Supporting material for
Alkali Metal-Cationized Serine Clusters Studied by Sonic Spray Ionization Tandem Mass Spectrometry
Sergio C. Nanita†, Ewa Sokol and R. Graham Cooks*
Address reprint requested to*
Purdue University, Department of Chemistry
560 Oval Dr., West Lafayette, IN 47907, USA.
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† Current address:
DuPont Crop Protection
Stine-Haskell Research Center
1090 Elkton Rd, S315/1220
Newark, DE 19711
I. The calculation of chiral preference for serine clusters ions
The chiral preferences calculated were calculated for serine tetramers, octamers, dodecamers and heptadecamers, formed from a solution containing 2,3,3-d3-L-serine (5 mM), D-serine (5 mM) and 2% of acetic acid or 0.25 mM salt of the cation of interest. The results are presented in Figure 4.
Sonic spray mass spectra of racemic serine samples, where one of the enantiomers was isotopically labeled, led to isotopic distribution of serine clusters, where the formation of homochiral and heterochiral cluster ions was observed. Therefore, the isotopic labeling experiment was performed to study the chiral preferences associated with the formation of the “magic number” clusters of serine.
In order to compare the relative abundances of homochiral and heterochiral serine aggregates within the cluster population (e.g. serine tetramers ionized by sodium) and between the clusters ionized by different cations (e.g. family of serine tetramers), the ion currents of each serine aggregate within the cluster population were normalized to the sum of the intensities of the entire population:
(1)
where Pi is a normalized intensity of the particular cluster within the cluster population, Ii is the signal intensity of the particular cluster ion.
In other words the relative abundances of particular serine cluster within the population were expressed as probabilities, and the sum of probability of all possible outcomes (an entire cluster population) would give 1:
(2)
For that reason we were able to make comparison between each set of experimental data and statistical prediction.
The experimental data were compared with the statistical prediction - a binomial distribution, calculated for each cluster population:
(3)
where x is the number of L or D enantiomers within a serine cluster, n is total number of serines in the cluster, p is probability of the incorporation of L or D serine into the cluster, in case of racemic solution p = 0.5 and is combination of (n, x).
The normalized experimental data for each population of cluster ions, e.g. serine octamers ionized by H+, Li+, Na+, K+, Rb+ or Cs+, were compared to these calculated from binomial distribution. If the distribution of clusters obtained from the experimental data follows the statistical distribution, than the serine aggregation occurs in a random fashion, and there is no preference between an incorporation of homochiral or heterochiral serines into the cluster. On the contrary, the aggregation of serine with the chiral preference would result in a distribution, where the homochiral clusters are greatly enhanced in abundance. The preferential incorporation of the serines of opposite chirality may also be observed; in this case the abundances of heterochiral clusters are greater than statistical prediction. In the ideal situation, where an absolute homochiral or heterochiral preference is present, we would observe the explicit formation of homochiral or the heterochiral clusters.
In order to compare the experimental data with these calculated from binomial distribution, the variances between experimental and predicted data were calculated for each cluster within the population (Equation 4). The outcomes were applied to calculate the standard deviations for the entire population (Equation 5).
(4)
The factor si2 is a variance of the normalized experimental intensities of the particular cluster ions within the cluster population (Pi) from the intensities of the clusters calculated from binomial distribution (PBDi).
(5)
The factor s is a standard deviation of the experimental distribution of cluster ions, calculated for the entire cluster population, from the distribution of clusters calculated from binomial distribution.
The estimation of expected maximum and minimum values of the standard deviation were necessary to provide a complete picture of observed serine clustering events, that are given by the product of the individual probabilities of homochiral and heterochiral clusters formation. The expected maximum / minimum values of the standard deviation from the binomial distribution were calculated for the model set of data where an ideal homochiral (Equation 6) or heterochiral (Equation 7) preference is observed. A standard deviation between model set of data and binomial distribution were set as +1 for the absolute chiral preference and -1 for the absolute heterochiral preference:
(6)
(7)
where smax is the maximum expected value of the standard deviation from the binomial distribution and smin is the minimum.
The positive and negative sign to the calculated values was assigned base on the shape of the cluster population compared to the statistical prediction. The cluster formation with homochiral preference displays the great enhancement in abundances of homochiral clusters (characteristic v shape), whereas distribution of the clusters formed with heterochiral preference reveals the characteristic maximum (or maxima) in the formation of racemic clusters, which is greater than calculated from statistical prediction.
The standard deviations calculated from the experimental data were weighted to the standard deviations calculated from a model data.
or (8)
where the positive value of CP (chiral preference) factor indicates a preference for homochirality in cluster formation, and in the ideal case (absolute homochiral preference) the factor CP = 1. The negative value of CP factor (–CP) indicates a preference for heterochiral cluster formation, and in the case where only the clusters composed from equal number of L and D enantiomers are formed, the CP = -1.
