Reaction Field Analysis and Lipid Bilayer Location for Lipophilic

Article pubs.acs.org/JPCB

Reaction Field Analysis and Lipid Bilayer Location for Lipophilic Fluorophores Edward G. Randles† and Peter R. Bergethon*,†,‡ †

Department of Biochemistry, Boston University School of Medicine, 650 Albany St., X-140, Boston, Massachusetts 02118, United States ‡ Department of Anatomy and Neurobiology, Boston University School of Medicine, 650 Albany St., X-140, Boston, Massachusetts 02118, United States ABSTRACT: Environment polarity can cause changes in absorbance or emission maxima, for a given fluorophore. This is termed solvatochromism. In this study semiempirical models of solvatochromic shifts are used to predict their lipid bilayer location. Four reaction field models are analyzed and compared, to provide the most accurate prediction of fluorophore solvatochromic shifts using a modified version of the Lippert equation. For curcumin, the reaction field of Block and Walker gave the strongest agreement between experimental and predicted values (r = 0.978, p < 0.0001). For aluminum phthalocyanine disulfonic acid (AlPcS2), the reaction field of Wertheim, based on statistical mechanics, gave the best agreement (r = 0.951, p = 0.001) only when dispersion forces and solute polarizability are considered. The results of these models are correlated to the Dimroth−Reichardt ET(30) solvent polarity scale used by Frimer and colleagues. Using the model predicted values, curcumin is estimated to be 1−1.2 nm from the phospholipid− water interface, in the acyl chain region of the lipid bilayer. AlPcS2 is predicted to be 0.7−0.9 nm from the interface, at the fatty acid carbonyl. This investigation provides semiempirical methods to efficiently link fluorophore solvatochromic shifts to a location in the lipid bilayer via reaction field models.

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INTRODUCTION The polarity of a solvent affects the photophysical properties of a fluorophore. A solvent-dependent chromic shift in the absorbance or emission maxima for a given fluorophore is termed solvatochromism. Upon binding to a lipid bilayer the chemical environment of the fluorophore is different to the aqueous phase, and it undergoes a solvatochromic shift. As such, studying the solvatochromic shifts of lipophilic fluorophores provides a method to understand lipid bilayer dynamics, lipid structure, and permeability. In this investigation, semiempirical models of solvatochromism provide a measure of the lipid bilayer location of curcumin (Figure 1A) and aluminum phthalocyanine disulfonic acid (AlPcS2, Figure 1B). The solvatochromic models also provide information on the structure of the solvent surrounding curcumin and AlPcS2, as well indicating the role of dispersion forces. The Lippert equation describes the relationship between solvent polarity and the empirically determined solvatochromic response of a fluorophore.1,2 The relationship is dependent on the use of a reaction field. The reaction field describes the electrical field that acts on a fluorophore due to the perturbation of the dielectric medium because of the presence of the fluorophore itself.3 Onsager developed the first reaction field.4 Together, the reaction field and the Lippert equation describe the relationship between a solvatochromic shift and the solvent polarity in terms of the relative permittivity and the refractive index of the solvent.5 The derived model provides a © 2013 American Chemical Society

method to estimate the polarity of any chemical environment, such as the lipid bilayer, given the solvatochromic shift induced upon binding of a lipophilic fluorophore. This approaches facilitates the construction of membrane polarity profiles.6 Modification of the Lippert equation to allow for polarizability of the fluorophore improves the performance of the derived models4,7,8 and provides a more comprehensive model of solvatochromism.8−11 The amphipathic photosensitizer AlPcS2 is a photodependent modulator of lipid bilayer stability and permeability.12 AlPcS2 binds to liposomes, increases lipid bilayer stability, and decreases permeability. Then, upon irradiation, the photodynamic activity of AlPcS2 increases liposome permeability, allowing flux of encapsulated material.12 The location of AlPcS2 in the lipid bilayer must play a significant role in mediating these properties. In this investigation, the solvatochromism of AlPcS2 is modeled using the methodology of Marsh. The results of the model are compared against the “molecular ruler” developed by Frimer and colleagues.13−15 The “molecular ruler” correlates solvent polarity, as measured by the Dimroth− Reichardt ET(30) scale, to a nanometer scale depth into the lipid bilayer.16 Curcumin is a lipophilic molecule that undergoes large solvatochromic shifts17−19 and has reported phospholipid Received: March 22, 2013 Revised: July 8, 2013 Published: July 10, 2013 10193

dx.doi.org/10.1021/jp402861x | J. Phys. Chem. B 2013, 117, 10193−10202

The Journal of Physical Chemistry B

Article

required. The concentration of phospholipids in liposome suspensions was determined using the Stewart assay21 calibrated against egg PC stock. Absorbance Spectra. All absorbance spectra were measured using a Beckman Coulter DU 640 spectrophotometer (Beckman Coulter) at 22 °C. All measurements were recorded in triplicate. Further experimental conditions are as stated. Emission Spectra. Emission spectra recorded on a Hitachi F4500 spectrofluorimeter fitted with a Ushio UXL-152H xenon arc lamp (Ushio America Inc. Cypress, CA) using a Hellma Suprasil Quartz Cuvette (Thermo Fisher Scientific, Waltham, MA). The temperature was maintained by water-jacketed cuvette holder and a circulating water bath (Neslabs, Thermo Fisher Scientific, Waltham, MA). Emission spectra of AlPcS2 were recorded with excitation slit widths of 5 nm for all experiments. The emission intensity was recorded via PMT with a voltage of 700 V.

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THEORETICAL BASIS Reaction Field in the Ground State. The derivation of the Lippert equation given here for the reader is a more direct version of that by Marsh.7 The electric dipole moment of the fluorophore ground state (mg) is dependent on the ground state permanent dipole moment (pg) plus the reaction field (Rg), modified by the polarizability of the fluorophore ground state (αg). mg = pg + αg R g (1)

Figure 1. (A) Chemical structure of curcumin. (B) Chemical structure of aluminum phthalocyanine disulfonic acid (AlPcS2).

