Article pubs.acs.org/ac
Calculation of Membrane Lipid Ratios Using Single-Pixel Time-ofFlight Secondary Ion Mass Spectrometry Analysis Rainer Kassenböhmer,* Felix Draude, Martin Körsgen, Andreas Pelster, and Heinrich F. Arlinghaus Physikalisches Institut, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Straße 10, 48149 Münster, Germany S Supporting Information *
ABSTRACT: Much evidence suggests that membrane domains, termed lipid rafts, which are enriched in sphingomyeline and cholesterol play important roles in the regulation of physiological and pathophysiological processes. A label-free quantitative imaging method for lipids is lacking at present. We report an algorithm which enables us to identify and calculate the percentages of the ingredients of lipid mixtures from single-pixel time-of-flight secondary ion mass spectrometry (TOF-SIMS) spectra in model systems. The algorithm is based on a linear mixing model. Discriminant analysis is used to reduce the dimension of the data space. Calculations were separately performed for positive and negative ion mass spectra. Phosphatidylcholine and sphingomyeline which have identical headgroups and cannot be easily distinguished from another by positive ion mass spectra were included in the analysis. The algorithm outlined may more generally be used to calculate the percentages of ingredients of mixtures from spectra acquired by quite different methods such as X-ray photoelectron spectroscopy.
T
he cell is the smallest structural and functional entity of the organism. Physiological and pathophysiological events of higher organisms can only be understood if the underlying cellular processes are known. Involved in many of these processes are membranes, which envelop the cell itself as well as all cellular organelles. The basic structure of the membrane is a phospholipid bilayer with interlaced cholesterol molecules.1,2 The arrangement of these lipids depends on functional requirements and varies substantially not only between different but also within the same layers.3−8 Domains within the outer membrane layer, so-called lipid rafts, which contain preferentially sphingolipids and cholesterol, seem to play an important role in signal transmission and membrane mediated transport processes.9−11 The lateral distribution of phospholipids and cholesterol, which contribute to most of the constituents of the lipid bilayer, is usually visualized by fluorescence microscopy.12−14 Labeling with fluorophores, however, may affect the mobility and distribution of the lipid molecules. Imaging time-of-flight secondary ion mass spectrometry provides a label-free and very sensitive technique for simultaneously detecting sputtered ions over a wide mass range with nanometer-scale spatial resolution.15−19 For unambiguous identification of particular phospholipids at each primary ion position, enough counts of lipid-specific secondary ions, such as complete molecules or high-mass characteristic fragments which usually originate from the headgroups, have to be detected. However, the substantial fragmentation of many biological molecules by ion bombardment makes it difficult to identify membrane components with high specificity and sensitivity even though the development of cluster ion sources led to an enhancement of the yields of organic molecules.20−22 © 2015 American Chemical Society
Furthermore, distinction between the phospholipids phosphatidylcholine and sphingomyeline, which possess identical headgroups, is very difficult. Thus, time-of-flight secondary ion mass spectrometry (TOF-SIMS) analyses of biological membranes include only single and the most abundant phospholipids.23−25 More sensitive as well as quantitative information about the phospholipid distribution can only be obtained if low mass fragment ions that are common to multiple lipid species are included in the analyses. For this reason, multivariate analysis was employed to quantify the varying percentage of cholesterol using TOF-SIMS data from regions of more than 1 mm2.26 One limitation of this method is the requirement for well-defined calibration samples for each mixture. The goal of the present work is to develop a method to identify individual lipids within lipid mixtures and to calculate their percentages in single pixels using multivariate analysis.