I. The experimental data employed in calculation of chiral preference
Summary of the observation of the serine clusters formed via sonic spray ionization of solution containing 2,3,3-d3-L-serine (5 mM), D-serine (5 mM) and 2% of acetic acid or 0.25 mM salt of the cation of interest, such as LiCl, NaCl, KCl, RbCl, or CsCl.
Supporting Table 1a. Serine tetramers – experimental data
Cation / Cluster enantiomeric composition4D:0L / 3D:1L / 2D:2L / 1D:3L / 0D:4D / S
H+ / Ii / 3 / 14 / 37 / 26 / 5 / 85
Pi / 0.034 / 0.160 / 0.440 / 0.311 / 0.055 / 1
s2 / 0.001 / 0.008 / 0.004 / 0.004 / 0.000
Li+ / Ii / 9 / 38 / 52 / 47 / 20 / 165
Pi / 0.053 / 0.230 / 0.312 / 0.286 / 0.119 / 1
s2 / 0.000 / 0.000 / 0.004 / 0.001 / 0.003
Na+ / Ii / 7 / 26 / 54 / 28 / 7 / 121
Pi / 0.056 / 0.213 / 0.445 / 0.227 / 0.059 / 1
s2 / 0.000 / 0.001 / 0.005 / 0.001 / 0.000
K+ / Ii / 1.08 / 0.04 / 0.53 / 0.12 / 0.63 / 2
Pi / 0.451 / 0.016 / 0.221 / 0.049 / 0.262 / 1
s2 / 0.151 / 0.055 / 0.024 / 0.040 / 0.040
Rb+ / Ii / 13 / 6 / 5 / 2 / 10 / 37
Pi / 0.349 / 0.161 / 0.150 / 0.064 / 0.276 / 1
s2 / 0.082 / 0.008 / 0.051 / 0.034 / 0.046
Cs+ / Ii / 7 / 1 / 3 / 1 / 7 / 19
Pi / 0.362 / 0.064 / 0.178 / 0.030 / 0.366 / 1
s2 / 0.090 / 0.035 / 0.039 / 0.049 / 0.092
Supporting Table 1b. Serine tetramers – binomial distribution of serine clusters
Cation / Cluster enantiomeric composition4D:0L / 3D:1L / 2D:2L / 1D:3L / 0D:4D / S
Q+ / ni / 4 / 3 / 2 / 1 / 0
Pi / 0.062 / 0.250 / 0.375 / 0.250 / 0.062 / 1
Supporting Table 1c. Serine tetramers – model distribution of serine clusters
Absolute homochiral preference4D:0L / 3D:1L / 2D:2L / 1D:3L / 0D:4D / S
Pi / 0.500 / 0.000 / 0.000 / 0.000 / 0.500 / 1
s2 / 0.191 / 0.063 / 0.141 / 0.063 / 0.191
Absolute heterochiral preference
4D:0L / 3D:1L / 2D:2L / 1D:3L / 0D:4D / S
Pi / 0.000 / 0.000 / 1.000 / 0.000 / 0.000 / 1
s2 / 0.004 / 0.063 / 0.391 / 0.063 / 0.004
Supporting Table 1d. The standard deviation of the experimental and model distribution of serine cluster ions, calculated from the variance between the experimental or model data and statistical prediction. Chiral preference (CP) represents the relative value of standard deviation for the cluster population compared with the standard deviations, calculated in the ideal cases (absolute preference for homochirality or heterochirality).
