Doxyl nitroxide probes and the intrinsic flexibility ... - ACS Publications

ency of the ionic heads toward segregation in layers, in order to minimize their ... School of Pharmacy, University of California, San Francisco, CA. ...
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J. Phys. Chem. 1983,87, 1635-1643

Bilayers on the contrary can grow without any contacts between ionic and hydrocarbon parts, and their electrostatic energy is lower, the number of ionic coordination vacancies being reduced; they thus appear to be by far the best possible solution.

Conclusions Our X-ray diffractometric investigation of the disordered phases of the long-chain primary n-alkylammonium chlorides, and comparison of its results with existing data on several other classes of hydrocarbon single-chain molecules with an ionic end g r o u ~pointed , ~ ~ ~out for these compounds a common stepwise melting behavior. The key to such a behavior is to be found in the tendency of the ionic heads toward segregation in layers, in order to minimize their electrostatic energy. The ionic layers are stable up to temperatures well above the onset of conformational disorder of the hydrocarbon tails,which undergo with increasing temperature a number of rearrangements from the polyethylenic-like packing to

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one or more conformationally molten states strictly analogous to the well-known "fluid" state of the lipid bilayer membranes.23 The layered organization persists even in the clear liquid, in which-for the n-alkylammonium chlorides-smectic domains are found. Acknowledgment. Thanks are due to the National Research Council (C.N.R.) and to the Ministry of Public Education of Italy for financial assistance. Registry No. Hexylammonium chloride, 142-81-4; heptylammonium chloride, 142-93-8; octylammonium chloride, 142-95-0; nonylammonium chloride, 2016-39-9; decylammonium chloride, 143-09-9; undecylammonium chloride, 2016-37-7; dodecylammonium chloride, 929-73-7; tridecylammonium chloride, 2016-55-9; tetradecylammonium chloride, 1838-04-6; pentadecylammonium chloride, 1838-05-7; octadecylammonium chloride, 1838-08-0. (23) Cf., for example, J. Seeling and A. Seeling, Q.Rev. Biophys., 13, 19 (1980), and references therein.

Doxy1 Nitroxide Probes and the Intrinsic Flexibility Gradient, A Slow-Motional Line Shape Analysis Study Michelle S. Broldo*+ and Eva Melrovltch' Depa&?"e of Isotope Research, Weizmann Institute of Science, 76 100 Rehovot, Israel (Received: July 13, 1982; I n Flnal Form: December 6, 1982)

The ESR spectra of seven doxyl-labeledstearic acids and stearic methyl esters dissolved in the liquid crystalline solvent Phase V have been examined over a wide range of temperature with the intent of addressing both the question of the intrinsic flexibility gradient of such probes in a gradient-free environment and questions related to the dynamics and ordering details of such systems. We find that slow-motional effects are observable in the ESR spectra at temperatures as high as 45 O C and that with the full line shape analysis derived from the stochastic Liouville equation a wealth of information is obtainable from these systems. Our results support the model of an intrinsic flexibility gradient originating at the center of mass of the probe; further, the spectra are not interpretable without invoking a dependence of solute dynamics on environment such as that arising from anisotropic viscosity.

I. Introduction Fatty acid doxy1 nitroxi& probes and labels have been used in a wide variety of ordered systems, particularly in both model and native In most of these systems, the acid end either is covalently bound (spin-label) or is hydrogen bonded or otherwise anchored (spin probe) to the hydrophilic region of the membrane bbyer.W I t has been found in such systems that as the position of the nitroxide gets further from the acid group the order parameter decreases steadily-'d2 This @'adient" has been the subject of much investigation, and one question which has been addressed is whether or not this flexibility gradient is inherent in the probes5 or is, indeed, a property of hydrocarbon chains in a lipid bilayer.ld@ 2H N M R results of deuterium-labeled hydrocarbon chains also show a flexibility gradient,'^^ and there now seems to be a consensus in the literature that the flexibility gradient is due, in part, to an intrinsic property of the bilayer Current address: Department of Pharmaceutical Chemistry, School of Pharmacy, University of California, San Francisco, CA 94143.

structure and, in part, to increased probability in the probe molecule for kink formation the greater the number of carbons from the anchoring acid groUp.'d'2 In their study of doxy1 probes in the nematic liquid crystal MBBA (p-methoxybenzylidene-n-butylaniline) ,5 LBon and co-workers addressed the question of whether there is an intrinsic flexibility gradient of doxyl-labeled (1) (a) Seelig, J. "Spin Labeling: Theory and Applications";Berliner, L. J., Ed.; Academic Press: New York, 1976; pp 373-409. (b) Smith, I. C. P.; Butler, K. W. Ibid., pp 411-51. (c) Griffith, 0. H.; Jost, P. C. Zbid., PP 454-523. (d) McConneut c. Ibid.?PP 525-60. (2) Marsh, D. "Membrane Spectroscopy"; Grell, E., Ed.; SpringerVerlag: West Berlin, 1981;pp 51-142. (3) Schreier, S.; Polnaszek, C. F.; Smith, I. C. P. Biochim. Biophys. Acta 197% 5159 395-436. (4) Sanson, A.; Ptak, M.; Rigaud, J. L.; Gary-Bobo,C. M. Chem. Phys. Lipids 1976, , 435-44. (5) &n, V.; Bales,B. L.; Villoria, F. Mol. Cryst. Liq. Cryst. Lett. 1980, 569 229-35. (6) Dill, K. A.; Flory, P. J. Proc. Natl. Acad. Sci. U.S.A. 1980, 77, 3115-9. (7) Mantach, H. H.; Saito, H.; Smith, I. C. P. Progr. Nucl. Magn. Reson. Spectrosc. 1976,ii, 211-72. (8) Seelig, J.; Seelig, A. Q. Rev. Biophys. 1980, 13, 19-61.

