Chemometrics: Theory and Application

6 Analysis of the Electron Spin Resonance of Spin Labels Chemometrics: Theory and Application Downloaded from pubs.acs.org by UNIV OF CALIFORNIA SAN DIEGO on 11/30/15. For personal use only.

Using Chemometric Methods JAMES R. KOSKINEN* and BRUCE R. KOWALSKI Laboratory for Chemometrics, Department of Chemistry, University of Washington, Seattle, WA 98195

Spin labels are being used to study the structure of model membrane systems and biological membranes (1,2.). The spin label ing technique involves incorporating a nitroxide free radical (the spin label) into a membrane system and studying the free radical using electron spin resonance (ESR) spectrometry. Lipid spin labels that are diffused into a membrane orient themselves in a specific configuration and undergo anisotropic molecular motion. When this motion is rapid on the ESR time scale, the ESR spectra that are observed can be correlated with the struc ture of the membrane. Molecules have been constructed so that the long axis of the molecule is parallel to one of the principal axes of the nitrox ide. Anisotropic motion about the long axis of the molecule corresponds to rotation about one of the principal axes of the nitroxide. The ESR spectra of this type of molecule in a well defined inclusion crystal have been studied and synthesized in order to better understand the membrane spin labeling experi ments (3, 4, 5). Studies using s p i n l a b e l s i n v o l v e a considerable e f f o r t f o r the chemist i n the c o l l e c t i o n and a n a l y s i s o f the s p e c t r a . In the p a s t , s p e c t r a were c o l l e c t e d as two dimensional p l o t s on a p i e c e o f paper and the u s e f u l information e x t r a c t e d from the p l o t s using a r u l e r and a p e n c i l . With the i n t r o d u c t i o n o f l a b o r a t o r y computers t h i s task has been made much e a s i e r (6). Spectra are now c o l l e c t e d by computer c o n t r o l l e d spectrometers and are saved i n computer compatible format ( i . e . , on paper tape, magnetic tape, o r d i s k s ) . T h i s use o f computers a l s o allowed •Present address:

Ford Motor Company S c i e n t i f i c Research Laboratory, Box 2053 Dearborn, Michigan 48121

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Chemometrics: Theory and Application Downloaded from pubs.acs.org by UNIV OF CALIFORNIA SAN DIEGO on 11/30/15. For personal use only.

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CHEMOMETRICS : THEORY AND APPLICATION

