). Note that in Fig. 3, the interface thicknesses are just indicatively sketched. An exhaustive and quantitative definition is not trivial and depends on the assumed physicochemical model [78]. Such a deep insight is unessential here and will be, therefore, skipped. Also note that analogous argumentations are at the base of the thermodynamics dealing with size effects on solid solubility and melting temperature [79] and led to revisit the traditional Gibbs phase rule in order to properly describe capillary system [80]. In view of the above considerations, we start the analysis by considering the change in Gibbs free energy between state I and V for the whole system [81]:

dG ¼ SdT þ Vdp þ

N X

li dni þ ðr þ quÞdR

ð6Þ

Now, as we are considering non-ideal solutions, the chemical potentials take the following form:

li þ l0 þ RT ln ai By merging Eqs. (11) and (12), it follows that:

Dr G ¼ Dr Gb0 þ

Dr þ xre þ RT ln aLR  RT ln aL  RT ln aR  jRT CLR

 ln aC

s

l

dG ¼ dG þ dG þ dG

r

ð7Þ

Since the interface is infinitely thin, it cannot perform volumetric work; therefore, Vr = 0 and V = Vs + Vl. Furthermore, since it is flat (planar), both phases exert the same pressure p = ps = pl at the interface. In view of this and summing up the entropy terms, S = Ss = Sl = Sr, Eq. (6) can be expanded in its specific terms:

dG ¼ SdT þ Vdp þ lL dnL þ lR dnR þ lLR dnLR þ jlC dnC þ rR dRR þ rLR dRLR þ qR uR dRR þ qLR uLR dRLR

ð8Þ

where the subscripts L, R, LR, and C refer to the ligand, the receptor, the ligand–receptor complex, and the free electrolyte, respectively; and li and ni are the chemical potential and amount of species i, respectively. We now observe that to an area increase dRLR of LR interfacial phase corresponds an area decrease dRR of the R interfacial phase, and thus we may write dR ¼ dRLR ¼ dRR . Also, we can introduce the extent of reaction variable, n, defined so that if it changes of dn, the change in amount of any species is given by dn multiplied by the species stoichiometric number. By these considerations, Eq. (8) rearranges into

dG ¼  SdT þ Vdp þ ðrLR  rR ÞdR þ ðqLR uLR  qR uR ÞdR þ ðlLR  lL  lR  jlC Þdn

ð9Þ

By gathering the mechanical and electrostatic forces, Dr ¼ ðrLR  rR Þ, and xre ¼ ðqLR uLR  qR uR Þ, Eq. (9) becomes:

dG ¼ SdT þ Vdp þ DrdR þ xre dR þ ðlLR  lL  lR  jlC Þdn ð10Þ The change of the (molar) Gibbs free energy of the reaction is then obtained by taking the partial derivative with respect to n of Eq. (10) at constant p and T:

Dr G ¼

  @G Dr þ xre ¼ þ ðlLR  lL  lR  jlC Þ @n p;T CLR

ð11Þ

dn dnLR  is the interfacial excess density of moles of LR dR dR molecules. Remarkably, in the considered system, all of the LR molecules are confined at the interface, thus CLR directly represents the number of LR moles per interface unit (this equivalence is not valid in general [78]). Here, CLR ¼

ð13Þ

Dr Gb0

where is the standard molar Gibbs free energy change in free solution assuming a non-ideal dilute water solution. When equilibrium is attained Dr G ¼ 0, the activities assume their equilibrium value, and Eq. (13) finally rearranges into:

Dr Gb0 ¼ RT ln

i¼1

where li and ni are the chemical potential and amount of species i, while r and qu identify the generalized forces exerted by the system to create (or disrupt) the surface area dR [82]. Now, for the two-phase system (solid s and liquid l) with one interface (solid–liquid r), the total change of the Gibbs free energy is:

ð12Þ

aLR aR aL ajC



Dr þ xre ½CLR 

ð14Þ

Now, if we compare term by term Eq. (14) with Eq. (3) properly rearranged:

Dr Gb0 ¼ Dr Gr0  W r

ð15Þ

we can finally assign its specific type of work to each free energy term. Namely

Dr Gr0 ¼ RT ln Wr ¼

Dc ½CLR 

aLR aR aL ajC

¼ RT ln K r ;