0022-3654/83/2087-1635$01.50/00 1983 American Chemical Soclety

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Broido and Meirovitch

The Journal of Physical Chemistry, Vol. 87, No. 9, 1983

alkyl chains, such as the stearic acids or stearic methyl esters, in a medium in which there is no environmental flexibility gradient (i.e., a nematic liquid crystal). To do so, they measured order parameters of the probes 16doxylstearicacid (16DA),methyl 16-doxylstearate(16DM), 12-doxylstearic acid (12DA), methyl 12-doxylstearate (12DM), 5-doxylstearic acid (5DA), and methyl 5-doxylstearate (5DM) and found order parameters decreasing 5DA > 12DA = 12DM > 5DM > 16DA = 16DM. Considering only the acid probes, they found a flexibility gradient similar to that obtained in the lipid bilayer systems. When one compares the acid and ester probes, the ordering 5DA > 5DM suggests "... some specific interaction of the acid head group with MBBA [while] [flurther away from the head group, the order of the acids and esters is essentially the same which shows that the specific interaction with the acid does not affect the intrinsic flexibility gradient of interest here."5 From the relative ordering of the methyl ester probes, the authors speculate that there is an intrinsic flexibility gradient in the doxyl probes which originates with the center of mass as anchor point and which should be approximately symmetric with respect to label position from either end. Although we find such a speculation plausible, we do not feel that their arguments are conclusive. To say that further away from the head group than C5 (probes 5DA and 5DM) the orders of the acids and esters are essentially equal when the next closest labeled position is C12seems to us to be a rather large jump. If proximity to the head group removes probes 5DA and 5DM from the discussion, then only two probe positions are being considered, and one of them is removed by only one methylene group from the terminal methyl group. This position would be, by far, the least highly ordered position whether the anchor point is the head group or whether the anchor point is the center of mass. We therefore consider the intrinsic flexibility gradient of aliphatic (doxyl-labeled) chains still to be an open question and one which we address in this study using complete line shape analysis. One of the problems in assessing such a flexibility gradient is that the center of mass changes as the position of the spin-label changes. Levine et al. have measured the 13C Tls of n-octadecane (C18H38) and found a monotonic decrease in T1 (consequently, monotonic decrease in rotational diffusion rate) as one progressed inward from the terminal methyl group to the fifth carbon from either end.g The central eight carbons were not resolved, but their bulk T1 was less than that of the carbons at the 5-positions. These two sets of results, nitroxide and 13C,are in agreement and, since interpretation of bilayer results must take into account intrinsic properties of the probes used, it is indeed imperative to establish the "intrinsic anchoring point" of such flexible chains. Nitroxide probes are of great value in investigating ordered systems, both because of the high experimental sensitivity of the ESR technique, leading to low concentration requirements, and because of the high sensitivity of resulting spectra to details of motion and ordering. We report here on the behavior of seven doxyl nitroxide-labeled stearic acids and stearic methyl esters, illustrated in Figure 1,when dissolved in the nematic liquid crystal Phase V, with the intent of addressing both the question of the intrinsic flexibility gradient of such probes in a gradient-free environment and questions as to the dynamics and ordering details of such systems. We show that a wealth of information is obtainable when spectra are (9)Levine, Y. K.; Birdsall, N. J. M.; Lee, A. G.; Metcalfe, J. C.; Partington, P.; Roberts, G. C. K. J. Chem. Phys. 1974, 60,2890-9.

H3C-( CH2)m-A- (CH2)n - COOR 0 NO I m -

16DA 12 DA 12 DM IODA 7 DA 5 DA 5DM

Yn

I

5 5 7 IO 12 12

Phase V eutectic mixture of

-

R

14 IO IO

H

H

CH3 H H H CH3

a

5 3 3

Q

CH34CHz)" -phenyl- N= N-phenyl- OCH3 CH3- ( CH2In- pheny I- N= N- pheny I- OC H3

0 n= 1,3 Flgure 1. Doxylstearic acid and methyl stearate probes used in this study. At bottom is structure of liquid crystalline solvent Phase V.

analyzed by using the full line shape analysis derived from the stochastic Liouville equation and point out the errors inherent in more simplified analyses. The ambiguities of the MBBA study are overcome in this study by the wider variety of probes used, by the (apparently) much decreased interaction of the acid group with the Phase V solvent molecules, and by the full line shape analysis. In the following section we present experimental details. Section I11 contains a brief introduction to slow-motional spectral line shape analysis and is followed by results and discussion in section IV. Our conclusions are summarized in section V.

11. Materials and Methods Licristal Phase V was purchased from E. Merck, Darmstadt, and used without further purification. Doxy1 probes 16-doxylstearic acid (16DA), 10-doxylstearic acid (lODA), 7-doxylstearic acid (7DA), 5-doxylstearic acid (5DA),and methyl 5-doxylstearate (5DM) were purchased from Molecular Probes; 12-doxylstearicacid (12DA) and methyl 12-doxylstearate (12DM) were purchased from Syva. Samples were 10-4-10-3M in spin probe and were contained in 4-mm 0.d. Wilmad Pyrex tubes no. 412; samples were pumped on a vacuum line at room temperature to remove possible trace amounts of solvent from probe or liquid crystal. The spectra were run by using a Varian E-12 ESR spectrometer equipped with a Varian E-257 variable temperature control unit controlling temperature to f0.5 "C. Temperatures were measured with a copper-constantan thermocouple and the isotropic-nematic phase transition of each sample was measured with a Mettler FP5 hot stage. To correct for thermocouple placement differences between samples, all temperatures measured with the thermocouple were adjusted by the difference between the phase transition temperature measured with the hot stage and that observed in the ESR spectrum; these corrections were typically 2 "C. Samples were heated to the isotropic phase while in the spectrometer and then were cooled to the nematic phase. Spectra taken in the nematic phase were independent of rate of cooling and raising or lowering of temperature. Power levels, modulation amplitude, filtering, and concentrations were checked to ensure that no saturation or distortion of the signals occurred.