■
METHODS
Discriminant Analysis. Unlike principal component analysis, discriminant analysis does not serve the purpose of identifying groups by means of common characteristics, but the groups, in this case the lipids, must be defined by the user.27−29 Since correct classification of the various lipids which are used as standards is crucial for the following calculations, discriminant analysis was used to answer the questions whether Received: April 18, 2015 Accepted: July 5, 2015 Published: July 5, 2015 7795
DOI: 10.1021/acs.analchem.5b01456 Anal. Chem. 2015, 87, 7795−7802
Article
Analytical Chemistry Table 1. Lipids Used for Analyses
(ΣgG= 1Σkng= 1(xgki − xg̅ i)(xgkj − xg̅ j))ij which contain the deviations between and within the groups (xgki, value of ith variable, kth measurement, and gth group; xg̅ i, mean value of ith variable and gth group; xi̅ , mean value of ith variable). As only (s − 1) equations are linearly independent, normalization is possible in a way that the standard deviation of the discriminant scores of each group is 1. If the variables differ by several orders of magnitude, these normalized discriminant coefficients not necessarily can be compared. If the ith normalized discriminant coefficient is multiplied by the ith diagonal element of the within covariance matrix S = (1/(ng − g))W, which corresponds to the pooled standard deviation within a group, one obtains the directly comparable standardized discriminant coefficients. When G is the number of groups, not more than (G − 1) eigenvalues are nonzero. Therefore, the dimension of the discriminant space is less than or equal to (G − 1). The most common statistic indicating the quality of the discriminant function is the significance test for Wilks’ lambda,
metric variables are capable of isolating groups and how relevant single variables are to isolating groups. A TOF-SIMS image can be regarded as a stack of p = n × m pixels each containing a complete spectrum of s peaks. Usually the data are presented within the s-dimensional data space in the form of a p × s matrix with ion peak areas as entries. The original s variables Xi (specific mass peaks) are usually not suitable for separating the groups. In discriminant analysis the coordinate system is changed. The new coordinate axes are defined by so-called discriminant functions Dj s
Dj =
∑ aijXi i=0
(1)
that are linear functions of the Xi with the discriminant coefficients aij. They enable the optimal separation of different groups. The projections of the variables on the new axes are called discriminant scores. In the easiest case of only two groups, the discriminant coefficients are calculated by maximizing the quotient λ(a) = BdWd−1 of the deviance between different groups Bd and the deviance within the groups Wd. a is the (s × s − 1) matrix with the entries aij. More generally, if more than two groups exist, each with ng measurements, the calculation of λ can be considered as the eigenvalue problem28 (B − λ ·W) ·a = 0
Λ=
1 1+λ
(3)
which is the quotient of the variance in the discriminant scores not explained and the total variance. The greater the eigenvalue λ, the smaller is Λ. Computation of Mixture Ratios. In TOF-SIMS imaging of phospholipid mixtures, the ion peak areas are the variables and the different phospholipids form the groups for discriminant
(2)
with B being the (s × s) between-matrix with entries (ΣgG= 1ng(xg̅ i − xi̅ )(xg̅ j − xj̅ ))ij and W the s × s within-matrix with entries 7796
DOI: 10.1021/acs.analchem.5b01456 Anal. Chem. 2015, 87, 7795−7802
Article