Rg is the electrical field that results from the electrical displacement of the dielectric medium induced by the presence of the fluorophore dipole moment (pg) itself. Therefore, Rg is a function of mg. mg R g = f mg ≡ f (εr) 3 4πε0reff (2)

interactions well. Therefore, curcumin provides a control to validate the methodology developed in this investigation. A time-averaged lipid bilayer location is predicted for both curcumin and AlPcS2 using the models of solvatochromism and the “molecular ruler”. The semiempirical analysis presented here provides an effective measure of solvent induced shifts in photophysical properties and relies on data that is quickly obtained.7 In contrast, quantum mechanical models provide detailed fundamental understanding of the solvatochromic effect but require time-intensive computational studies.20 Semiempirical analyses, such as those presented here, complement more intensive and fundamental studies and provide for the rational description of empirical data. The methodology used here can be performed routinely using a standard laptop, helping the bench scientist to model their data, thereby improving access and understanding of lipid−fluorophore interactions.

ε0 is the vacuum permittivity, εr is the relative dielectric permittivity of the solvent, and reff is the effective radius of the fluorophore. Equation 3 gives an expression for the fluorophore ground state Rg, allowing for polarizability. Rg =

f p 1 − αgf g

The total dipole moment in the ground state is: pg mg = 1 − αgf

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METHODS Materials. All solvents were purchased from Sigma Aldrich (St. Louis, MO) and were of HPLC grade. Aluminum chloride phthalocyanine disulfonic acid (AlPcS2) was purchased from Frontier Scientific (Logan, UT). Liposome Extrusion and Lipid Concentration. A chloroform solution of egg phosphotidylcholine (Avanti Polar Lipids, Alabaster, AL) was dried under a UHP nitrogen stream (Airgas, Salem, NH). The dried lipids were resuspended in 10 mM Tris-HCl with 100 mM KCl, pH 7.4 via vortexing. Liposomes were prepared via the extrusion method through 100 nm diameter porous membrane at 40 °C using the Avanti mini extruder (Avanti Polar Lipids, Alabaster, AL). The resulting liposome suspension was stored at 4 °C until

(3)

(4)

The energy of pg in its own reaction field is given by: 1 Wg = − pg ·R g (5) 2 Equation 6 includes both the work done in polarizing the dielectric and the energy of the fluorophore dipole in the reaction field.

Wg = −

f 1 |p | 2 1 − αgf g

(6)

Reaction Field in the Franck−Condon Excited State. The total electric dipole moment of the fluorophore in the Franck−Condon (FC) excited state (me) is related to the 10194



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permanent dipole moment (pe) and the FC state reaction field (RFC e ) modified by the polarizability of that state. me = pe + αe R eFC

WeFC = −

(7)

−

is the reaction field in the FC state induced by photon absorbance. pe increases in the excited state. A relative dielectric permittivity ε∞ = n2, where n is the solvent refractive index, captures the immediate solvent response to increased pe. RFC e is the sum of two components; the electric (Rele ) and the orientation. Equation 8 describes Rele of the induced reaction field. RFC e

R ele = f ′me ≡ f (n2)

f′ (p + α R or g) 1 − αef ′ e

(9)

f − f′ p 1 − αgf g

(10)

⎛ f (εr) hc Δνa̅ = −⎜ 3 ⎝ 1 − (α /4πε0reff )f (εr) −

(11)

−

This allows a new expression for RFC e . R eFC

⎛ f − f′ ⎞ 1 ⎜⎜f ′p + = p⎟ 1 − αef ′ ⎝ e 1 − αgf g ⎟⎠

⎛ α (f − f ′) ⎞ 1 ⎜⎜p + e p⎟ 1 − αef ′ ⎝ e 1 − αgf g ⎟⎠

1−

⎞ (pe − pg ) ·pg ⎟ 3 4πε0reff

3 (α /4πε0reff )f (n 2 ) ⎠

(|pe|2 − |pg |2 ) f (n 2 ) 1 − Df (n2) 3 3 2 1 − (α /4πε0reff )f (n2) 4πε0reff

Fluorescence Spectra. Relaxation of the solvent during the excited state lifetime of the fluorophore means that emission occurs from an equilibrium state to a Franck−Condon ground state. Therefore, the solvent-dependent shift in fluorescence emission is obtained in a similar fashion as the absorbance shift in eq 17.

(12)

⎛ f f′ ⎞ hc Δνf̅ = −⎜ − ⎟(p − pg ) ·pe 1 − αf ′ ⎠ e ⎝ 1 − αf f′ 1 (|p |2 − |pg |2 ) − Df ′ − 2 1 − αf ′ e

(13)

Energy in the Franck−Condon State. The FC state is not an equilibrium state, and this precludes the use of an analogy to eq 5. The work done in polarizing the dielectric and the energy of the dipole in the reaction field are evaluated independently. The energy of the fluorophore in the FC excited state (WFC e ) is: WeFC =

f (n 2 )

(18)

From eqs 7 and 12, me becomes: me =

(17)

Using explicit substitutions from eqs 2 and 8, eq 17 is expressed as follows. Equation 18 also includes the term f ′D to consider the dispersion forces between the fluorophore and the surrounding solvent.