Doxy1 Nitroxide Probes

The Journal of Physical Chemistry, Vol. 87, No. 9, 1983 1637

Computer simulations were performed on the Weizmann Institute computers: an IBM 165, an IBM 4341,and the GOLEM B. Programs used were written by Dr. Carl Polnaszek’O and Dr. Giorgio Moro.’l 111. Background The method of ESR line shape analysis by spectral simulation derived from solution of the stochastic Liouville equation has been detailed by Freed and co-workers in several papers.1°J2-15 Here we summarize the important features and parameters of the Polnaszek, Bruno, and Freed (PBF) theory12J3and refer the reader to the original work for details. We also assume some familiarity with rudimentary properties of liquid crystals on the p& of the reader and mention only those features relevant to this discussion. The stochastic Liouville equation for motion describes the time dependence of the spin density matrix, p , according to a(p,t)/at = - w ( Q , ~ ) , M Q , ~ ) - p O ( ~ ) )-i r,w) (1) where po is the equilibrium spin density matrix, and the random variable Q is the set of Euler angles specifying molecular orientation. r, is the timedependent rotational diffusion operator; the time dependence of Q is described by a stationary Markov process and is the corresponding Markov operator, Le. a ~ ( ~ , t ) /=a -r$w,t) t (2) where P(Q,t)is the probability of being at orientation Q at time t.1°J4J5 The spin Hamiltonian can be separated into three parts, go %,(Q) + &), where eoincludes the orientation-independent nuclear and electronic Zeeman interactions and the isotropic part of the 14N hyperfine interaction, and %,(Q) contains the anisotropic parts of the various terms in the spin Hamiltonian, of which the hyperfine interaction and the electronic Zeeman interaction (the A and g tensors, respectively) are the most important. c ( t ) is the time-dependent interaction of the electron spin with the oscillating electromagnetic field needed for spectral observati~n.’~J~ Since we are interested in the behavior of a solute undergoing Brownian rotational diffusion in the presence of an orienting potential exerted by the liquid crystalline solvent, the diffusion equation 2 becomes dP(Q,t)/at = -M-[R-IW(Q)/lzT + R*&kJP(Q,t)(3) = -rp(n,t)

+

where M is the vector operator which generates infinitesimal rotation and can be identified with the angular momentum operator, U(Q) is the potential exerted by solvent on solute, and R is the molecular diffusion tensor.14 Solution of eq 1requires that all component terms be specified in the same coordinate frame; this is achieved through appropriate application of the Wigner rotation matrices. The different coordinate frames of relevance are defined as follows: 1. (a) The laboratory frame, denoted x,y,z, is defined by the external magnetic field Ho,Hobeing directed along the z direction. (b) The director frame is defined by the (10) Polnaszek, C. F. Ph.D. Dissertation, Cornel1 University, Ithaca, NY, 1976. (11) Moro, G.,Cornel1 University, unpublished report, 1980. (12) Freed, J. H.;Bruno, G. V.; Polnaszek, C. F. J.Phys. Chem. 1971, 75,3385-99. (13) Polnaszek, C. F.; Bruno, G. V.; Freed, J. H. J. Chem. Phys. 1973, 58,3185-99. (14) Polnaszek, C. F.; Freed, J. H. J. Phys. Chem. 1976,79,2283-306. (15) Freed, J. H.“Spin Labeling: Theory and Applications”;Berliner, L.J., Ed.; Academic Press: New York, 1976; pp 53-132.

liquid crystalline solvent. Phase V aligns with its director, ii, parallel to the magnetic field; l6 i.e., the average orientation of the long axis of the liquid crystal molecules is parallel to the field. In a common nematic phase, z is parallel to ii, and this allows an identification of the director frame with the laboratory frame. 2. (a) The molecular frame, denoted x’,y’,z’, is defined by the geometry of the probe molecule; i.e., for an all-trans aliphatic chain conformation, z’ lies along the carbon skeleton. (b) The diffusion frame is that in which the rotational diffusion tensor is diagonal and is usually assumed to be identical with the molecular frame x’,y’,z’. However, see below. 3. The magnetic frame, denoted x”’,y’”,zl’’, is that frame in which the magnetic tensors (g and A, assumed to have the same principal axes) are diagonal. By convention? z”’ of a nitroxide is defined as lying along the nitrogen p orbital (or the N-0 T orbital), x’” lying along the N-0 bond, y ’”being perpendicular to the other two. For doxy1 nitroxides, the manner of attachment of the nitroxide ring to the carbon skeleton is such that z”’ is parallel to z’, provided that the portion of the chain containing the nitroxide moiety is in an all-trans conformation. Using full line shape analysis, one can obtain details of the dynamics and ordering of probe molecules dissolved in liquid crystalline solvents, i.e., details of reorientational rates, molecular flexibility, order parameters, and coupling of the dynamic behavior of probe and solvent mole~ules.’~J~ For an axially symmetric diffusion frame, two rotational diffusion constants are defined, Rl, and R,, the former being that for rotation parallel to the z axis of the appropriate coordinate frame and the latter being perpendicular to it.15 In all but a very fe4w cases, the diffusion tensor R and the rotation operator M have been considered to be diagonal in the molecular frame x’,y’,z’, as mentioned above, in which case, when R,, # R,, one refers to “anisotropic d i f f ~ s i o n ” . ’ ~ ~Physically, ’ ~ ~ ~ ~ ~ this ’ ~ ~means ~~ that the principal axes of rotational diffusion (that coordinate system in which the diffusion tensor is completely specified by RIland R,) are determined solely by the geometry of the molecule. Differences in the behavior of a probe molecule in anisotropic vs. isotropic media are thus due only to ordering, as defined below. When the diffusion tensor is diagonal in the director frame, x,y,z, rather than in the molecular frame, the situation is considered to be one of “anisotropic v i s c ~ s i t y ” . ~ ~The J ~ Jprincipal ~ axes of diffusion of the solute are then determined not by solute geometry but by solvent properties. The elements of the tensor diagonal in this frame are denoted RIland R,. Aniso!ropy_pm-ameters N and N are defined by N = Rllf R , and N = R,,/R,. Liquid crystalline solvent molecules exert an ordering potential on solute molecules such that the latter are no longer randomly distributed in space but, instead, order preferentially in some given direction.15J6J8*In general, by ordering of a cylindrical object in a given direction, it is meant that the orientational distribution of the main molecular symmetry axis is centered at that direction. A higher degree of ordering means a narrower width to the distribution. This ordering is explicitly represented in the mathematical formulation needed for simulating ESR spectra of such systems (see, for example, eq 3). (16) Doane, J. W.“Magnetic Resonance of Phase Transitions”;Owens, F. J., Poole, C. P., Farach, H.A,, Eds.; Academic Press: New York, 1979; pp 171-246. (17) Lin, W.-J.; Freed, J. H. J. Phys. Chem. 1979, 83, 379-401. (18) (a)Priestly, E.B. “Introduction t o Liquid Crystals”;Priestly, E. B., Wojtowicz, P. J., Sheng, P., Eds.; Plenum Press: New York, 1975, pp 1-13. (b) Wojtowicz, P. 3. Ibid., pp 45-58.