Analytical Chemistry Table 2. Total Counts/Pixel of Pure Phospholipid Preparations positive ion mode
negative ion mode
phospholipid
mean total counts/pixel
standard deviation
range
mean total counts/pixel
standard deviation
range
PC SM PE PS CH
1348.68 1399.23 1066.77 648.49 1187.24
191.49 235.74 204.27 112.69 81.92
1023−2034 837−2165 588−1750 370−1523 1036−1474
795.19 895.82 1302.30 995.00 684.41
116.31 206.24 197.97 171.12 142.88
630−1932 433−3044 849−3189 834−2192 429−1538
Table 3. Signal Intensities (Counts/Pixel) of Specific and Characteristic (Marked As Bold) Phospholipid Fragments in Pure Phospholipid Preparations m/q
PC +
58.08 ([C3H8N] ) 60.09 ([C3H10N]+) 86.10 ([C5H12N]+) 88.05 ([C3H6NO2]+) 102.09 ([C6H14O]+) 104.11 ([C5H14NO]+) 124.02 ([C2H7PNO3]+) 125.01 ([C5H4PNO]+) 142.03 ([C2H9PNO4]+) 146.99 ([C4H4PO4]+) 150.08 ([C5H13PNO2]+) 166.07 ([C5H13PNO3]+) 184.10 ([C5H15PNO4]+) 198.12 ([C6H17PNO4]+) 208.03 ([C3H8PNO6 Na]+) 224.13 ([C8H19PNO4 ]+) 225.12 ([C7H18PN2O4 ]+) 367.33 ([C27H43]+) 368.35 ([C27H44]+) 369.36 ([C27H45]+) 383.34 ([C27H43O]+) 384.34 ([C27H44O]+) 385.35 ([C27H45O]+) 520.52 ([C34H66NO2]+) 575.53 ([C37H67O4]+) 703.59 ([C39H80PN2O6]+) 577.54 ([C39H67O4]+) 603.56 ([C39H71O4]+) 605.63 ([C39H73O4]+) 633.66 ([C41H77O4]+) 725.58 ([C39H79PN2O6Na]+)
SM
68.67 14.44 47.92
61.36 17.91 54.07
6.89 18.80
7.41 25.80
8.93
12.23
PE
PS
m/q
CH 747.57 758.55 760.56 790.57 812.56 122.00 140.02 163.03 168.05 178.04 180.06 182.03 196.05 208.08 383.32 385.35 401.34 402.24 404.27 447.30 598.44 600.45 616.45 642.48 687.55 714.56 716.57 742.59 744.60 766.60
1.57
0.86 0.05 2.27 9.79 25.63
2.81 3.81 10.39 57.70 2.44 0.16
5.21 0.88 1.21 2.25 10.86 0.36 1.19 2.77 0.11 0.03 0.07 0.07 0.05 0.13
0.05 0.01
i ,j
PE
([C39H74PNO10] ) ([C42H81PNO8]+) ([C42H83PNO8]+) ([C44H89PNO8]+) ([C44H88PNO8Na]+) ([C2H5PNO3]−) ([C2H7PNO4]−) ([C5H8PO4]−) ([C4H11PNO4]−) ([C5H9PNO4]−) [C5H11PNO4]− ([C5H11PO5 ]−) [C5H11PNO5]− ([C7H15PNO4]−) ([C27H43O]−) ([C27H45O]−) ([C27H45O2]−) ([C20H37PNO5]−) ([C20H39PNO5]−) ([C26H42PNO3]−) ([C34H65PNO5]−) ([C34H67PNO5]−) ([C34H67PNO6]−) ([C36H69PNO6]−) ([C38H76PN2O6]−) ([C39H73PNO8]−) ([C39H75PNO8]−) ([C41H77PNO8]−) ([C41H79PNO8]−) ([C43H77PNO8]−)
PS
CH
Calculation of Membrane Lipid Ratios Using Single-Pixel Time-ofFlight Secondary Ion Mass Spectrometry Analysis Rainer Kassenböhmer,* Felix Draude, Martin Körsgen, Andreas Pelster, and Heinrich F. Arlinghaus Physikalisches Institut, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Straße 10, 48149 Münster, Germany S Supporting Information *
ABSTRACT: Much evidence suggests that membrane domains, termed lipid rafts, which are enriched in sphingomyeline and cholesterol play important roles in the regulation of physiological and pathophysiological processes. A label-free quantitative imaging method for lipids is lacking at present. We report an algorithm which enables us to identify and calculate the percentages of the ingredients of lipid mixtures from single-pixel time-of-flight secondary ion mass spectrometry (TOF-SIMS) spectra in model systems. The algorithm is based on a linear mixing model. Discriminant analysis is used to reduce the dimension of the data space. Calculations were separately performed for positive and negative ion mass spectra. Phosphatidylcholine and sphingomyeline which have identical headgroups and cannot be easily distinguished from another by positive ion mass spectra were included in the analysis. The algorithm outlined may more generally be used to calculate the percentages of ingredients of mixtures from spectra acquired by quite different methods such as X-ray photoelectron spectroscopy.