some simple data a n a l y s i s techniques t o be performed on the spectra. These techniques i n c l u d e d b a s e - l i n e c o r r e c t i o n s and s p e c t r a l smoothing. Computers have made i t r e l a t i v e l y easy to c o l l e c t and s t o r e a l l the ESR s p e c t r a f o r a p a r t i c u l a r study. T h i s paper w i l l present examples o f the use o f computers t o a i d the chemist i n the a n a l y s i s o f ESR s p e c t r a . The f i r s t a p p l i c a t i o n w i l l i n volve the use o f Chemometric methods t o study two s p i n l a b e l s i n d i f f e r e n t i n c l u s i o n c r y s t a l s . T h i s a p p l i c a t i o n w i l l demonstrate the general usefulness o f chemometrics t o a n a l y z i n g ESR s p e c t r a . The second a p p l i c a t i o n w i l l concern s p i n l a b e l s i n a model membrane system. Methodology The data a n a l y s i s methods used i n t h i s paper come under the general heading o f Chemometrics (7/8) · The methods used are the ones t h a t w i l l e x t r a c t f e a t u r e s from the ESR s p e c t r a , c a l c u l a t e the importance o f the e x t r a c t e d f e a t u r e s t o a p a r t i c u l a r property o f the s p i n l a b e l , and f i n a l l y , d i s p l a y the r e s u l t s . A l l the s p e c t r a used i n t h i s study were c o l l e c t e d under computer c o n t r o l and s t o r e d i n d i g i t a l form as 980 data p o i n t s . The 980 data p o i n t s can be used as f e a t u r e s t h a t d e s c r i b e each spectrum. However, such a l a r g e number o f f e a t u r e s can present d i f f i c u l t i e s f o r some data a n a l y s i s methods. A method t h a t reduces the number o f f e a t u r e s d e s c r i b i n g the s p e c t r a without l o s i n g chemically u s e f u l information i s c l e a r l y needed. The method o f choice i n t h i s study i s the F o u r i e r transform. F o u r i e r transform methods have been used q u i t e e x t e n s i v e l y i n other forms o f spectroscopy f o r a v a r i e t y of purposes (9). The e f f e c t o f the F o u r i e r transform i s t o condense the information o f the t o t a l ESR spectrum i n t o the low frequency end of the t r a n s formed spectrum. Figure 1 shows a t y p i c a l ESR spectrum, the r e a l and imaginary p a r t s o f the F o u r i e r transform o f the spectrum, and the power spectrum. The low frequency end o f the transformed spectrum contains a l l the information needed t o r e c o n s t r u c t the o r i g i n a l spectrum v i a the i n v e r s e o r back transform. This process i s g r a p h i c a l l y presented i n F i g u r e 2. The f i r s t 64 p o i n t s o f the transformed spectrum are r e t a i n e d while the r e s t o f the p o i n t s are s e t t o zero. The i n v e r s e transform r e t u r n s the o r i g i n a l spectrum showing t h a t no information l o s s r e s u l t s . The spectrum r e s u l t i n g from the i n v e r s e transform appears t o be smoother than the o r i g i n a l spectrum because the high frequency noise has been d i g i t a l l y f i l t e r e d by the transform. By using the F o u r i e r transform, 64 features t h a t completely d e s c r i b e the spectrum have been generated out o f a spectrum o f 980 data p o i n t s . Once the f e a t u r e s have been generated i n t h i s manner, the other Chemom e t r i c methods can be a p p l i e d . Two s t a t i s t i c a l methods are used t o determine the importance o f the generated f e a t u r e s i n modeling a property o f the s p i n l a b e l . The property o f i n t e r e s t i n the f i r s t a p p l i c a t i o n i s the


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KOSKINEN AND KOWALSKI

Figure 1.

Electron Spin Resonance of Spin Labels119

Typical ESR spectrum and its Fourier transform

temperature o f the s p i n l a b e l and the property o f i n t e r e s t i n the second a p p l i c a t i o n i s the amount o f s p i n l a b e l present. The f i r s t method c a l c u l a t e s the c o r r e l a t i o n between the generated features and the property. The second method i s step-wise regress i o n a n a l y s i s t h a t determines which o f the features does the b e s t job o f modeling the property with a l i n e a r model. P l o t s o f the generated features vs. the property are a l s o constructed as p a r t o f the a n a l y s i s . A l l o f the methods d e s c r i b e d are p a r t o f the ARTHUR p a t t e r n r e c o g n i t i o n system (10) which was used i n t h i s study.


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Figure 2. Graphical demonstration that only the first 64 points of the Fourier transform of an ESR spectrum are needed to regenerate the spectrum from the transform Spin Labels i n I n c l u s i o n C r y s t a l s The f i r s t system s t u d i e d using the above d e s c r i b e d methodology c o n s i s t e d o f 3-doxyl-5a-cholestane (I) (the 4',4 -dimethyloxazoladine-N-oxyl d e r i v a t i v e o f 3-keto-5ot-cholestane) i n an i n c l u s i o n c r y s t a l o f t h i o u r e a . The question t o be answered i n t h i s study i s : can the temperature o f the i n c l u s i o n c r y s t a l system be c o r r e l a t e d t o the ESR spectrum? The data s e t contains 16 ESR s p e c t r a o f the s p i n l a b e l i n c l u s i o n c r y s t a l system corresponding t o a range o f temperatures from -82.0°C t o 59.2°C. Table I l i s t s the data a n a l y s i s steps taken t o analyze t h i s s e r i e s o f s p e c t r a . Feature number four, generated using the F o u r i e r transform, i s found t o be the most important feature i n modeling the temperature o f the system. F i g u r e 3 shows a p l o t o f the temperature vs. feature f o u r . 1