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The Journal of Physical Chemistry, Vol. 87,No. 9, 1983

Broido and Meirovitch a

The mean orienting potential for probes dissolved in a liquid crystalline solvent is written, most generally, as

where the 2)s are elements of the Wigner rotation matrices of rank L and the Q = (cu,P,r) are the Euler angles between the molecular and director frame^.'^^^^^'^ Symmetry considerations allow for the simplification of the potential expression in several ways. The uniaxial nature of nematic liquid crystals, i.e., the equivalence of 6 and -6, reduces the problem to terms of even L only. With the reasonable assumption of cylindrical symmetry abr lut 6, any averaging over y vanishes unless M = 0.10J4J5Also, one need not consider a)& in the potential since this is an isotropic term. Thus, for an axially symmetric probe in a cylindrically sopmetricuniaxial medium, the potential can be expanded by using the Legendre potentials, PL,as the basis

U’(P) = CCL’PL(COS 6) L

1

b

(5)

The commonly used order parameter, S, is defined by

S = ((1/2)(3 cos2 6 - 1))= (a)&)

-

S d Q exp(-U/kt)a)&(Q)

-

JdQ exp(-U/kt)

(6) Flgwe 2. Spectra of 7doxylstearic acid (7DA) in Phase V as a function

where cos 6 = z.zf.14 For many systems it is useful and of temperature: (-) experimental spectrum; (---) spectrum simulated valid to assume cylindrical molecular symmetry, implying with anisotropic viscosity and anisotropic diffusion; (- -) spectrum that the ordering of x ’is identical with that of y ’. In this simulated with anisotropic viscosity only; (-. -) spectrum simulated with anisotropic diffusion only. For exact simulation parameters, see case, the potential U reduces to the Maier-Saupe potential Table I . in which only the first term, a)& or P2, in the expansion is kept. When the assumption of identical x ’ and y’ orcisely the need for, and use of, these parameters which dering is not valid, it is necessary to consider additional terms in the expansion of the ordering ~ 0 t e n t i a l . lThis ~ ~ ~ ~ allows for the extraction of detailed information about probe molecules in ordered systems. In contrast to using necessitates using the a)koexpansion since the Legendre slow-motional line shape analysis, most ESR spectra in the polynomials are functions only of the single angle, 6. (It literature have been analyzed according to simplified should be noted, however, that when the molecular ortechniques valid only in the motional narrowing limit. dering is cylindrically symmetric, inclusion of the P4term Furthermore, whenever the ESR spectrum was comprised may be necessary, e.g., in the case of strong jump diffuof three distinguishable lines, it has been unequivocably sion.)lg assigned to the motional narrowing regime, although this When the geometry of the probe molecule dictates use was shown lately to be an erroneous and misleading criof the Wigner matrix expansion of the potential, Freed has terion.Ig With these simplified analyses, correlation times found that the most important terms are those of second are derived from line widths (assuming, often incorrectly, rank.14 Using the real linear combinations of the Bs, one that experimental line shapes are true Lorentzians), which can show that, in the x ’,y ’,z’ system requires that the noninhomogeneously broadened intrinsic line width and the superhyperfine constants be known, the U ( Q )= €$&(Q) + (c; + €22)(a)$O(Q) + a)!2o(Q)) (7) Maier-Saupe potential is almost always used whether valid which is equivalent to or not, order parameters are calculated directly from experimental splittings without taking into account dynamic U(a,P) = -kTX cos2 p - kTp sin2 6 cos 201 (8) frequency shifts and/or slow-motional effects, and the where (-kT)(2/3)X = ti and (-kT)(2/(6)lI2)p = 6; + diffusion tensor is assumed to be diagonal in the molecular For a long ellipsoidal molecule, it is expected that z’ will frame.20 Unfortunately, many of these assumptions are be more strongly ordered (parallel or perpendicular to the not always valid and often lead to erroneous conclusions, director) than x’or y’, thus, X > p . p is a measure of the as illustrated below. difference in ordering of the x and y ’axis; that is, it is a IV. Results and Discussion measure of the asymmetry in the fluctuations of the long molecular axis about the dire~tor.’~,’~ Preferential ordering The temperature-dependent X-band ESR spectra of of y greater than x ’along the director corresponds to p seven doxyl probes (see Figure 1) dissolved in the liquid > 0, and p = 0 leads to the Maier-Saupe potential. crystalline nematic solvent Phase V were recorded and In slow-motional line shape analysis, it is the rotational analyzed by slow-motional line shape analysis following diffusion constants, the ordering parameters, and the anisotropies therein which are varied to obtain best-fit sim(20) Schindler and Seelig (J. Chem. Phys. 1973, 59, 1841-50) have ulations. We discuss in detail the sensitivity of spectra to analyzed the fast-motional ESR triplet line widths from doxyl probes dissolved in phospholipid bilayers to find asymmetric ordering tensors, these parameters below, and we point out that it is pre+ 02%)# 0. Zannoni et al. (J.Magn. Le., p # 0 or, alternatively, (a&, Reson. 1981,43,141-53) interpreted their studies of a similar system (and reinterpreted Schindler and Seelig’s results) in terms of (a&)(or PJ # (19)Rao,K. V. s.; Polnaszek, C. F.; Freed, J. H. J.Phys. Chem. 1977, 0, rather than (ato + 332,) # 0. 81,449-56.

The Journal of Physical Chemistry, Vol. 87,No. 9, 1983

Doxy1 Nitroxide Probes

TABLE I: Parameters for Best-Fit Spectral Simulationsa,b

temp,

(a;,)

t

"C

h

25 44 55.5 65.5

1.6 1.2 1.05 0.84

0.36 0.27 0.23 0.18

24.5 36.5 43.5 54.5 64

2.8 2.1 1.9 1.45 1.2

0.51 0.45 0.4 2 0.32 0.27

16DA 0.1 0.021 (0.05) (0.013) (0.05) (0.014) (0) (0.0) 12DA 0.5 0.055 0.4 0.065 0.2 0.036 0.2 0.045 (0.05) 0.013

20 31.5 41.5 49.5 58 65.5

2.8 2.3 1.9 1.65 1.4 1.1

0.57 0.49 0.42 0.37 0.31 0.24

20.5 34.5 41.5 47.5 63

2.6 1.95 1.8 1.6 1.1

22.5 29.5 37.5 46 52.5 67

R l , S-'

pc

1.5 X 10' 5 x 10' 8 X lo8 1x 1 0 9

N, (=N) 5 3 3 1

3 x 107 6 x lo7 1 x 10' 2 x lo8 3 x 10'