T
he cell is the smallest structural and functional entity of the organism. Physiological and pathophysiological events of higher organisms can only be understood if the underlying cellular processes are known. Involved in many of these processes are membranes, which envelop the cell itself as well as all cellular organelles. The basic structure of the membrane is a phospholipid bilayer with interlaced cholesterol molecules.1,2 The arrangement of these lipids depends on functional requirements and varies substantially not only between different but also within the same layers.3−8 Domains within the outer membrane layer, so-called lipid rafts, which contain preferentially sphingolipids and cholesterol, seem to play an important role in signal transmission and membrane mediated transport processes.9−11 The lateral distribution of phospholipids and cholesterol, which contribute to most of the constituents of the lipid bilayer, is usually visualized by fluorescence microscopy.12−14 Labeling with fluorophores, however, may affect the mobility and distribution of the lipid molecules. Imaging time-of-flight secondary ion mass spectrometry provides a label-free and very sensitive technique for simultaneously detecting sputtered ions over a wide mass range with nanometer-scale spatial resolution.15−19 For unambiguous identification of particular phospholipids at each primary ion position, enough counts of lipid-specific secondary ions, such as complete molecules or high-mass characteristic fragments which usually originate from the headgroups, have to be detected. However, the substantial fragmentation of many biological molecules by ion bombardment makes it difficult to identify membrane components with high specificity and sensitivity even though the development of cluster ion sources led to an enhancement of the yields of organic molecules.20−22 © 2015 American Chemical Society
Furthermore, distinction between the phospholipids phosphatidylcholine and sphingomyeline, which possess identical headgroups, is very difficult. Thus, time-of-flight secondary ion mass spectrometry (TOF-SIMS) analyses of biological membranes include only single and the most abundant phospholipids.23−25 More sensitive as well as quantitative information about the phospholipid distribution can only be obtained if low mass fragment ions that are common to multiple lipid species are included in the analyses. For this reason, multivariate analysis was employed to quantify the varying percentage of cholesterol using TOF-SIMS data from regions of more than 1 mm2.26 One limitation of this method is the requirement for well-defined calibration samples for each mixture. The goal of the present work is to develop a method to identify individual lipids within lipid mixtures and to calculate their percentages in single pixels using multivariate analysis.
■
METHODS
Discriminant Analysis. Unlike principal component analysis, discriminant analysis does not serve the purpose of identifying groups by means of common characteristics, but the groups, in this case the lipids, must be defined by the user.27−29 Since correct classification of the various lipids which are used as standards is crucial for the following calculations, discriminant analysis was used to answer the questions whether Received: April 18, 2015 Accepted: July 5, 2015 Published: July 5, 2015 7795
DOI: 10.1021/acs.analchem.5b01456 Anal. Chem. 2015, 87, 7795−7802
Article
Analytical Chemistry Table 1. Lipids Used for Analyses
(ΣgG= 1Σkng= 1(xgki − xg̅ i)(xgkj − xg̅ j))ij which contain the deviations between and within the groups (xgki, value of ith variable, kth measurement, and gth group; xg̅ i, mean value of ith variable and gth group; xi̅ , mean value of ith variable). As only (s − 1) equations are linearly independent, normalization is possible in a way that the standard deviation of the discriminant scores of each group is 1. If the variables differ by several orders of magnitude, these normalized discriminant coefficients not necessarily can be compared. If the ith normalized discriminant coefficient is multiplied by the ith diagonal element of the within covariance matrix S = (1/(ng − g))W, which corresponds to the pooled standard deviation within a group, one obtains the directly comparable standardized discriminant coefficients. When G is the number of groups, not more than (G − 1) eigenvalues are nonzero. Therefore, the dimension of the discriminant space is less than or equal to (G − 1). The most common statistic indicating the quality of the discriminant function is the significance test for Wilks’ lambda,