ð16Þ ð17Þ

where K r ¼ aLR j is the surface equilibrium constant, and aR aL aC Dc ¼ Dr þ xre is the thermodynamic surface tension, for simplicity hereafter referred as surface tension, that gathers both the mechanical and electrostatic contributions (see Ref. [83] for more details about the definition of thermodynamic surface tension). Eqs. (14)–(17) define the set of the thermodynamic equations that can be used to describe biomolecule surface transformations. Selection of the useful equation depends on the system under consideration as well as on the experimental needs and data. Eqs. (14)–(16) identify different forms of the law of mass action modified for surfaces and interfaces. They state that the presence of electrostatic and mechanical surface work concurs with the concentration of the interacting species to determine the overall equilibrium of the system. In classic terms, this means that Le Châtelier principle – If a chemical system at equilibrium experiences a change in temperature, pressure, concentration, or number of molecules per volume unit, then the equilibrium shifts to counteract the imposed change and a new equilibrium is established [84] – must be complemented with the change in surface mechanical and electrostatic nanoscale interactions when the chemical system is brought to an interface. The surface law of mass action is the thermodynamic justification to the fact that biomolecules at surfaces might denature or function, in terms of binding capabilities and other functionalities, in a different way than in solution. This view can be extremely useful to frame and quantify aspects of the biological–inorganic interface that have been elusive so far. In addition, it suggests that, unique to surface confinement, biomolecular nanoscale movements can co-operatively cumulate and trigger surface work, disclosing a nano-tomicroscale bridge with many surprises ahead. The next sections will be dedicated to exemplify some of these aspects. Before that, however, it is worth to explicitly outline the principal assumptions underpinning the above thermodynamic model. Having this clear is a fundamental point for both application as well as further developments. First, in writing Eq. (12) for the i species confined at the interface, we do the implicit assumption that the solution at the interface behaves as a non-ideal solution. This is a strong assumption,

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however, in line with the thermodynamic description of real solutions, it looks acceptable for a first approximation, and it is justified a posteriori by the comparison of the drawn equations with the experimental results [2,85]. Second, we assumed a separate contribution by mechanical and electrostatic work and did not attempt to explicit the electrostatic potential /. Further developments of the model in this direction might start from recent papers by Levicky and co-workers [63]. Perhaps, it must be taken into account also the Hofmeister series perspective [86] as well as the fact that in the interface featured by the model the electrical double layer partially penetrates the solid phase (as for biological membranes) and this can be represented as a particular case of Gouy–Chapman–Stern double layer, often called ‘‘porous’’ double layer [5]. 3. Corollary: Ligand–receptor binding affinity in solution and at the solid–solution interface We present here a corollary of the surface law of mass action introduced in the previous section that relates equilibrium constants of DNA hybridization in solution and at the solid–solution interface. This relation accounts for the astonishing differences determined experimentally that span over 27 orders of magnitude [55,59,63], contributing to settle this open issue. Let us start by merging Eqs. (15) and (16) to obtain the new relation

Dr Gb0 ¼ RT ln K r  W r Reminding that

Dr Gb0

ð18Þ

r

Fig. 4. Comparison between the theoretical values of KK b predicted by Eq. (19) for the surface work 160 kJ mol1 < Wr < 75 kJ mol1 (solid black line) and the experr imental values of KK b determined in various studies on DNA surface hybridization. r The projections of the KK b experimental values onto the Wr axis by Eq. (19) are also Kr evidenced. K b experimental values refer to DNA surface hybridization under different conditions of ionic strength (0.1–1 M), temperature (10–70 °C), and strand length (10–30 bp). Red squares refer to data from quartz crystal micro-balance (QCM) biosensors [90], green circles from experiments on microparticle-DNA conjugates with fluorescent labels [91], and the blue diamond from cyclic voltammetry [59]. Adapted with permission from Ref. [66].

ing of the charge interactions on the protein [74]. Therefore, Eq. (1) becomes:

A þ jC¡B

ð20Þ

b

¼ RT ln K , the relation becomes

  Wr ¼ exp  RT Kb

Kr

ð19Þ

Eq. (19) directly links the parameters that describe the equilibria of a ligand–receptor binding reaction in bulk solution and confined at a solid–solution interface. The solution equilibrium is defined by a single constant parameter referred to standard conditions, Kb, while the interface equilibrium is defined by a couple of parameters, Kr and Wr. We note that for a given value of Kb, infinite couples of valr ues of Kr and Wr that satisfy Eq. (19) can exist. So, the value of KK b is r determined by the range of values that W can assume in different interfacial environments. For DNA hybridization, the Wr window can be identified from the literature specific to MCs biosensors featuring endtethered 10–30 nucleotides long probe ssDNA hybridizing with full complementary, same length target ssDNA at different MC-solution interfacial environments [87–89,57]. It reports that 90 kJ mol1 < Wr < 75 kJ mol1. Upon substitution into Eq. r (19), this Wr window sets up that KK b ranges over 29 orders of magnitude, namely from 1016 to 1013, fairly matching the 27 orders of magnitude filed by Levicky and co-workers in their recent papers [55,59,63]. These results are summarized in Fig. 4. 4. Protein thin film machines In this section, we will apply the model to describe how submolecular nanoscale rearrangements of a thin film of surface bound proteins fueled by cycling the surrounding solution salinity can accumulate to perform a reversible and tailored microscale mechanical task, such as bending a microcantilever (MC). Let us start by reframing Eq. (1) for describing the conformational equilibrium of proteins confined on a surface with electrolytes in solution. The conformational states of a protein can be represented by two states, A and B. In dilute electrolyte solutions, equilibrium can be significantly shifted toward one of the states by the electrolyte concentration, C, which changes the number of electrolytes bound by the protein, j, and the Debye–Hückel screen-

where j and C are the j electrolytes C that associate with the protein in state A and bring it to state B. At equilibrium, the surface law of mass action (expressed in the general form by Eq. (14)) for the system described by Eq. (20) reads

Dr Gb0 ¼ RT ln

½ CB  ½CA ½Cj



Dc ½ CB 

ð21Þ

where [CA] and [CB] are the equilibrium surface molar densities of the proteins in state A and B, respectively, and [C] is the equilibrium concentration of the electrolyte C in solution. (note that since we are dealing with dilute water solutions, the activities have been approximated by the molar concentrations.) Eq. (21) says that the equilibrium of the system is determined by a balance between the concentrations of proteins in states A and B, the electrolyte concentration, and, since the protein film is at the solid–solution interface, the surface work W r ¼ Dc=½CB . This indicates that the work performed by proteins when adsorbing on a surface in a given buffer solution may be compensated by a change in the ratio between the conformational states A and B (degree of folding/unfolding), in full agreement with recent experimental and computational investigations on interaction of proteins with planar surfaces [92,93] and nanoparticles [94–97]. On the other hand, this also suggests that changing the salinity of the solution can shift the conformational equilibrium of the surface bound proteins together with triggering a surface work. To experimentally proof this hint, we studied self-assembled monolayers of proteins deposited on the top face of Au coated Si MC beams [67]. Based on the thermodynamics laid out above, the working principle of these ‘‘protein thin film machines’’ is the following (see Fig. 5 panel A for a sketch). At the starting stage, the film-MC system is in chemomechanical equilibrium with the surrounding saline buffer solution. Modulation of the salt concentration C shifts the conformational equilibrium of the proteins between conformational states A and B and in turn unbalances the in-plane intermolecular forces within the film. The resultant forces cumulate and trigger a surface work, Wr (i.e., induce a

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Fig. 5. (a) Scheme of the working principle of a protein thin film machine on a MC. (b) Experimental deflection of a MC driven by a cytochrome c thin film that is fueled by cycling the surrounding solution from 50 mM PBS (gray area) to 10 mM PBS (white area) (left panel), and scheme of the top face of a HCC–BPS–Au MC (right panel). Adapted with permission from Ref. [67].