10 8 5 5 3

12DM 0.5 0.055 0.5 0.073 0.2 0.036 0.15 0.031 0.1 0.023 (0.05) (0.013)

3 x 107 5 x 107 1 x 10' 1.5 x l o 8 2 x 10' 3 x 10'

10 5 5 5 4 3

0.54 0.42 0.39 0.35 0.24

10DA 0.5 0.061 0.5 0.088 0.4 0.076 0.3 0.063 (0.05) (0.013)

3.2 5.5 1x 1.4 3x

x 107 x 107

10 6 5 5 3

2.8 2.5 2.1 1.8 1.6 1.1

0.57 0.52 0.45 0.40 0.35 0.24

7DA 0.5 0.5 0.4 0.2 0.2 (0.05)

3 x 107 4.5 x 107 6 X lo7 1x l o 8 1.5 X l o 8 3 x lo*

10

25.5 30.5 43.5 54.5 61.5 66.5

2.5 2.1 1.8 1.3 1.2 1.03

0.52 0.45 0.39 0.29 0.27 0.23

5DA 0.5 0.065 0.5 0.081 0.3 0.057 (0.05) (0.012) (0.05) (0.013) (0.05) (0.014)

3.5 4x 8x 2x 2.5 3.5

x 107

10' x 10'

10 8 7 3 3 3

26.5 40 49.5 55.5 67

2.3 1.8 1.5 1.3 1.0

0.49 0.40 0.33 0.29 0.22

5DM 0.5 0.013 0.2 0.038 0.15 0.033 (0.05) 0.012 (0.05) 0.014

5 x 107 1x l o 8 1.5 X 10' 2 x lo8 4 x 10'

8 6 5 3 1

0.055 0.065 0.065 0.038 0.042 0.013

10' X 10' 10'

107 107 lo8 X

I

I

I

1639

I I 5 5 3

a This table contains both the ordering potentials h and p and the corresponding averages of the Wigner rotation matrix elements (DOZ,)and (D:, t DZ,,). These latter parameters are related in a straightforward manner to Saupe's ordering tensor components and to Snyder's ordering parameters.I4 Magnetic parameters used: g,, = 2.0088, g,, = 2.0061, g,, = 2.0021, A,, = 5.89 G, A,, = 5.42 G, A,, = 31.42 G, T,* -' = 0.5 G. Maximum values of L in the eigenfunction expansion ranged from 6 to 1 4 ; K was typically L - 2, all truncation being checked for convergence. Spectra are insensitive to p < 0.1.

PBF theory. Typical spectral behavior is illustrated by probe 7DA in the series of spectra shown in Figure 2 (solid lines). The parameters for best-fit spectral simulations of all seven probes are listed in Table I. As mentioned above, it is often the case that order parameters (or equivalently, A) are determined from experimental splittings, according to

where ( a ) is the experimental hypefine splitting, aN is the isotropic hyperfine splitting (equal to one-third the trace of the hyperfine tensor), A,, is the principal component

12-doxyl stearic acid

0

20

40 T ("C)

60

Flgure 3. Potential coefficient A vs. temperature for 5doxylstearicacid (5DA) and 12doxylstearic acid (12DA) in Phase V: (0) A,; (X) A,; (A)A, in MBBA.5

of the hyperfine tensor in the z"' direction and it is assumed that z' / / z"', and a, is a correction factor which may be needed if aNand A,, were obtained in a phase of different polarity than that of the relevant e ~ p e r i m e n t . ~ ? ' ~ We have calculated S for the doxyl probes in Phase V over a range of temperatures directly from the experimental spectra using eq 9 and determined the corresponding value of the potential parameter A, (experimental).lo Concomitantly, we have determined the X values (denoted A,) from slow-motional line shape analysis. Plotted in Figure 3 are X, and X, vs. temperature for probes 5DA and 12DA. Although at higher temperatures the two potential parameters are equal, below -45 "C the A, and A, curves begin to diverge, the A, curve giving increasingly higher relative ordering as temperature decreases. Such discrepancies between A, and X, have been observed by Rao et al., in their study of cholestane spin probe in Phase V; for example, they found X,/X, to be 1.17 at 35 "C and 1.42 at 19 "C.19 That A,/& # 1is seen at temperatures as high as 65 "C for cholestane whereas for the doxyl probes this is not observed until -45 "C is not surprising, given the greater rigidity and slower tumbling of the cholestane molecule. What is, perhaps, surprising is that, even at such relatively high temperatures and rapid motion, the spectra of the flexible doxyl probes cannot be adequately analyzed by using the motional narrowing theory. Also plotted in Figure 3 are the A, values for probes 5DA and 12DA in the nematic liquid crystal MBBA, where the X values are determined from the order parameters measured from experimental splittings by LBon et aL5 Their results parallel our results for A, in Phase V, and we strongly suggest that, should their spectra be analyzed with full line shape theory, the resulting X, values would indicate much lower orderings for these probes in MBBA than those which they claim. Simulations. In simulating the spectra, we first tried the simple model of anisotropic diffusion and .axially symmetric ordering, Le., N # 1, X # 0, N = 1, p = 0. For rigid molecules such as cholestane, N is determined simply from the geometry of the molecule and should be insensitive to temperature, although sensitivity to N decreases as motions are slowed beyond a certain rate (dependent