The difference between Rg and the electrical component, Relg , el is equal to Ror g . Rg is equal to f ′mg in analogy to eq 8 giving eq 11. R or g = R g − f ′mg =

(16)

⎛ f f′ ⎞ hc Δνa̅ = −⎜ − ⎟(p − pg ) ·pg 1 − αf ′ ⎠ e ⎝ 1 − αf f′ 1 (|p |2 − |pg |2 ) − 2 1 − αf ′ e

f ′(pe + α R or g) 1 − αef ′

(15)

h is Planck’s constant, and c is the speed of light in vacuo. Using eqs 6 and 15, assuming the polarizability of the ground state and the excited state are equal, eq 16 is rewritten as:

Using this expression, RFC e becomes: R eFC = R ele + R or g =

2

hc Δνa̅ = WeFC − Wg

(8)

The time taken for the solvent to reorient in response to pe is orders of magnitude larger than the absorbance. Therefore, the orientation component of RFC e is the same as that in the ground el or state, Ror g . Equation 9 re-expresses Re in terms of Rg and includes the polarizability of the fluorophore; R ele =

⎞ (f − f ′)|pg |2 ⎟⎟ (1 − αgf ) ⎠ 1 − αef

To simplify this expression the polarizability of the ground state and the excited state are assumed to be equal (αg = αe). Absorbance Spectra. Interaction of the dipole with the solvent induces a shift in the wavenumber of the absorbance band (Δν̅a). This shift is due to a change in the energy of the fluorophore in the ground (Wg) and FC state (WFC e ).

me 3 4πε0reff

⎛ 2(f − f ′) 1 1 ⎜f ′|p |2 + p ·p 2 1 − αef ′ ⎜⎝ e 1 − αgf e g

(19)

Expressed in terms of solvent properties this becomes: ⎛ f (εr) hc Δνf̅ = −⎜ 3 ⎝ 1 − (α /4πε0reff )f (εr)

1 1 1 mg ·R or me·R ele − pe ·R eFC − αe |R eFC|2 g + 2 2 2

−

(14)

With the exception of = f ′me, identities for the reaction fields and total dipole moments used in eq 14 have been given above. Equation 15 describes WFC upon substitution and e rearrangement. Rele

⎞ (pe − pg )·pe ⎟ 3 3 1 − (α /4πε0reff )f (n2) ⎠ 4πε0reff f (n 2 )

(|pe|2 − |pg |2 ) f (n 2 ) 1 − − Df (n2) 3 2 3 2 1 − (α /4πε0reff )f (n ) 4πε0reff (20) 10195



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Table 1. Absorption and Emission Frequencies of Curcumin in Protic and Aprotic Solventsa solvent

relative permittivity (ε)

refractive index (n)

DMSO DMF acetonitrile methanol ethanol isopropanol acetone butanol ethyl acetate benzene liposomes

47.24 38.25 36.64 33.00 25.30 20.80 21.01 17.84 6.08 2.28

1.479 1.4305 1.3441 1.3284 1.3614 1.3959 1.3586 1.3993 1.372 1.501

Δν̅a (× 103 cm−1) 23.310 23.256 23.697 23.364 23.256 23.810 23.202 23.310 23.866 23.923 23.810

Δν̅f (× 103 cm−1) 18.692 18.519 18.587 17.668 18.083 19.608 18.349 19.305 20.243 21.552 20.080

Δν̅a − Δνf̅ (× 103 cm−1) 4.618 4.737 5.109 5.697 5.173 4.202 4.853 4.005 3.623 2.372 3.729

Δνa̅ + Δνf̅ (× 103 cm−1) 42.002 41.774 42.284 41.032 41.339 43.417 41.550 42.615 44.109 45.475 43.890

Δν̅a = the absorption peak wavenumber, Δν̅f = the emission peak wavenumber, Δν̅a − Δν̅f = Stokes shift, Δν̅a + Δν̅f = the sum of the absorption and emission peak frequencies.

a

Stokes Shift and Frequency Sum. The difference between the absorbance and fluorescence emission frequencies is the Stokes shift. Consideration of the Stokes shift, instead of the absorbance or emission independently, simplifies eqs 18 and 20. hc ΔνStokes ̅

Later, Block and Walker proposed an alternative model ( f BW).8 The solution of Laplace’s equation provides the analytical solution below that describes the reaction field dependence on εr. fBW =

⎛ f (εr) = hc(νa̅ − νf̅ ) = ⎜ 3 1 − ( α /4 πε0reff )f (εr) ⎝

⎞ (pe − pg ) ·pe f (n ) ⎟ − 3 3 1 − (α /4πε0reff )f (n2) ⎠ 4πε0reff

Another later variant, described by Ehrenson, (f E) uses a numerical solution to Laplace’s equation. fE = 6.313 × 10−2 × [1 + 1.058 ln εr − 0.190(ln εr)2

(21)

+ 0.009(ln εr )3 ]ln εr

Similarly, the sum of the absorbance and emission frequencies simplifies eqs 18 and 20.

(|pe|2 − |pg |2 ) 3 4πε0reff

2(εr − 1) 2εr + 1

(25)

Wertheim developed the fourth model tested here.10,11 This model uses a statistical mechanics approach, relying on a mean spherical approximation. Rewritten in the reaction field formalism, a numerical solution is found that approximates the reaction field.

f (εr) 3 1 − (α /4πε0reff )f (εr)

− 2Df (n2)

fW ≈ 0.6666 × [1 + 0.0017 ln εr − 0.00432(ln εr)2

(22)

+ 0.000158(ln εr )3 ]ln εr

Equations 21 and 22 provide methods of analyzing the solvatochromic shifts of any given fluorophore using explicit solvent properties. Furthermore, a comparison of the frequency sum method to the Stokes shift allows evaluation of the role of dispersion forces in the solvatochromic shift. Both of these equations are forms of the Lippert equation2 and take into account the polarizability of the fluorophore.7 Equation 21 describes the relationship between the Stokes’ shift (Δν̅Stokes) of a fluorophore in a given solvent and the polarity of the solvent. In this equation, the solvent polarity is function of the relative permittivity (εr) and refractive index (n). Equation 22 is an alternate version of the Lippert equation describes the relationship between the sum of the absorbance and emission frequencies (Δν̅a + Δνf̅ ) and the solvent polarity. Similar to eq 21, it also includes the polarizability of the fluorophore. D is a coefficient describing the role of the dispersion forces. Reaction Field Models. Four reaction field models were tested. Onsager proposed the first reaction field model.4 The Onsager model uses a step function to switch from ε0 to the bulk solvent permittivity (ε0εr) at reff. The solution of Laplace’s equation provides Onsager’s expression (f O) for the reaction field dependence on εr. fO =