\

Structure I

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Electron Spin Resonance of Spin Labels

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Table I Steps Taken i n Data A n a l y s i s


I II

III IV V VI

C o l l e c t Spectra Generate Features Using F o u r i e r Transform A Zero F i l l Spectra t o 1024 P o i n t s (Requirement o f F a s t F o u r i e r Transform) Β Perform Fast F o u r i e r Transform C S e l e c t the F i r s t 64 C o e f f i c i e n t s o f t h e Real P a r t o f the Transform C a l c u l a t e C o r r e l a t i o n between the 64 Features and Property Perform Stepwise Regression A n a l y s i s o f the 64 Features Generate P l o t s o f Features S e l e c t e d i n Steps I I I and IV vs. the Property Analyze R e s u l t s

I e d a l l y , Figure 3 should show a s t r a i g h t l i n e i n d i c a t i n g t h a t feature four i s l i n e a r l y r e l a t e d t o the temperature. The s c a t t e r o f p o i n t s about the l i n e can be i n t e r p r e t e d as meaning t h a t the a n i s t r o p i c motion o f the molecule i s somewhat r e s t r i c t e d . The s h o r t e r steps between f e a t u r e four values a t the high temperature end i n d i c a t e s t h a t the r o t a t i o n about the long a x i s o f the mole c u l e i s being optimized. • 59 2° c

-82.0° C FEATURE

FOUR

Figure 3. Plot of the Fourier transform generated feature number four (the ordinate) vs. the temperature of the system (the abscissa) in sample one


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CHEMOMETRICS: THEORY AND APPUCATION

The second system s t u d i e d c o n s i s t e d o f the s p i n l a b e l l a u r y l n i t r o x i d e (II) ( 2 , 2 , 6 , 6 - t e t r a m e t h y l - 4 - p i p e r i d i n o l - l ~ o x y l dodecanoate) i n an i n c l u s i o n c r y s t a l o f β-cyclodextrin. The data s e t f o r t h i s system contains 20 ESR s p e c t r a o f the s p i n l a b e l i n the i n c l u s i o n c r y s t a l corresponding t o a temperature range o f -196°C t o 63°C. Table I again l i s t s the data a n a l y s i s steps taken i n the a n a l y s i s o f these s p e c t r a . F o u r i e r transform f e a t u r e number three i s shown by the s t e p wise r e g r e s s i o n a n a l y s i s t o be the most important f e a t u r e i n modeling the temperature o f the system. Once again a l i n e a r p l o t o f the f e a t u r e and the temperature i s expected. Figure 4 shows the a c t u a l p l o t which appears t o be l i n e a r from the low tempera ture end (-196°C) t o a temperature o f about 35°C. Then the value o f the f e a t u r e does not get any l a r g e r . I t remains n e a r l y con s t a n t from about 35°C t o 63°C. In the low temperature r e g i o n , the ESR spectrum approaches the r i g i d g l a s s l i m i t . As the tem perature i n c r e a s e s , the molecule s t a r t s t o r o t a t e more f r e e l y about i t s long a x i s . A t approximately 35°C the r o t a t i o n about the n i t r o x i d e p r i n c i p a l x-axis i s f a s t enough on the ESR time s c a l e such t h a t the y and ζ c o n t r i b u t i o n s are averaged out. A f u r t h e r i n c r e a s e i n temperature has no a d d i t i o n a l e f f e c t on the a n i s t r o p i c motion. I t i s i n t e r e s t i n g t o compare both s p i n l a b e l s i n t h e i r r i g i d m a t r i c e s . The l a u r y l n i t r o x i d e i s able t o r o t a t e q u i t e f r e e l y and reaches an optimum value. The 3-doxyl-5a-cholestane i s not a b l e t o r o t a t e as f r e e l y as the l a u r y l n i t r o x i d e and appears not to reach an optimum v a l u e . T h i s d i f f e r e n c e i n r o t a t i o n can be accounted f o r by the s t r u c t u r e o f the molecules. L a u r y l n i t r o x ide i s a long, c y l i n d r i c a l - s h a p e d molecule, w h i l e the 3-doxyl-5acholestane i s a r e c t a n g u l a r shaped molecule. I t i s e a s i e r f o r the c y l i n d r i c a l molecule t o r o t a t e about i t s long a x i s i n a c a v i t y i n a matrix than i t i s f o r the rectangular-shaped molecule. Now t h a t the Chemometric methods have been shown t o be use f u l i n the study o f s p i n l a b e l s i n w e l l - d e f i n e d i n c l u s i o n c r y s t a l s the methods can be used i n the study o f s p i n l a b e l s i n a model membrane system. The l a s t p a r t o f t h i s paper w i l l d e a l w i t h the a p p l i c a t i o n o f Chemometric methods t o the study o f such a model membrane system.