change of the surface tension Dc), that the MC counterbalances by bending till chemomechanical equilibrium is restored [98]. We selected as model protein the cytochrome c (cyt-c) because its structure and folding have been extensively characterized in both solution and at the Au-solution interface [99–104]. In particular, we probed the behavior of horse cytochrome c (HCC) and yeast cytochrome c (YCC) on Au coated MCs capped with the Au ligand bis-(p-sulfonatophenyl)phenylphosphine, BPS, that leads a negatively charged surface. Fig. 5 panel b shows the mean MC differential deflection signals (left ordinate axis) and mean differential surface tension (right ordinate axis) of the HCC–BPS–Au MCs when the solution is cycled from 50 mM PBS (gray area) to 10 mM PBS (white area). Error bars are reported at significant points and represent the standard deviation of the mean of homologous MCs. Upon a decrease of the salt concentration from 50 mM to 10 mM, the HCC–BPS–Au MCs undergo a downward mean differential deflection of 105 nm, balancing a compressive (repulsive) surface work of the HCC thin film onto the Au MC face. The downward spikes appearing at the switching between the 10 mM PBS solution and the 50 mM PBS solution are due to the different responses of the HCC–BPS–Au MCs and of the reference MCs to the change. The figure also evidences that the HCC film switch could perform reversible motion cycles. To a first approximation, Dc can be related to Dz by Stoney’s Equation [105], which yields for Dz = 105 nm a Dc = 23 mN m1. In the paper, we explored also the effect of surface coating ligand, and we found that the choice of ligand can significantly affect the MC movement, and even completely reverse its direction. In particular, we probed bending of Au coated MCs functionalized with YCC intercalated or not with BPS. Upon a salinity cycle (50– 10 mM), the YCC–Au–MCs undergo a downward mean differential deflection of 160 nm, corresponding to a compressive (repulsive) Dc of 34 mN m1. Under the same salinity changes, the YCC–BPS–

Au–MCs undergo an upward mean differential deflection of +240 nm, corresponding to a tensile (attractive) Dc of 52 mN m1. This ‘‘oscillating’’ behavior with inter-protein separation also allowed inferring how the nanoscale rearrangements of the protein can cumulate to create microscale mechanical work and origin in building up hydration forces as the primary mechanism. Protein thin film machines are key examples of the successful application of the presented thermodynamic framework, which is, therefore, amenable to aid in progress stimuli-responsive surfaces realized with biomolecules [28,29]. 5. Molecular directed self-assembly of nanoparticles Another example of our recent activity useful to exemplify the effectiveness of the thermodynamic description is offered by the nanoparticle–biomolecule interface [68]. In particular, we applied the concept of biomolecule surface-bulk transformation cycle (Section 2.1, Fig. 2) to describe and measure the energetics associated with the interface for the model system of Thrombin Binding Aptamer (TBA) conjugated to gold nanorods (NRs), varying experimental relevant parameters such as TBA surface density, TBA sequence, and surface chemistry. Consider the interaction of thrombin with TBA immobilized on NRs represented in Fig. 6. Because thrombin binds specifically to TBA at exosite I and exosite II, binding results in thrombin-directed aggregation of TBA-decorated NRs (NR-TBA), illustrated in Fig. 6 by the passage from the free state (state I) to the aggregated state (state IV). The overall surface effect on aggregation can be understood if we construct a hypothetical alternative path for the system to go from the state I to state IV. A useful one can be the cycle represented in Fig. 6, broken down into three steps, each of them characterized by a standard molar Gibbs free energy. The first step

S. Federici et al. / Journal of Colloid and Interface Science 375 (2012) 1–11

7

Fig. 6. Thermodynamic cycle describing the aggregation of NR-TBA in the presence of thrombin. Adapted with permission from Ref. [68].

describes release of TBA from the NR to the solution (I to II, Dr Grel 0 Þ, the second step TBA–thrombin recognition in solution (II to III, Dr Gbind Þ, and the third conjugation of the TBA–thrombin complexes 0 to the NR (III to IV, Dr Gconj Þ. Note that for the sake of simplicity, in 0 first approximation, the role of condensed ions has been considered negligible and, therefore, excluded by the cycle. For the surface-bulk transformation cycle under consideration, Eq. (3) reads:

Dr Gagg ¼ Dr Gbind þ Wr 0 0

ð22Þ

Eq. (22) can be worked out into an equation that allows to evaluate Wr and binding efficiency h from fitting dose–response data (see Ref. [68]). Framed in a historical perspective, this equation can be seen as a Langmuir isotherm specifically implemented to describe molecular interaction directed self-assembly of NPs – This equation has indeed noble ancestors, including the Stern equation (proposed in 1924 for describing electrolyte adsorption at a charged surface), and the modified Langmuir by Fowler and Guggenheim (implemented in 1952 to take into account lateral interactions in adsorption of gases on solids). For a review see [78] – . Therefore, we used the thermodynamic model to map how Wr changes as a function of the binding efficiency h after varying of TBA coverage and surface chemistry of the nanorods (Fig. 7). We report here the salient findings. The resulted values for Wr are all negative and about 10 kJ mol1, indicating that Wr significantly participates along with TBA–thrombin recognition in driving aggregation. Quantitatively, from Eq. (22) and taking into account that thrombin–TBA 1 recognition energy is Dr Gbind ¼ 37 kJ mol [106], it follows that 0 nearly 30% of the aggregation energy, Dr Gagg 0 , which results 50 kJ mol1, comes from Wr. This shows, for the first time, that aggregation is not due solely to TBA–thrombin binding, as it is predominantly assumed. Further analysis indicated that Wr results from accumulation of in-plane molecular forces of tens of pN magnitude [107] and with a lifetime below 1 s. These results are consistent with unfolding forces from single-molecule experiments [23].

Fig. 7. h and [Th]T versus Wr for the different samples probed. Adapted with permission from Ref. [68].

6. Nanomechanical biosensors 6.1. Introduction As shown in the previous sections, surface conjugation and transformation of biomolecules come with nanoscale rearrangements of the molecules themselves that are mirrored by variation of in-plane intermolecular forces. These forces are often non-negligible and appear as a variation of the solid–solution interfacial tension, or, from another standpoint, as an additional surface pressure acting on the solid.

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Now, the key biosensing concept is that these effects can be exploited to probe the recognition event in a label-free fashion. In practice, the surface work performed by the ligand–receptor interaction, which may range from few to several tens of mJ/m2, can be measured by standard tensiometers and/or detected thorough the nanomechanical effects it drives on NEMS and MEMS of proper geometry. Starting from the above physicochemical facts, we developed CONAMORE (CONtact Angle MOlecular Recognition), a brand new biosensing approach based on ‘‘reinventing’’ contact angle experiments [70,71], and we implemented static nanomechanical microcantilevers, MCs, that in the last 10 years proofed to be a very promising sensing platform [69]. The working principle of these nanomechanical biosensors is sketched in Fig. 8. We successfully applied MCs and CONAMORE in sensing DNA hybridization, proteins, peptides, single amino acids, antibiotics, and angiogenic growth factors – angiogenesis is a key mechanism in tumor growth and proliferation, and its inhibition is a highly promising cancer molecular therapy – with competitive performances in terms of reliability, sensitivity, and costs. Both the techniques display unique features with respect to the biosensors to date on the market. In primis, they feature label-free and ‘‘energy-based’’ transduction of the binding event and, therefore, promise to be a valuable tool in problematic investigation/ screening, including those involving low molecular weight (LMW) species (molecular weight below 1 kDa) and multimeric and/or allosteric interactions, that is in the cases in which the standard ‘‘mass-based’’ biosensors, such as SPR (Surface Plasmon Resonance) and QCM (Quartz Cristal Microbalances) fail [46]. Furthermore, they present individual intrinsic advantages. CONAMORE features extreme instrumental and operational lowcosts. It can be performed with standard contact angle platforms that cost about 10.000 €, employing few hundreds nanoliters of ligand solution and standard flat 10  10 mm2 squared Si chips. MCs, on the other hand, can easily perform parallel and real time detection and had shown outstanding sensibility. Finally, in addition to straight on–off sensing, CONAMORE and MCs may significantly contribute to achieve the control of the surface environment that is mandatory to fully exploit sensors in biomedicine [66,108] as well as to envision new sensing geometries [109].