(24) 9

2

hc∑ ν ̅ ≡ hc(νa̅ + νf̅ ) = −

3εr ln εr 6 − −2 εr ln εr − εr + 1 ln εr

(26)

Fitting the Models to the Data. To simplify eqs 21 and 22 the polarizability of the fluorophore (α), was parametrized by a, which is given by the Lorentz−Lorenz equation (eq 27). n0 is the refractive index of the fluorophore extrapolated to zero frequency. Three values of a are evaluated, 0, 0.25, and 0.5. The molecule has zero polarizability when a = 0. a=

(n0 2 − 1) α = 3 4πε0reff (n0 2 + 2)

(27)

Each of the four reaction field models is evaluated using eqs 21 and 22. The measured stokes shift (eq 21) for each solvent condition is plotted against [f(εr)/(1 − af(εr)) − f(n2)/(1 − af(n2))] for the four models using the three different values of a. Linear regression yields a line of best fit in the form of eq 28. ⎛ f (ε ) f (n 2 ) ⎞ r ⎟ + ν0̅ νa̅ − νf̅ = K f ⎜ − 1 − af (n2) ⎠ ⎝ 1 − af (εr)

(28)

Treatment of eq 22 in the same fashion yields a line of best fit in the form of eq 29. ⎛ f (εr) ⎞ νa̅ + νf̅ = K f ⎜ − ⎟ − 2Df (n2) ⎝ 1 − af (εr) ⎠

(23) 10196

(29)



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Table 2. Absorption and Emission Frequencies of AlPcS2 in Protic and Aprotic Solventsa solvent

relative permittivity (ε)

refractive index (n)

DMSO DMF methanol ethanol acetone isopropanol butanol liposomes

47.24 38.25 33.00 25.30 21.01 20.80 17.84

1.4793 1.4305 1.3284 1.3614 1.3586 1.3959 1.3993

Δν̅a (× 103 cm−1) 14.749 14.837 14.793 14.815 14.903 14.837 14.826 14.881

Δνf̅ (× 103 cm−1) 14.542 14.652 14.599 14.641 14.735 14.684 14.663 14.728

Δν̅a − Δνf̅ (× 103 cm−1) 0.207 0.185 0.194 0.174 0.168 0.153 0.163 0.153

Δν̅a + Δν̅f (× 103 cm−1) 29.291 29.489 29.391 29.456 29.638 29.521 29.489 29.608

Δν̅a = the absorption peak wavenumber, Δν̅f = the emission peak wavenumber, Δν̅a − Δν̅f = Stokes shift, Δν̅a + Δν̅f = the sum of the absorption and emission peak frequencies.

a

Using this method, for each fluorophore there are a maximum of 24 possible fits to evaluate. To ensure an unbiased approach in evaluating accuracy of each model, the lines of best fit given by eqs 28 and 29 are used to calculate a set of “model predicted” solutions to eqs 21 and 22. A significance value of 2% is used for all correlations.

Both curcumin and AlPcS2 bind to liposomes.12,18,19,23 By calibrating the solvatochromic response of each of these molecules, it is possible to estimate the polarity of the chemical environment resulting from liposome binding. Upon liposome binding, the absorbance and fluorescence peaks of curcumin are most similar to ethyl acetate, which has a relative permittivity of 6.08. The absorbance and emission peaks of AlPcS2 are most similar to acetone, which has a relative permittivity of 21. These estimates with experience can be subjectively associated with regions of the lipid bilayer. This provides a qualitative location of either curcumin or AlPcS2 in the lipid bilayer. However, a more quantitative and analytical approach is desirable. In this investigation, the Lippert equation as derived by Marsh7 is used to analyze the solvatochromic calibration data and provide a quantitative basis for describing the polarity and location of liposome bound curcumin and AlPcS2. Reaction Field Models. Equation 21, a modified version of the Lippert equation, describes the relationship between the Stokes’ shift (Δν̅Stokes) of a fluorophore in a given solvent and the polarity of that solvent. Equation 22 is an alternative form of the Lippert equation that relates the sum of the absorbance and emission frequencies (Δν̅a + Δν̅f) to the solvent polarity. In contrast to eq 21, eq 22 includes a term to describe the dispersion forces between the fluorophore and the solvent. In this investigation, comparing the results of eqs 21 and 22 indicates if it is necessary to consider dispersion forces in the effect of the solvent on the fluorophore. Figure 2A gives a graphical comparison of f O, f BW, and f E as defined by eqs 23, 24, and 25, respectively. The step function of the Onsager model is clearly identifiable, with the relative permittivity reaching that of the bulk solvent beyond the effective molecular radius of the fluorophore. The Block and Walker model has a more gradual transition, only reaching the bulk relative permittivity at very large distances. The Ehrenson model provides a more rapid transition reaching half the bulk solvent relative permittivity at three times the effective radius of the fluorophore proposed an alternative. Figure 2A also shows the range of the Block and Walker model versus the Ehrenson model in response to different bulk relative permittivity. The Block and Walker model is more sensitive to the bulk permittivity, with larger distances required to achieve bulk permittivity. Figure 2B shows the effect of fluorophore polarizability on the function f(εr)/[1 − af(εr)], where a is defined by eq 27, in each of the four reaction field models. The function f(εr)/[1 − af(εr)] describes the strength of the reaction field produced by a solvent with relative permittivity εr. Figure 2B shows that the Onsager model (f O, blue line) saturates at high values of εr. Including fluorophore polarizability only increases the value of