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•63 0 ° C

•196.o°C

FEATURE THREE Figure 4. Plot of the Fourier transform generated feature number three (the ordinate) vs. the temperature of the system (the abscissa) in sample two Spin Labels i n Model Membrane

Systems

The model membrane system s t u d i e d i s the cytochrome oxidase protein containing spin labeled phospholipids. The s p i n l a b e l used i s 16-doxyl s t e r i c a c i d (III) (the 4 ,4·-dimethyloxazoladineN-oxyl d e r i v a t i v e o f 16-keto s t e a r i c a c i d ) . F i g u r e 5 shows the s p e c t r a o f r e p r e s e n t a t i v e samples o f the cytochrome oxidase p r o t e i n w i t h d i f f e r e n t concentrations o f p h o s p h o l i p i d s . The amount o f l i p i d i n each sample i s expressed as the r a t i o o f mg o f phosp h o l i p i d p e r mg o f p r o t e i n . The sample i n F i g u r e 5a has a r a t i o 1

Structure I I I

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Figure 6. Graphical presentation of the generation of a composite ESR spectrum by using scaled amounts of Fourier transform of two ESR spectra


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of 0,10; F i g u r e 5b corresponds t o a r a t i o o f 0.24; and F i g u r e 5c i s 0.73. The ESR spectrum o f the sample with the lowest l i p i d content (Figure 5a) i s c h a r a c t e r i s t i c o f strong i m m o b i l i z a t i o n o f the s p i n l a b e l s w h i l e the spectrum o f the sample with the h i g h e s t l i p i d content (Figure 5c) i s c h a r a c t e r i s t i c o f a more mobil s p i n l a b e l (11). The question t o be answered i n t h i s experiment i s : i s i t p o s s i b l e t o q u a n t i f y the amount o f each k i n d o f s p i n l a b e l i n a composite system as shown i n Figure 5b? The data s e t i n c l u d e s e i g h t s p e c t r a o f samples o f v a r y i n g amounts o f the p r o t e i n and s p i n l a b e l e d p h o s p h o l i p i d . The f e a t u r e generation methodology used i s the same as d e s c r i b e d i n the p r e vious examples. The property o f i n t e r e s t i n t h i s example i s the amount o f immobilized l i p i d present i n the model membrane system. By u s i n g stepwise r e g r e s s i o n a n a l y s i s i t i s p o s s i b l e t o a r r i v e a t an equation t o c a l c u l a t e the amount o f the l i p i d present. By using t h i s equation, i t i s p o s s i b l e t o look a t the F o u r i e r transform o f an ESR spectrum o f the membrane system and c a l c u l a t e the amount o f immobilized l i p i d present. A p r a c t i c a l proof o f the v a l i d i t y o f t h i s equation i s t o s y n t h e s i z e an ESR spectrum f o r t h e s e r i e s s t u d i e d using s p e c t r a o f the immobilized s p i n l a b e l and the mobil s p i n l a b e l . Since the equation was developed u s i n g the F o u r i e r transform t o the ESR s p e c t r a , they w i l l be used i n p l a c e o f t h e s p e c t r a . The F o u r i e r transform o f the immobilized s p i n l a b e l spectrum (Figure 5a) i s m u l t i p l i e d by t h e c a l c u l a t e d s c a l e f a c t o r and the r e s u l t i s added t o the F o u r i e r transform o f the mobil s p i n l a b e l s c a l e d by the c a l c u l a t e d f a c t o r . Then the i n v e r s e transform i s a p p l i e d t o t h i s composite t o g i v e the spectrum. In t h i s case the F i g u r e 5b i s the spectrum t h a t i s being s y n t h e s i z e d . The s c a l e f a c t o r f o r the immobilized s p i n l a b e l i s 0.24, and the f a c t o r f o r the mobil s p i n l a b e l i s 0.76. T h i s p r o cess i s shown g r a p h i c a l l y i n F i g u r e 6. The r e s u l t a n t s y n t h e t i c spectrum appears smoother than the experimental spectrum because the h i g h frequency n o i s e has been d i g i t a l l y f i l t e r e d . In t h i s a p p l i c a t i o n Chemometric methods were used t o show t h a t c e r t a i n ESR s p e c t r a o f a model membrane system are a composi t e o f s p e c t r a o f an immobilized s p i n l a b e l and a mobil s p i n l a b e l . Conclusions Chemometric methods have been used t o analyze experimental ESR s p e c t r a . The methods have provided a d d i t i o n a l i n s i g h t i n t o the processes i n v o l v e d i n p u t t i n g a s p i n l a b e l i n t o an i n c l u s i o n crystal. They have a l s o been used t o examine the ESR s p e c t r a r e s u l t i n g from s p i n l a b e l s d i s p e r s e d i n a model membrane system. Chemometrics does p r o v i d e a powerful t o o l t o a i d the chemist i n the a n a l y s i s o f ESR s p e c t r a o f s p i n l a b e l s i n model membrane systems.