metric variables are capable of isolating groups and how relevant single variables are to isolating groups. A TOF-SIMS image can be regarded as a stack of p = n × m pixels each containing a complete spectrum of s peaks. Usually the data are presented within the s-dimensional data space in the form of a p × s matrix with ion peak areas as entries. The original s variables Xi (specific mass peaks) are usually not suitable for separating the groups. In discriminant analysis the coordinate system is changed. The new coordinate axes are defined by so-called discriminant functions Dj s
Dj =
∑ aijXi i=0
(1)
that are linear functions of the Xi with the discriminant coefficients aij. They enable the optimal separation of different groups. The projections of the variables on the new axes are called discriminant scores. In the easiest case of only two groups, the discriminant coefficients are calculated by maximizing the quotient λ(a) = BdWd−1 of the deviance between different groups Bd and the deviance within the groups Wd. a is the (s × s − 1) matrix with the entries aij. More generally, if more than two groups exist, each with ng measurements, the calculation of λ can be considered as the eigenvalue problem28 (B − λ ·W) ·a = 0
Λ=
1 1+λ
(3)
which is the quotient of the variance in the discriminant scores not explained and the total variance. The greater the eigenvalue λ, the smaller is Λ. Computation of Mixture Ratios. In TOF-SIMS imaging of phospholipid mixtures, the ion peak areas are the variables and the different phospholipids form the groups for discriminant
(2)
with B being the (s × s) between-matrix with entries (ΣgG= 1ng(xg̅ i − xi̅ )(xg̅ j − xj̅ ))ij and W the s × s within-matrix with entries 7796
DOI: 10.1021/acs.analchem.5b01456 Anal. Chem. 2015, 87, 7795−7802
Article
Analytical Chemistry Table 2. Total Counts/Pixel of Pure Phospholipid Preparations positive ion mode
negative ion mode
phospholipid
mean total counts/pixel
standard deviation
range
mean total counts/pixel
standard deviation
range
PC SM PE PS CH
1348.68 1399.23 1066.77 648.49 1187.24
191.49 235.74 204.27 112.69 81.92
1023−2034 837−2165 588−1750 370−1523 1036−1474
795.19 895.82 1302.30 995.00 684.41
116.31 206.24 197.97 171.12 142.88
630−1932 433−3044 849−3189 834−2192 429−1538
Table 3. Signal Intensities (Counts/Pixel) of Specific and Characteristic (Marked As Bold) Phospholipid Fragments in Pure Phospholipid Preparations m/q
PC +
58.08 ([C3H8N] ) 60.09 ([C3H10N]+) 86.10 ([C5H12N]+) 88.05 ([C3H6NO2]+) 102.09 ([C6H14O]+) 104.11 ([C5H14NO]+) 124.02 ([C2H7PNO3]+) 125.01 ([C5H4PNO]+) 142.03 ([C2H9PNO4]+) 146.99 ([C4H4PO4]+) 150.08 ([C5H13PNO2]+) 166.07 ([C5H13PNO3]+) 184.10 ([C5H15PNO4]+) 198.12 ([C6H17PNO4]+) 208.03 ([C3H8PNO6 Na]+) 224.13 ([C8H19PNO4 ]+) 225.12 ([C7H18PN2O4 ]+) 367.33 ([C27H43]+) 368.35 ([C27H44]+) 369.36 ([C27H45]+) 383.34 ([C27H43O]+) 384.34 ([C27H44O]+) 385.35 ([C27H45O]+) 520.52 ([C34H66NO2]+) 575.53 ([C37H67O4]+) 703.59 ([C39H80PN2O6]+) 577.54 ([C39H67O4]+) 603.56 ([C39H71O4]+) 605.63 ([C39H73O4]+) 633.66 ([C41H77O4]+) 725.58 ([C39H79PN2O6Na]+)
SM
68.67 14.44 47.92
61.36 17.91 54.07
6.89 18.80
7.41 25.80
8.93
12.23
PE
PS
m/q
CH 747.57 758.55 760.56 790.57 812.56 122.00 140.02 163.03 168.05 178.04 180.06 182.03 196.05 208.08 383.32 385.35 401.34 402.24 404.27 447.30 598.44 600.45 616.45 642.48 687.55 714.56 716.57 742.59 744.60 766.60
1.57
0.86 0.05 2.27 9.79 25.63
2.81 3.81 10.39 57.70 2.44 0.16
5.21 0.88 1.21 2.25 10.86 0.36 1.19 2.77 0.11 0.03 0.07 0.07 0.05 0.13
0.05 0.01
i ,j
PE
([C39H74PNO10] ) ([C42H81PNO8]+) ([C42H83PNO8]+) ([C44H89PNO8]+) ([C44H88PNO8Na]+) ([C2H5PNO3]−) ([C2H7PNO4]−) ([C5H8PO4]−) ([C4H11PNO4]−) ([C5H9PNO4]−) [C5H11PNO4]− ([C5H11PO5 ]−) [C5H11PNO5]− ([C7H15PNO4]−) ([C27H43O]−) ([C27H45O]−) ([C27H45O2]−) ([C20H37PNO5]−) ([C20H39PNO5]−) ([C26H42PNO3]−) ([C34H65PNO5]−) ([C34H67PNO5]−) ([C34H67PNO6]−) ([C36H69PNO6]−) ([C38H76PN2O6]−) ([C39H73PNO8]−) ([C39H75PNO8]−) ([C41H77PNO8]−) ([C41H79PNO8]−) ([C43H77PNO8]−)
PS
CH