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RESULTS AND DISCUSSION Solvatochromic Shifts of Curcumin and AlPcS2. Table 1 shows the literature reported values for the solvatochromic response of curcumin.18,19,22−27 The relative solvent permittivity and refractive index are used to describe the solvent polarity. In response to increasing solvent polarity, the emission peak for curcumin undergoes a red shift. There is a significant correlation between the solvent relative permittivity and the fluorescence emission peak (r = 0.747, p = 0.013). Similarly, the Stokes shift increases in magnitude with increasing solvent polarity. There is a significant correlation between the Stokes shift and the solvent relative permittivity (r = 0.742, p = 0.013). There is no significant correlation between the solvent relative permittivity and the absorbance peak. Splitting the solvents into two classes, protic and aprotic, clarifies some relationships. There is a clear trend between solvent relative permittivity and the absorbance peak when aprotic solvents are considered. The absorbance peak undergoes a red shift with increasing solvent polarity, when considering only the aprotic solvents. This recapitulates the fluorescence emission-solvent polarity relationship. However, the magnitude of the red shift is much smaller for the absorbance data. In the case of the aprotic solvents, the absorbance red shift only spans 613 cm−1, compared with 1860 cm−1 in the fluorescence data. The correlation between the photophysical parameters and the solvent refractive index does not achieve significance. The red shift in fluorescence emission with increasing solvent polarity indicates that curcumin undergoes positive solvatochromism. This results from stabilization of the excited state relative to the ground state of the molecule. Dispersion forces may account for the stabilization of the curcumin ground state in polar, aprotic solvents. Table 2 shows the solvatochromic shifts of AlPcS2 (Figure 1B). The data shows that AlPcS2 undergoes a red shift with increasing solvent polarity, indicating positive solvatochromism. The data therefore suggest that polar solvents stabilize the excited state of AlPcS2. Consideration of the protic solvents separately from the aprotic shows that the two solvent classes have different solvatochromic effects on AlPcS2. The magnitude of the solvatochromic shifts is smaller than that of curcumin. However, there is a significant correlation between the Stokes shift and the solvent relative permittivity (r = 0.921, p = 0.003). 10197



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Figure 2. Reaction field models. (A) The radial dependence (r) of the solvent relative permittivity (ε) for different reaction field models. reff is the effective molecular radius of the fluorophore. εB is the bulk relative permittivity of the solvent. (B) The relationship between the reaction field and the solvent relative permittivity. The effect of fluorophore polarizability is demonstrated. a = α/(4πε0r3eff), where α describes the polarizability of the molecule. Three values of a are shown, 0, 0.25, and 0.5. Adapted with permission from ref 7. Copyright 2009 Elsevier.

Figure 3. Plots of the Block and Walker model, which provides the best fit for the solvatochromism of curcumin. (A) The solvent dependence of ν̅a − ν̅f for curcumin can be classified according to protic (■) versus aprotic solvents (□). The lines of best fit have the form; ν̅a − ν̅f = Kf[f(εr)/(1 − af(εr)) − f(n2)/(1 − af(n2))] + ν̅0. The value of a is 0.25. The line of best fit provides a set of model predicted Stokes shifts that are correlated to the empirical data to assess each model. The ν̅a − ν̅f for liposome-bound curcumin is given (○). (B) Comparison of the four reaction field models at a = 0.25. The Block and Walker model (f BW) provided the strongest correlation between model derived and literature reported solvent-dependent ν̅a − ν̅f for curcumin (r = 0.978, p < 0.0001).

f(εr)/[1 − af(εr)] in the Onsager model and does not prevent saturation. Fluorophore polarizability has little effect on either f BW or f E at values of εr less than 10. Beyond a εr value of 10, the rise of f(εr)/[1 − af(εr)] increases when polarizability is included in either f BW or f E. The Wertheim model shows the largest response to fluorophore polarizability. When polarizability is not considered (a = 0) in f W, there is a linear relationship between f(εr)/[1 − af(εr)] and log εr. At higher values of a, there is an exponential relationship between f(εr)/ [1 − af(εr)] and log εr. Reaction Field Analysis of Curcumin Solvatochromism. The solvent-dependent Stokes shifts of curcumin (Table 1) were evaluated using eq 21, for each of the four reaction field models. Three discrete values of the coefficient a were considered (0, 0.25, and 0.5). As shown in Figure 3A, separating the data into protic and aprotic solvents provided two lines of best fit, both of the form described by eq 28. Figure 3A shows the linear regression fit of the curcumin Stokes shifts to the Block and Walker reaction field model (eq 24) with a = 0.25. Each line of best fit provided a solution to eq 28 and therefore predicted Stokes shifts. The Stokes shifts in Table 1 were correlated with the model predicted values with a

significance value of 2%. Figure 3B graphically summarizes these correlations across the four reaction field models for a = 0.25. Statistically, the Block and Walker model provides the strongest correlation (r = 0.978, p < 0.0001). The four reaction field models were also evaluated using eq 22, using all three values of a. However, the strongest correlations used eq 21. Equation 21 does not include the D term to describe the dispersion forces. The model suggests that dispersion forces do not play a role in the solvatochromism of curcumin. However, the data in Table 1 indicate that the absorbance peak of curcumin undergoes a red shift with increasing solvent polarity. The red shift indicates stabilization of the ground state at higher solvent polarities. The best fitting model does not account for this through dispersion forces. Other mechanisms, outside of the scope of either eq 21 or 22, might account for the red-shift observed in the curcumin ground state. Despite, the discrepancy, there is a robust agreement between the model and the data in Table 1. Using the Block and Walker model and eq 21 the relative permittivity of the dielectric medium for 10198