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Acknowledgments We wish t o acknowledge Drs. P a t r i c i a J o s t and 0. Hayes G r i f f i t h f o r k i n d l y p r o v i d i n g us w i t h the ESR s p e c t r a used i n t h i s study. We a l s o wish t o acknowledge the f i n a n c i a l support o f the O f f i c e o f Naval Research under C o n t r a c t No. N00014-75-C-0536.


Literature Cited

1. McConnell, Η. M. and McFarland, B. F., Quart. Rev. Biophys., (1970) 3, 91-136. 2. Jost, P., Waggoner, A. S., and Griffith, Ο. Η., in "Structure and Function of Biological Membranes," Rothfield. L. (Ed.) pp. 84-144, Academic Press, New York, 1971. 3. Birrell, G. B., Van, S. P., and Griffith, O. H., J. Amer. Chem.Soc.,(1973) 95, 2451. 4. Birrell, G. Β., Griffith, O. Η., and French, D., J. Amer. Chem.Soc.,(1973) 95, 8171. 5. Griffith, Ο. Η., J. Chem. Phys., (1964) 41. 1093. 6. Klopfenstein, C. E., Jost, P., and Griffith, Ο. Η., in "Computers in Chemical and Biochemical Research," Klopfenstein C. E. and Wilkins, C. L. (Eds.), pp. 175-221, Academic Press, New York, 1972. 7. Kowalski, B. R., Anal. Chem. (1975), 47, 1152A. 8. Kowalski, B. R., J. Chem. Infor. & Compt. Sci., (1975), 15, 201. 9. Marshall, A. G. and Comisarow, Μ. Β., Anal. Chem., (1975), 47, 491A. 10. Duewer, D. L., Koskinen, J. R. and Kowalski, B. R., "ARTHUR" available from B. R. Kowalski, Laboratory for Chemometrics, Department of Chemistry, University of Washington, Seattle, Washington 98195. 11. Jost, P.C.,Griffith, O. H., Capaldi, R., and Vanderkooi, G., Proc. Nat. Acad. Sci. USA, (1973), 70 (2), 480-484.

Chemometrics: Theory and Application

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