6.2. MCs The thermodynamic model developed can be applied to describe the experimental results from microcantilever biosensors. In order to exploit Eq. (14) for calculations, we express the activities as molar concentrations (see also Section 4). Moreover, in most cases of experimental interest, [L] and [C] do not change significantly upon LR complex and Eq. (14) rearranges into

Dr Gb0 ¼ 

Dc ½CLR   RT ln ½CLR  ½CR ðLÞin ðCÞjin

ð23Þ

Let us also observe that the concentration of the species C does not change significantly before and after the reaction set in Eq. (1). So, we can assume that the related term can be, in first approximation, collapsed in the bulk term. Accordingly, Eq. (23) can be expressed as 0

Dr Gb0 ¼ 

Dc ½CLR   RT ln ½CR ðLÞin ½CLR 

ð24Þ

Eq. (24) can be further optimized by introducing the hybridization efficiency, a [110], and, therefore, the relations:

½CLR  ¼ aðCR Þin ;   1 1 ½CR  ¼ ½CLR 

ð25Þ

a

Accordingly, Eq. (24) rearranged into 0

Dr Gb0 ¼ 

   Dc 1  RT ln ðLÞin 1 aðCR Þin a

ð26Þ

Eq. (26) is the operative equation that can be used to evaluate 0 Dr Gb0 from experimental parameters and results of MC bending driven by ligand–receptor recognition confined on one of its faces (Fig. 8). (L)in, a and T are set by the experimental conditions, and Dc can be related to measured MC deflection by the Stoney’s Equation [105]. A free on-line utility to ease these calculations was recently implemented [111]. 0 Note that Dr Gb0 is the Gibbs free energy that can be evaluated by computational analysis or by isothermal titration calorimetry (ITC) experiments. Eq. (9), therefore, allows to compare results from nanomechanical sensing to results from bulk techniques. Furthermore, this approach can be in principle extended to all the other solid-phase bioassays, contributing to solve the problem of the differences between the thermodynamic parameters evaluated by surface and bulk assays (see also Section 3). 0 Eq. (26) was tested on DNA hybridization. In particular, Dr Gb0 evaluated by the equation starting from MC experiments was com0 pared to the nominal Dr Gb0 obtained from the nearest-neighbor model [112]. The values resulted consistent in all the considered cases that comprised DNA hybridization supported by different surface environments such as bare gold [66] and polymer brush derivatized surfaces [69]. 6.3. CONAMORE

Fig. 8. Scheme of a MC and CONtact Angle MOlecular Recognition (CONAMORE) nanomechanical assays.

By shifting perspective, it is well known that solid–solution interfacial tension can be directly measured by contact angle, CA, analysis, which is perhaps the top classic technique for the investigation of surfaces [78], prompting the abduction that CA might play the unedited role of label-free probe of ligand–receptor binding. The term inedited is used because CA and related tensiometric techniques are extensively used to study unspecific protein adsorption [7] and were applied to study streptavidin–biotin interaction [6], but they were never explicitly proposed and tested in molecular recognition experiments. We named this technique CONAMORE (CONtact Angle MOlecular REcognition).

S. Federici et al. / Journal of Colloid and Interface Science 375 (2012) 1–11

When a droplet is placed onto a solid surface, it reaches equilibrium with the surface and the surroundings under the action of the interfacial tension at the contact line at which drop, surface, and surroundings meet, forming a definite CA. The transposition of this familiar phenomenon to molecular recognition is sketched in Fig. 8. Here, the surface, phase S, is functionalized with a receptor; the droplet, phase B, is a solution of unspecific or specific ligands for the immobilized receptor (panels a and b, respectively); and C is the surroundings phase. Specific binding featured by system ‘‘b’’ of Fig. 8 makes a specific contribution to the solid–solution interfacial tension, cSB, that is missed in the interfacial tension of the unspecific system (a), c0SB . Binding is thus univocally associated with the differential of the solid–solution interfacial tensions of the two systems, DcSB ¼ cSB c0SB , that through the Young–Dupré equations written for the two systems can be expressed as a function of the contact angles:

DcSB ¼ cSB  c0SB ¼ c0BC cos h0  cBC cos h

ð27Þ

where h0 and h are the contact angles of the unspecific and of the specific system, respectively, and, analogously, c0BC and cBC are the solution-surrounding phase interfacial tensions of the unspecific and of the specific systems, respectively. Eq. (27) allows to directly determine the transduction signal DcSB by measuring h0 and h by sessile drop contact angle experiments, provided that c0BC and cBC were previously determined. This working principle was tested on the classic benchmark of DNA hybridization supported by gold coated silicon wafers. In Fig. 9, the mean DcSB values of solution droplets containing 1 lM non-complementary ssDNA, 1 lM 50% complementary ssDNA, and 1 lM complementary ssDNA with respect to a pure solution droplet are showed. DcSB driven by complementary DNA hybridization is significantly higher than the DcSB driven by the other interactions that result sorted according to the strand sequence affinities. Thus, DcSB unambiguously transduced DNA duplex formation in an energy-based fashion. Success with DNA hybridization encouraged us to apply to investigate the interactions between cell membrane receptors and angiogenic growth factors. In particular, we chose the interaction between the tumor-derived pro-angiogenic vascular endothelial growth factor-A (VEGF-A) and the extracellular domain of its receptor VEGFR2 [71]. CONAMORE was able to detect the high

buffer non-complementary 50% complementary complementary

9

affinity binding of VEGF-A at nanomolar concentrations to surface-immobilized VEGFR2 with a consistent transduction signal despite the presence of a 10-fold molar excess of an unrelated protein (1.0 lM BSA) or of irrelevant immunoglobulins. The experimental output was also distinguished from the non-specific interactions occurring after denaturation of the receptors. Finally, the detection of the interaction between Cyclo-VEGI, a 2 kDa cyclo-peptide, and VEGFR2 demonstrated the technique capability to evaluate the binding of LMW molecules to surfaceimmobilized proteins. 7. Conclusions and perspectives In this article, we attempted to gather and present in a unified framework our efforts in developing a thermodynamic description of biomolecule surface transformations that got inspiration from classic applications of thermodynamics to colloids and interfaces. Although at a rudimentary stage, we showed this approach can yield a quantitative picture of how biomolecules behave when tethered to or in close proximity of a surface in several typical cases, including ligand–receptor surface binding, protein thin film machines, nanomechanical aspects of the biomolecule–nanoparticle interface, and nanomechanical biosensors. Indeed, the work is at the beginning, and the actual model is restricted to the simplest cases. It is immediately apparent that the field could evolve in numerous directions, for example: – to include surface curvature explicitly and in a general form (the actual models are strictly valid only for planar and spherical surfaces); – to implement proper analytical expressions of the surface electrostatic potential; – to work out the models in proper forms for analysis of other systems, for example, to investigate stimuli-responsive inorganic–biological surfaces or to address the open question of protein adsorption from buffer saline solutions and biological fluids; – to cover the cases in which both ligand and receptor are surface confined, as, for example, in the relevant case in which both ligand and receptor are labeled with NPs (the actual models only consider surface bound receptor and solution ligands); – to extend the model to account for multiple binding and other more complicated biomolecule–ligand interactions, such as allosteric interactions; – to extend the analysis to membrane–protein systems and their interactions with ligands that are at the base of the biochemical mechanisms by which the cell translates the cues from the extracellular environment into the intracellular events that drive its response to those cues. Addressing these issues will widen the soundness of the unified thermodynamic framework, contributing to the growth of the understanding of biological and inorganic–biological interfaces and to moving forward their revolutionary applications as well as their technological exploitation.

Fig. 9. Mean differential solid–solution interfacial tension, DcSB, of droplets of pure buffer (circles), of a 1 lM buffered solution of non-complementary ssDNA (down triangles), of a 1 lM buffered solution of 50% complementary ssDNA (up triangle), and of complementary ssDNA (diamonds). The errors are the SD of the mean. The images below the panel are representative examples of 500 nl sessile drops and refer from left to right to a buffer droplet, to a 50% complementary ssDNA droplet, and to a complementary ssDNA droplet, respectively. The surrounding solution is cyclohexane, a liquid phase lighter than water that avoids nl water solution droplets to evaporate in few seconds. Adapted with permission from Ref. [70].

Acknowledgments We thank Kimberly Hamad-Schifferli and her group, with whom we faced biomolecule surface nanomachinery and Ivano Alessandri for his constructive criticism, insightful discussions, and noise tolerance in these years of research. We also gratefully acknowledge Paolo Colombi, Marcella Chiari, Marina Cretich, Marco Presta, Stefania Mitola, Helena de Puig for the fruitful past

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[111] For Calculations of Molar Gibbs Free Energy According to the Thermodynamical Model in [66]. . [112] For Calculations of Molar Gibbs Free Energy According to Nearest-Neighbour Model. .