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It is clear that the data derived from the solvatochromic models do not replicate the data presented in Tables 1 and 2 with complete fidelity. A comparison of the model-derived values with the empirical data qualitatively suggests that there is a discrepancy. The incompleteness of the models suggests that some further modification of the Lippert equation is required. This would result in additional coefficients that would likely require parametrization from experimental values. For example, according to the model, the dispersion force coefficient (D) has the same value in both the ground and the excited states. This may not be the case but would require extensive experimental characterization. An additional limitation of these models is the treatment of the cavity in the solvent occupied by the fluorophore as spherical. For curcumin, but more so AlPcS2, this is unlikely. Additionally, the solvatochromic models rely on the absorbance and emission dipole having the same orientation in space. Despite these limitations there are advantages to using the solvatochromic models. For example, in the case of curcumin, the Block and Walker model provided the best fit. The Block and Walker model, as depicted in Figure 2A, only achieves bulk permittivity at very large distances. Therefore, the model suggests that the dipole moment of curcumin has a very large effect on the solvent structure and that this effect dissipates slowly as a function of distance from the molecule. In the case of AlPcS2, dispersion forces are required to provide the best fit, providing further information on the fluorophore−solvent relationship. Overall, it is clear that the solvatochromic models employed in this investigation provide useful information and a sound basis for clear analysis of fluorophore solvatochromism. It was hypothesized that the model predictions could be further used to quantitatively predict the lipid bilayer location for curcumin and AlPcS2. Model Predictions of Lipid Bilayer Location. Frimer and colleagues have developed a “molecular ruler” using solvatochromic shifts to measure a time-average lipid bilayer location of lipophilic fluorophores.15 The method has been validated against NMR data13−15 and is in close agreement with literature reported values for curcumin.19,24 The technique developed depends on classifying the solvents used in the solvatochromic calibration via the Dimroth−Reichardt (ET(30)) solvent polarity scale. The result of this technique equates the ET(30) values with a nanometer scale depth from the phospholipid−water interface, providing a time-averaged, lipid bilayer location for any given lipophilic fluorophore. The zero point for the phospholipid−water interface is defined as the nitrogen on the headgroup of the phospholipid.14,15 The Block and Walker model showed the strongest correlation when considering the Stokes shift of curcumin. The use of literature reported values provides a control, against which the model predicted values are to be tested. Figure 5A shows the correlation between the literature reported Stokes shift of curcumin (Table 1) and the ET(30) values of the solvent. Separating the data into protic and aprotic solvents reveals a strong correlation between the Stokes shift and the ET(30) value for each solvent used in the solvatochromic calibration. Plotting the literature reported stokes shift for liposome bound curcumin, the predicted ET(30) value is between 166.2 kJ mol−1 and 171.2 kJ mol−1. Using the “molecular ruler”, curcumin is located between 1 and 1.2 nm from the phospholipid−water interface. This is in strong agreement with literature reported values for a neutral pH environment.22 Figure 5B shows the relationship between solvent ET(30) values and the model predicted Stokes shifts.

liposome bound curcumin is between 10 and 14.7. Therefore, the environment surrounding liposome bound curcumin has a relative permittivity higher than ethyl acetate, but lower than that of butanol, in agreement with the qualitative estimate given above. The validation of the model fitting method with curcumin provides a useful control point allowing application of the method to AlPcS2. Reaction Field Analysis of AlPcS2 Solvatochromism. Both eqs 21 and 22 were used with the four reaction field models to analyze the solvatochromic shifts of AlPcS2 at all three values of a. The data was separated into protic and aprotic solvents. Linear regression yielded lines of best fit according to eqs 28 or 29. The lines of best fit allowed “model predicted” solutions to eqs 28 and 29. Correlation of the model predictions with experimentally determined values allows identification of the best fitting model. Figure 4 graphically

Figure 4. Plot of the Wertheim model, which provides the best fit for the solvatochromism of AlPcS2. The solvent dependence of ν̅a + ν̅f for AlPcS2 can be classified according to protic (■) versus aprotic solvents (□). Comparison of the four reaction field models at a = 0.25. The Wertheim model ( f W) provided the strongest correlation between model and empiricially derived ν̅a + ν̅f for AlPcS2 (r = 0.978, p < 0.0001).

represents the strong correlation between the data and the Wertheim model predicted values. Figure 4 also shows the poor correlation between the data and the other three reaction field models. Both the Block and Walker and the Ehrenson model give a reasonable agreement at lower values of εr. At higher values of εr, both the Block and Walker model and the Ehrenson model diverge from the experimentally determined values. In contrast, the Onsager model fails to even approach the experimental values. The strongest correlation was found for the Wertheim model using eq 22 and a = 0.25 (0.951, p < 0.001). In contrast to curcumin, eq 22 and not eq 21, provided the strongest correlation. Using the Wertheim model, eq 22 (a = 0.25) the relative permittivity of the dielectric medium surrounding liposome bound AlPcS2 is approximately that of ethanol, 25. This is in contrast to the estimate that can be arrived at using the data in Table 2. The data in Table 2 show that the absorbance peak for liposome bound AlPcS2 is between that of AlPcS2 in ethanol and acetone. The fluorescence peak for liposome bound AlPcS2 is most similar to that of AlPcS2 in acetone. The Δνa̅ + Δν̅f for liposome bound AlPcS2 is between that in acetone and isopropanol. 10199



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Figure 6. Wertheim model predictions for AlPcS2 lipid bilayer location. (A) The experimentally determined ν̅a + ν̅f for AlPcS2, when separated into protic (■) and aprotic solvents (□), have a strong relationship with the ET(30) solvent polarity scale. The predicted polarity for liposome bound AlPcS2 gives an ET(30) value between 176.6 kJ mol−1 and 186.4 kJ mol−1. The “molecular ruler” places AlPcS2 between 0.7 and 0.9 nm from the phospholipid−water interface. (B) The Wertheim model predicted ν̅a + ν̅f for gives 177.3 kJ mol−1 and 178.4 kJ mol−1 for liposome bound AlPcS2.