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upon details of anisotropies and dynamic modes).lg However, for flexible chains such as the doxyl probes, neither the N value nor its temperature dependence is obvious. Assuming C-C bond lengths of 1.5 A,C-H bond lengths of 1.1A,and tetrahedral bond angles, we can estimate the length-to-width ratio of an extended, all-trans stearic acid molecule to be 6.5-7, corresponding to N values of 9.9-11.1.21 If the nitroxide group of a stearic probe is considered in defining the molecular width, smaller N values pertain. For a flexible chain, we can think of N as defining that segment of the chain which acts as a single entity, and we would expect the effective length of that segment to increase as temperature decreases and motions are slowed (vide infra). At higher temperatures (faster motions) and lower ordering, line shifts due to dynamic effects are small,13and we could estimate X directly from experimental splitting. Splittings are very sensitive to small changes in X (or S) and we could easily distinguish spectra calculated with X = 1.0, 1.05, and 1.1 (S= 0.14,0.15, and 0.16, respectively) from each other. Thus,high accuracy can be obtained with proper simulation. Although we could, indeed, obtain simulated splittings equal to experimental splittings, we found no combination of R , and N(R,,)which would give the experimental relative intensities of the spectral lines. Furthermore, at lower temperatures, besides incorrect relative intensities, the line widths of the simulated spectra became increasingly greater than those in the experimental spectra. The experimental spectrum is actually a superposition of the spectra arising from a spatial (and dynamic) distribution of contributing molecules; as temperature decreases, less efficient positional averaging causes a broadening of the observed lines. In a liquid crystalline mesophase, as temperature decreases the ordering of the solvent molecules and the potential which they exert on the solute molecules increase, decreasing the width of the positional distribution and causing narrowing of the spectral lines. Clearly, increasing the order potential parameter X to compensate for the large increases in line width which we observed in the simulated spectra leads to improper splitting and hence is inappropriate, and we then considered introducing a nonzero potential asymmetry parameter, p. If we look at a space-filling model of a doxyl molecule, as in Figure 4, there is a clear inequality in the width of the molecule in the x ‘ and y ’directions. Thus, a nonzero p is physically reasonable. Introduction of nonzero p into the simulations did, indeed, have the desired effect on spectra, namely, decreased relative intensity of the low-field line and decreased line width; however, these effects were much less than were required for accurate simulation. Typical best-fit spectra obtained with anisotropic diffusion and asymmetric ordering are illustrated in Figure 2, and it is clear from the poor fit of these spectra that such a model is not sufficieni. Thus far we have considered R to be diagonal, and M to generate rotation, in the molecular frame x’,y’,z’. If, however, principal axes of rotation are determined not by geometry but by the solvent, i.e., if the liquid crystalline solvent molecules act as ‘‘wallsn which forcs a redefinition of the principal axes of rotation, R and M must now be expressed in the director frame x,y,z. This is what is defined above as anisotropic viscosity. In a study of the small nitroxide probe, PD-Tempone, Polnaszek and Freed found that inclusion of anisotropic viscosity in their simulations vastly improved the fit of the simulated spectra to the experimental spectra; in particular, relative inten(21) Woesnner, D. E.J. Chem. Phys. 1962,37,647-54.

Broido and Meirovitch

Figure 4. Space-filling model of ’Idoxylstearic acid (7DA). On left, N - 0 is facing side; on right, N - 0 is facing front.

sities of the three observed lines were reproduced.14 However, in the PD-Tempone system, anisotropic viscosity was not physically reasonable since the spectra so simulated resulted in an increasing rate of rotational diffusion as temperature decreased. In most general terms, the diffusion tensor being diagonal in the director frame is simply stating that there is some type of motional interdependence between the solvent and solute molecules, i.e., that the diffusion of the spin probe is not independent of its environment. In fact, the PD-Tempone spectra were finally analyzed by invoking a coupling of solvent and solute dynamic modes in the form of a slowly relaxing local structure, rather than anisotropic viscosity, and it has been shown that technically these two models have similar spectral consequence^.'^ It is perhaps possible to envision the dependence of the motion of the solute molecules on principal coordinate frame of the diffusion tensor by the illustration in Figure 5. In the case of anisotropic diffusion, the principal coordinate frame can be superimposed upon the molecular frame and we can think of rotation about the axes as indicated in the upper part of the figure. When the diffusion tensor is diagonal in the director frame, the rotation of the molecule is visualized as illustrated in the lower part of this figure. Whether this lower picture is an accurate representation or not, given the similarity in size and shape of the solvent and solute molecules in the labeled stearic acid-Phase V system and the motional cooperativity in liquid crystalline phases, it would not be surprising to see some effect of its environment on the probe dynamics. Consideration of anisotropic viscosity vastly improved the simulations of the doxyl probes at all temperatures. At higher temperatures, experimental spectra could be simulated with anisotropic viscosity and essentially axially

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A

Rl, ANISOTROPIC VISCOSITY

Flgwe 5. Schematic representation of (top) anisotropic diffusion and (bottom) anisotropic viscosity.

V Figure 6. Simulated spFctra showing sensitivity to potentiel asymmetry parameter p . R , = R , = 5 x io7 s-l;N = ri, = 5; x = 2.0;(-) p = 0.0;(---) p = 0.2;(..*) p = 0.5.

symmetric ordering. For the set of motional and ordering parameters needed to adequately describe the system under study here, the inclusion of the potential asymmetry parameter, p, allows for “fine tuning” of the simulations, as can be seen in Figure 6. It should be noted that, in the PD-Tempone-Phase V system, nonzero p was needed to adequately simulate the higher temperature spectra; l4that this is so illustrates that the sensitivity of spectra to motional and ordering parameters is dependent not only upon absolute values but also upon specific combinations of parameters. At lower temperatures, spectra could not be simulated without the inclusion of nonzero p. Below 36 “C, there is some discrepancy between the experimental spectra and those simulated with anisotropic viscosity and asymmetric ordering, but the latter simulations are exceedingly better than those obtained with anisotropic diffusion. This is illustrated in the 22.5 and 37.5 “C spectra in Figure 2. If we again try to picture the physical system, it seems reasonable that, for a fatty acid probe in a liquid crystalline environment, both the geometry of the probe and interactions with the environment should affect its motion. Freed and co-workers have considered the situation of combined anisotropic diffusion and anisotropic viscosity (see, in particular, Appendix C of ref 17); and when the diffusion tensor can be decomposed into two components, R time independent in the molecular frame and R time independent in the director frame, they obtain a time-independent diffusion operator analogous to that in eq 3.17 For the case of the slowly relaxing local structure (SRLS) mechanism for coupling of solvent and solute dynamic modes, Polnaszek and Freed have extended, for rapidly reorienting probe molecules considerably smaller than the liquid crystalline molecules, the theoretical formulation for the dynamic effects on the ESR ~pectnun.’~J~ Since long-chain fatty acid probes are similar in size to the

Flgure 7.- Simulated spectra showing relative sensitivity to N-and A . R , and R = , 3 X lo7 s-‘;h = 2.8; p = 0.5; (-) N,= 10, N = 10; ( e . .) N = ?, N = 10 (barely distinguishable from N = N = 10); (- - -) N = 10, N = 4.