Absolute Heterochiral Preference / H / Li / Na / K / Rb / Cs / Absolute Homochiral Preferences / 0.145 / 0.026 / 0.019 / 0.017 / 0.094 / 0.094 / 0.110 / 0.161
+/- s / -0.145 / -0.026 / -0.019 / -0.017 / 0.094 / 0.094 / 0.110 / 0.161
CP / -1.000 / -0.180 / -0.130 / -0.114 / 0.584 / 0.584 / 0.685 / 1.000
Supporting Table 2a. Serine octamers – experimental data
8D:0L / 7D:1L / 6D:2L / 5D:3L / 4D:4L / 3D:5L / 2D:6L / 1D:7L / 0D:8L / S
H+ / Ii / 42 / 109 / 236 / 164 / 101 / 77 / 252 / 76 / 60 / 1118
Pi / 0.037 / 0.098 / 0.211 / 0.147 / 0.090 / 0.069 / 0.225 / 0.068 / 0.054 / 1.000
s2 / 0.001 / 0.004 / 0.010 / 0.005 / 0.034 / 0.022 / 0.013 / 0.001 / 0.003
Li+ / Ii / 10 / 31 / 34 / 6 / 38 / 28 / 49 / 34 / 2 / 232
Pi / 0.041 / 0.132 / 0.149 / 0.027 / 0.163 / 0.122 / 0.210 / 0.147 / 0.009 / 1.000
s2 / 0.001 / 0.010 / 0.002 / 0.037 / 0.012 / 0.009 / 0.010 / 0.013 / 0.000
Na+ / Ii / 10 / 23 / 29 / 11 / 20 / 13 / 32 / 24 / 6 / 167
Pi / 0.061 / 0.136 / 0.176 / 0.065 / 0.117 / 0.075 / 0.192 / 0.141 / 0.038 / 1.000
s2 / 0.003 / 0.011 / 0.004 / 0.024 / 0.025 / 0.021 / 0.007 / 0.012 / 0.001
K+ / Ii / 0.08 / 0.13 / 0.37 / 0.25 / 4.37 / 0.40 / 1.69 / 0.65 / 0.19 / 8
Pi / 0.009 / 0.017 / 0.045 / 0.031 / 0.537 / 0.050 / 0.208 / 0.080 / 0.024 / 1.000
s2 / 0.000 / 0.000 / 0.004 / 0.035 / 0.069 / 0.029 / 0.010 / 0.002 / 0.000
Rb+ / Ii / 2 / 4 / 5 / 13 / 95 / 32 / 4 / 5 / 2 / 161
Pi / 0.010 / 0.022 / 0.031 / 0.079 / 0.588 / 0.199 / 0.027 / 0.029 / 0.015 / 1.000
s2 / 0.000 / 0.000 / 0.006 / 0.019 / 0.099 / 0.000 / 0.007 / 0.000 / 0.000
Cs+ / Ii / 2 / 2 / 3 / 8 / 32 / 5 / 2 / 1 / 1 / 55
Pi / 0.031 / 0.031 / 0.051 / 0.137 / 0.582 / 0.094 / 0.030 / 0.025 / 0.018 / 1.000
s2 / 0.001 / 0.000 / 0.003 / 0.007 / 0.095 / 0.015 / 0.006 / 0.000 / 0.000
Supporting Table 2b. Serine octamers – binomial distribution of serine clusters
Cation / Cluster enantiomeric composition8D:0L / 7D:1L / 6D:2L / 5D:3L / 4D:4L / 3D:5L / 2D:6L / 1D:7L / 0D:8L / S
Q+ / ni / 8 / 7 / 6 / 5 / 4 / 3 / 2 / 1 / 0
Pi / 0.004 / 0.031 / 0.109 / 0.219 / 0.273 / 0.219 / 0.109 / 0.031 / 0.004 / 1.000
Supporting Table 2c. Serine octamers – model distribution of serine clusters
8D:0L / 7D:1L / 6D:2L / 5D:3L / 4D:4L / 3D:5L / 2D:6L / 1D:7L / 0D:8L / S
Pi / 0.500 / 0.000 / 0.000 / 0.000 / 0.000 / 0.000 / 0.000 / 0.000 / 0.500 / 1.000
s2 / 0.246 / 0.001 / 0.012 / 0.048 / 0.075 / 0.048 / 0.012 / 0.001 / 0.246
Absolute heterochiral preference
8D:0L / 7D:1L / 6D:2L / 5D:3L / 4D:4L / 3D:5L / 2D:6L / 1D:7L / 0D:8L / S
Pi / 0.000 / 0.000 / 0.000 / 0.000 / 1.000 / 0.000 / 0.000 / 0.000 / 0.000 / 1.000
s2 / 0.000 / 0.001 / 0.012 / 0.048 / 0.528 / 0.048 / 0.012 / 0.001 / 0.000
Supporting Table 2d. The standard deviation of the experimental and model distribution of serine cluster ions, calculated from the variance between the experimental or model data and statistical prediction. Chiral preference (CP) represents the relative value of standard deviation for the cluster population compared with the standard deviations, calculated in the ideal cases (absolute preference for homochirality or heterochirality).
Absolute Homochiral Preference / H / Li / Na / K / Rb / Cs / Absolute Heterochiral Preferences / 0.092 / 0.0341 / 0.0342 / 0.0364 / 0.0431 / 0.0403 / 0.0397 / 0.090
+/- s / 0.0922 / 0.0341 / 0.0342 / 0.0364 / -0.0431 / -0.0403 / -0.0397 / -0.0895
CP / 1.000 / 0.370 / 0.371 / 0.395 / -0.481 / -0.450 / -0.444 / -1.000
Supporting Table 3a. Serine 12-mers – experimental data