Figure 5. Block and Walker model predictions for curcumin, which can be used to predict lipid bilayer location. (A) The literature reported ν̅a − ν̅f for curcumin, when separated into protic (■) and aprotic solvents (□), have a strong relationship with the ET(30) solvent polarity scale. The predicted polarity for liposome bound curcumin is between 166.2 kJ mol−1 and 171.2 kJ mol−1. Using the “molecular ruler”, curcumin is located between 1 and 1.2 nm from the phospholipid−water interface. (B) The model predicted νa̅ − ν̅f for curcumin, when separated into protic (■) and aprotic solvents (□), also have a strong relationship with the ET(30) solvent polarity scale. Plotting the νa̅ − ν̅f for liposome bound curcumin gives ET(30) values between 166.8 kJ mol−1 and 168.6 kJ mol−1 helping to validate the model.

phospholipid−water interface. As with curcumin, this provides a control, against which to compare the lipid bilayer location of AlPcS2 determined from the Wertheim model (a = 0.25) predictions. Figure 6B shows the relationship between model predicted frequency sum values and the solvent polarity according to the ET(30) scale. The relationship is not as strong as that observed when using experimentally determined values in Figure 6A. However, plotting the liposome values gives ET(30) values of 177.3 kJ mol−1 and 178.4 kJ mol−1 for liposome bound AlPcS2. This is within the range of the values determined from the experimental values, therefore supporting the predictions of the model. The model predicted values narrow the location of AlPcS2 in the lipid bilayer to between 0.8 and 0.9 nm. This demonstrates that the solvatochromic models can predict the location of both curcumin and AlPcS2 in the lipid bilayer using the “molecular ruler”. The method presented here provides a rationalization of solvatochromic shifts for lipophilic molecules, coupled to a quantitative prediction of the lipid bilayer location. The molecular ruler technique provides a useful prediction but is also subject to some limitations. The lipid bilayer location actually represents the center of the fluorophore dipole

The Stokes shift values for the protic and aprotic solvents in Figure 5B are from the Block and Walker model (a = 0.25) predictions. Plotting the Stokes shift for liposome bound curcumin gives ET(30) values between 166.8 kJ mol−1 and 168.6 kJ mol−1. This is in the range of the ET(30) values given above. The close agreement suggests that the Block and Walker model (a = 0.25) can predict the time-averaged location of curcumin in the lipid bilayer from Stokes shifts. To further test this finding, the AlPcS2 data was treated in the same way. Figure 6A shows the relationship between the experimentally determined Δνa̅ + Δν̅f values (Table 2) and the solvent polarity according to the ET(30) scale. Again, classification of the solvents as either protic or aprotic provided the strongest relationship. Plotting the experimentally determined frequency sum value for liposome bound AlPcS2 gives an ET(30) value between 176.6 kJ mol−1 and 186.4 kJ mol−1. The “molecular ruler” places AlPcS2 between 0.7 and 0.9 nm from the 10200


The Journal of Physical Chemistry B moment, not necessarily the center of the molecule. Therefore, the molecule extends beyond the location identified in the analysis presented above. The molecular ruler also does not give information on the orientation of the fluorophore relative to the lipid bilayer structure. It could be assumed that the long axis of the molecule would be orientated parallel to the lipid, allowing for intercalation; however there is no evidence to support this. Additionally, the “molecular ruler” is dependent on phosphatidylcholine lipids. It is possible that different rulers would be required for other phospholipids or mixtures of lipid head groups and acyl chain saturation. In spite of the limitations, the “molecular ruler” provides significant, quantitative information on the location of lipophilic fluorophores in the lipid bilayer.

ACKNOWLEDGMENTS

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REFERENCES

The authors wish to thank Dr. Elizabeth R. Simons for fluorimeter access and advice in preparing this manuscript. Thanks also to the Department of Biochemistry for their support.