,

liquid crystalline molecules and since, in most of the temperature range covered in this study, their Brownian reorientation is not sufficiently rapid for the SRLS formulation to be appli~able,’~ we did not carry out spectral simulations with this formulation. Using the approach of Lin and Freed,17we have simulated the doxy1 spectra in Phase V considering both Nand N # 1 and found that we could so obtain very good agreement between experimtntal and simulated spectra, the fit being best when N = N . Lin and Freed also found in their study of PD-Tempone in smectic phases that the be$ agreement in such simulations was obtained with N = N.17 Relative sensitivities to N and N are illustrated in Figure 7. The parameters listed in Table I are those obtained with N = N, although at higher temperatures spectra were insensitive to 1 < N < N. The lines corresponding to both anisotropic viscosity and anisotropic diffusion in Figure 2 are those obtained with N = N, at 37.5 “CJhe simulations obtained with N = N f 1 and N = 1 # N are barely distinguishable, and by 46 “C_ they are indistinguishable. This greater sensitivity to N than to N in slower motional spectra was predicted in the original PBF13work and supports the dependence of the long-chain probe motions on their environment. We would like to note that several observations as to the complexity of molecular motions in the more structured and viscous liquid crystalline phases appear in the ESR literature. Line shape analysis of slow-motional ESR spectra of 3’,3’-dimethyloxazolidinyl-N-oxy-2’,3,5t-cholestane (CSL) in N-03-butoxybenzy1idene)-p-n-octylaniline (40,8) and in N-(p-butoxybenzy1idene)-p-n-hexylaniline (40,6) pointed out an undue increase in N (of the CSL) upon lowering the temperature within the smectic A and smectic BA phases of these liquid crystals, and this was interpreted as reflecting the coupling-in of collective solvent modes.22 With a nitroxide-labeled fatty acid, nitroxide-labeled DPPC (1,2-dipalmitoyl-sn-glycero-3phosphocholine) and CSL dissolved in the LJ1) phase of uniform 2 w t 90 water content DPPC bilayers, the solute molecules were found to experience two superimposed dynamic modes: rapid, individual Brownian tumbling and a slow collective mode whereby chain distortions in the fatty acid residues of DPPC were being propagated through the medium.23 A similar cooperative motion was also detected with 2,2’,6,6’-tetramethy1(4-butoxybenzoy1)aminopiperidinyl-1-oxyin the smectic A phase of S2 (a eutectic mixture of three biphenyl derivatives) arid also in the supercooled nematic phase of 5CB (4-cyano4’-n-bi~henyl).~~ In the present study, the observed temperature dependence of N fits with those observations of cooperativity in the more ordered/lower temperature states of other spin probe-liquid crystal systems. (22) Meirovitch, E.; Freed, J. H. J . Phys. Chem. 1980,84, 2459-72. (23) Meirovitch, E.;Freed, J. H. J. Phys. Chem. 1980,84, 3281-95. (24)Meirovitch, E.;Igner, D.; Igner, E.; Moro, G.; Freed, J. H. J . Chem. Phys. 1982,77,3915-38.

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A few further comments about the simulations are in order. As mentioned above, motional narrowing analysis requires that the intrinsic line width be known. There is significant inhomogeneous broadening of spectral lines by neighboring protons, greatly complicating motional narrowing a n a l ~ s i s To . ~ rigorously account for this broadening, one needs to know the intrinsic line width T,*-l accurately, and, even for a perdeuterated probe, one must adequately account for (deuteron) superhyperfine splittings. For the rigid nitroxide PD-Tempone, the effect due to the 12 methyl deuterons can be accounted for precisely; for a flexible chain, different conformations will contribute differently to hyperfine line broadening and precise evaluation of T2*-' would not be possible. Slower motional spectra are less sensitive to proton-induced broadening of lines, and full line shape analysis can be performed on protonated species.lg Indications of slow motion are asymmetry in lines and inequivalence of m = +1to m = 0 and m = 0 to m = -1 hyperfine splittings, and, as found by Rao et al., in the cholestane study referred to above, such slow-motional effects can be seen at temperatures as high as 50-65 "C.19 Inclusion of these effects is inherent in full line shape analysis and, in fact, part of the sensitivity of full line shape analysis lies therein. One potential criticism of the method lies in the number of "free" parameters; however, hyperfine splitting asymmetry is very sensitive to the specific combination of motional and ordering parameters, and in most cases of relevance to this study this characteristic was indeed borne out by the experimental ESR spectra. Very Low-Temperature Spectra. Typical spectra of doxyl-labeled stearic acid in Phase V obtained at temperatures lower than 15 "C are illustrated in Figure 8a, and to our knowledge such spectra have not been reported elsewhere. The unusual feature of these spectra is the splitting of the central line in the spectrum,a feature which cannot be ascribed simply to anisotropy in g, A, or ordering, nor to a tilt of relative to x'. These spectra cannot be explained on the basis of two site spectra as there is no indication of splitting of the low- and high-field lines. Invoking anisotropic viscosity and large asymmetry in the potential was imperative for reproducing this prominent and unique feature. We found that below -7 "C the spectral changes on lowering the temperature are due primarily to a decrease in motional rates and that we could obtain good simulations at the different temperatures, shown in Figure 8b, with changes in R , while holding X and p constant. Invariance of the order parameters as a function of temperature in low-temperature smectics and in supercooled nematic phases has been reported e l s e ~ h e r e . ~Note ~ - ~also ~ that the motional rates R,, for temperatures below 7 O C , extrapolate satisfactorily from the higher temperature data. The exact values of the parameters R,, A, and p should, of course, be regarded with some reservation when the coupling of solute and solvent dynamic modes are of such apparent magnitude. Although the simulations obtained are not perfect, the trends in the experimental spectra are definitely reproduced, and we know of no other considerations which will result in such spectra. Flexibility Gradient, The model in which the intrinsic flexibility gradient of flexible-chain molecules originates at the center of mass of the chain is well supported by our results. Probes 12DA, 12DM, lODA, and 7DA, i.e., those labeled a t positions toward the center of the chain, are similarly ordered and are more highly ordered than molecules labeled at positions closer to the chain ends. Probes 5DA and 5DM are slightly less ordered than these and