(1) Lippert, E. Dipole Moment and Electronic Structure of Excited Molecules. Z. Naturforsch. 1957, 10, 541−545. (2) Lakowicz, J. R. Principles of Fluorescence Spectroscopy; Springer: New York, 2006; Vol. 1. (3) Liptay, W. Electrochromism and Solvatochromism. Angew. Chem., Int. Ed. 1969, 8, 177−188. (4) Onsager, L. Electric Moment of Molecules in Liquids. J. Am. Chem. Soc. 1936, 58, 1486−1493. (5) Brady, J.; Carr, P. An Analysis of Dielectric Models of Solvatochromism. J. Phys. Chem. 1985, 5759−5766. (6) Marsh, D. Membrane Water Penetration Profiles of Spin Labels. Eur. Biophys. J. 2002, 31, 559−562. (7) Marsh, D. Reaction Fields in the Environment of of Fluorescent Probes: Polarity Profiles in Membranes. Biophys. J. 2009, 96, 2549−58. (8) Block, H.; Walker, S. M. A Modification of the Onsager Theory for a Dielectric. Chem. Phys. Lett. 1973, 19, 363−364. (9) Ehrenson, S. Classical Electrical Contributions to Solvent Polarity Scales. J. Am. Chem. Soc. 1981, 1, 6036−6043. (10) Wertheim, M. S. Dielectric Constant of Non-Polar Fluids. Mol. Phys. 1973, 26, 1425−1444. (11) Wertheim, M. S. Theory of Polar Fluids I. Mol. Phys. 1973, 25, 211−223. (12) Randles, E. G.; Bergethon, P. R. A Photo-dependent Switch of Lipid Bilayer Stability and Permeability. Langmuir 2013, 29, 1490−7. (13) Cohen, Y.; Bodner, E.; Richman, M.; Afri, M.; Frimer, A. NMRBased Molecular Ruler for Determining the Depth of Intercalants within the Lipid Bilayer Part I: Discovering the Guidelines. Chem. Phys. Lipid 2008, 155, 98−113. (14) Cohen, Y.; Afri, M.; Frimer, A. NMR-Based Molecular Ruler for Determining the Depth of Intercalants within the Lipid Bilayer Part II: The Preparation of the Molecular Ruler. Chem. Phys. Lipid 2008, 155, 114−9. (15) Afri, M.; Naqqash, M. E.; Frimer, A. Using Fluorescence to Locate Intercalants with the Lipid Bilayer of Liposomes, Bioliposomes and Erythrocyte Ghosts. Chem. Phys. Lipid 2011, 164, 759−65. (16) Reichardt, C. Solvatochromic Dyes as Solvent Polarity Indicators. Chem. Rev. 1994, 94, 2319−2358. (17) Khopde, S. M.; Priyadarsini, K. I.; Palit, D. K.; Mukherjee, T. Effect of Solvent on the Excited State Properties of Curcumin. Photochem. Photobiol. 2000, 72, 625−31. (18) Priyadarsini, K. I. Photophysics, Photochemistry and Photobiology of Curcumin: Studies from Organic Solutions, Bio-mimetics, and Living Cells. J. Photochem. Photobiol. C 2009, 10, 81−95. (19) Kunwar, A.; Barik, A.; Pandey, R.; Priyadarsini, K. I. Transport of Liposomal and Albumin Loaded Curcumin to Living Cells: An Absorption and Fluorescence Spectroscopic Study. Biochim. Biophys. Acta 2006, 1760, 1513−20. (20) Parisio, G.; Marini, A.; Biancardi, A.; Ferrarini, A.; Mennucci, B. Polarity Sensitive Fluorescent Probes in Lipid Bilayers: Bridging Spectroscopic Behavior and Microenvironment Properties. J. Phys. Chem. B 2011, 115, 9980−9989. (21) Stewart, J. C. M. Colorimetric Determination of Phospholipids with Ammonium Ferrothiocyanate. Anal. Biochem. 1980, 14, 10−14. (22) Began, G.; Sudharshan, E.; Sankar, K.; Rao, A. Interaction of Curcumin with Phosphatidylcholine: A Spectrofluorometric Study. J. Agric. Food Chem. 2000, 48, 576. (23) Chignell, C. F.; Bilskj, P.; Reszka, K. J.; Motten, A. G.; Sik, R. H.; Dahl, T. A. Spectral and Photochemical Properties of Curcumin. Photochem. Photobiol. 2008, 59, 295−302.

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CONCLUSIONS The semiempiricial models of solvatochromic shifts developed in this investigation can predict a lipid bilayer location for a fluorophore. The predicted bilayer location is in agreement with effects of AlPcS2 on lipid bilayers. With AlPcS2 predicted to be located around 0.8 and 0.9 nm from the interface, the photosensitizer has access to the acyl chain region of the lipid bilayer. This predicted access provides support to the previous observation that AlPcS2 bound to lipid bilayers and interacted with the acyl chain region.12 The solvatochromic models also describe the polarity of the environment and indicate the solvent structure. Under the analysis in this investigation, it is also possible to evaluate the role of dispersion forces to the solvatochromism of a fluorophore. The models investigated here are sufficient to provide a lipid bilayer location for a lipophilic fluorophore. They cannot provide a complete understanding of the fundamental basis for the observed solvatochromic shifts. It is known that solvatochromism is a complex phenomenon involving the coupled dynamical processes of both the fluorophore and the solvent.3,20,28,29 There are many intermolecular forces to consider that require quantum mechanical approaches in addition to the semiclassical methodology employed in this investigation. However, the analysis above provides a method to link easily obtained empirical data to a physical and quantitative model of fluorophore lipid bilayer interactions. The methodology developed in this investigation has clear utility. The mathematical analysis is complementary to EPR and NMR methods for interrogating lipid bilayer polarity profiles.6,30 Together, such experimental approaches and solvatochromic models will provide rich information on lipid bilayer dynamics, permeability, and structure.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: peter.bergethon@pfizer.com. Present Addresses

E.G.R.: Vertex Pharmaceuticals Inc., Materials Discovery and Characterization, 130 Waverly Street, Cambridge, Massachusetts 02138, United States. P.R.B.: Pfizer Neuroscience Research Unit, 700 Main Street, Cambridge, Massachusetts 02138, United States. Notes

The authors declare no competing financial interest. 10201



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(24) Dahll, T. A.; Bilski, P.; Reszka, K. J.; Chignell, C. F. Photocytotoxicity of Curcumin. Photochem. Photobiol. 1994, 59, 290−294. (25) Nardo, L.; Paderno, R.; Andreoni, A.; Másson, M.; Haukvik, T. Role of H-Bond Formation in the Photoreactivity of Curcumin. Spectroscopy 2008, 22, 187−198. (26) Barika, A.; Goelb, N. Effect of Deuterated Solvents on the Excited State Photophysical Properties of Curcumin. J. Photosci. 2004, 11, 95−99. (27) Sholto, A.; Ehrenberg, B. Hydrophobicity, Topography in Membranes and Photosensitization of Silicon Phthalocyanines with Axial Ligands of Varying Length. Photochem. Photobiol. Sci. 2008, 7, 344−51. (28) Kepczynski, M.; Pandian, R.; Smith, K. M.; Ehrenberg, B. Do Liposome-Binding Constants of Porphyrins Correlate with Their Measured and Predicted Partitioning between Octanol and Water? Photochem. Photobiol. 2002, 76, 127−134. (29) Marini, A.; Munoz-Losa, A.; Biancardi, A.; Mennucci, B. What is Solvatochromism? J. Phys. Chem. B 2010, 114, 17128−17135. (30) Marsh, D. Polarity and Permeation Profiles in Lipid Membranes. Proc. Nat. Acad. Sci. U.S.A. 2001, 98, 7777−82.

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Reaction Field Analysis and Lipid Bilayer Location for Lipophilic

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