0

b

A

H

7

IOG

I Figure 8. (a) Experimental low-temperature spectra of 7doxylstearic acid (7DA) in Phase V. (b) Simulations reproducing ail features of expTrimental spectra in part a. N = fi = 10; = 2.8;p = 1.5; R I = R , indicated in flgure.

probe 16DA is significantly less ordered. Unless the segment of the molecule acting as a unit (that is, the length of chain defined by N) contains the chain ends, diffusion rates should be similar for all segments, as we find. As temperature decreases and the ordering potential exerted by the solvent on the chains increases, the length of the effective segmept should and did increase, as illustrated by the N (and N) temperature dependence. (Although N is not necessarily reflective of molecular dimensions, as is N , to the extent that it is-a measure of cooperativity between solute and solvent, N cannot be entirely independent of solute size.) The effective diffusion rate can be defined as Re = (@,)1/2 = (N)1/2R,, and, if this is, indeed, primarily a function of molecule size rather than label position, the activation energies for rotational diffusion of each of the doxy1 probes examined here would be identical, or nearly so. When plotted vs. reciprocal temperature, the Res of the probes (other than 16DA) all fall (approximately) on a single line, as illustrated in Figure 9. The scatter is not surprising; besides being indicative of some dynamic sensitivity to label position, we would expect sensitivity to the nonequivalence of the two ends of the molecules and, as suggested by LBon et al. in their MBBA study, there is the possibility of some interaction of the acid group with the solvent which would not be present for the methyl ester probe^.^ The plot of Re for end-labeled probe 16DA is parallel to that for the other probes, suggesting that, although the end position is much more flexible than the more central positions, the mechanisms which define the rotational process, including a coupling of solvent and

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The Journal of Physical Chemistry, Val. 87, No. 9, 1983

full line shape analysis and would not have been obtained had the spectra been analyzed with the simpler techniques.

T ("C)

V. Summary and Conclusions

5DM A 10DA 12DA 12DM

IXI091

5l 3

t

lXlO*

5

3

I

i 1i

c

I

1

29

I

31 I/T (K-')

1643

I

33

I

35

Flgure 9, R e vs. reciprocal temperature. Approximate activation energy for 16DA is 8.7 kcal/mol; for others it is 7.9 kcal/mol.

solute dynamics, are similar. The flexibility gradient observed in lipid and membrane probes and labels has been described as arising from kink (trans-gauche isomerization) diffusion, with the probability of a kink increasing toward the end of the chain.25@ This increase is due both to the increasing number, as one goes down the chain, of carbon-carbon single bonds about which rotation can occur and to the less restrictive environment in the hydrophobic region of the bilayer. Hsi et al. found that, in the alkoxy chains of a homologous series of thermotropic liquid crystalline molecules, the probability of trans-gauche isomerization increases toward the end of the chain.27 For both types of systems, temperature decrease leads to decreasing kink probability. The N and N temperature dependence observed in this study is consistent with such a picture; if N and N define a chain segment which can be described as ending where there is relatively high (and specific) kink probability, then at lower temperatures more carbon-carbon bonds will need to be included before that kink probability would be obtained. Also, the influence of environmental factors on kink probability is consistent with the need to describe the dynamic modes in this study by anisotropic viscosity, and we would suggest that anisotropic viscosity might well be needed to properly characterize membrane bilayer system, It should be noted that the observations of the N and N dependence on temperature of these doxyl probes and of the great importance of anisotropic viscosity result from (25) Kainosho, M.; Kroon, P. A,; Lawaczek, B.; Petersen, N. 0.; Chan, S . I. Chem. Phys. Lipids 1978,21, 59-68. (26) Edholm, 0. Chem. Phys. Lipids 1978,29, 213-24. (27) Hsi,S.; h m e r m a n , H.; Luz, Z. J. Chem. Phys. 1978,69,4126-46.

We have examined the X-band ESR spectra of seven doxyl-labeled stearic acid and stearic methyl ester probes dissolved in the nematic liquid crystalline solvent, Phase V, with the intent of examining the proposal of an "intrinsic flexibility gradient" in such probes and in order to obtain details of the dynamics of the systems. As has been observed in the study of the rigid nitroxide probe cholestane, slow-motional effects can be observed in the spectra of these flexible probes at relatively high temperatures (-45 "C for the doxyl probes) and even where the spectra are still comprised of three well-separated lines. Order parameters derived by assuming these spectra to be fast-motional spectra were found to deviate significantly from the order parameters obtained following slow-motional line shape analysis, and we would suggest that such deviations would be even more significant in biological systems in which rotational diffusion rates are lower and the ordering higher than in the Phase V system. At higher temperatures, spectra could be simulated by consideration of an axially symmetric ordering potential and anisotropic viscosity; as temperature decreased, the asymmetry of the ordering potential increased and it became necessary to include the effects of anisotropic reorientation with the anisotropic viscosity in describing the rotational diffusion. The unexpected result that anisotropic viscosity was found to be the dominant dynamic factor is indicative Qf the relative importance of the coupling of solvent and solute modes. At temperatures below 15 "C, the spectra obtained were very unusual and could only be explained by invoking collective interactions of solvent and solute, reflected in the anisotropic viscosity, and a highly asymmetric ordering potential. Our results support the model of an intrinsic flexibility gradient of such fatty acid molecules in which the central portion of the molecule is the most rigid and which is most highly ordered. The length of the segment of the chain which acts as an effective body increases with decreasing temperature, consistent with a definition of the segment as a region of the chain with low kink probability. Further, our results all suggest the need to consider coupling of solvent and solute dynamic modes when interpreting ESR spectra of such flexible probes in ordered systems, and such considerations cannot be made without full line shape analysis. Although such analysis is often difficult and requires extensive computer usage, we would like to suggest that the value of the information so obtained more than compensates for inherent difficulties in the method.

Acknowledgment. This study was made possible in part by funds granted by the Charles H. Revson Foundation (to E.M.). This work was also supported, in part, by NIH-NIGMS National Research Service Award GM-07932 (to M.S.B.). Registry No. 16DA, 53034-38-1; lODA, 50613-98-4; 7DA, 40951-82-4; 5DA, 29545-48-0; 5DM, 38568-24-0; 12DA, 29545-47-9; 12DM, 29639-21-2.