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Novel method for estimating isotope incorporation using the half-decimal place rule Ingo Fetzer Department of Environmental Microbiology userR Conference 2009, Rennes Problem 1.2e+7 100% 100% 0% 0% 50% 1.0e+7 Intensity 8.0e+6

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Department of Environmental Microbiology userR Conference 2009, Rennes

Novel method for estimating isotope incorporation using the ‘half-decimal place rule‘

Ingo Fetzer

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100%

100%

Problem

mass

835 840 845 850 855 860 865 870 875 880 0.0 2.0e+6 4.0e+6 6.0e+6 8.0e+6 1.0e+7 1.2e+7

Intensity

0% 0% 50%

Substrate fluxes in Procaryotes Function Activity Identitiy Interactions: Competition Mutualism

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Goal

Develop an algorithm for estimating 13C incorporation by using ‘half decimal place rule’

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‘Half-decimal place rule’ (HDPR)

Mann (1995)

m/z tryptic peptides Heliobacter pylori [Da] Decimal places

0% 100%

Schmidt et al 2003

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Outline

  • 1. Peptide mass calculation for 12C and 13C
  • 2. Estimation of 12C and 13C slopes (HDPR)
  • 3. Estimation of relative 13C incorporation rates

(of user data) implemented in ‘R‘ (R-project.org)

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Flowchart Script 1

Peptide database Peptide sequences

criterions AA molecular formula Atomic weights

Peptide sequence masses

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Peptide mass calculation for 12C and 13C

dataset M. tuberculosis H37Rv

315,579 peptide fragments amino acid sequences length 2 – 40 90,637 peptide sequences

ChemScore ≥ 10 Missing cleavage = 0 Modifications = Null

  • Mol. weight ≤ 5000 Da

Virtual digestion with MS-Digest

Sanger Institute

(ftp://ftp.sanger.ac.uk/pub/tb/sequences/TB.pep)

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Peptide mass calculation for 12C and 13C

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Peptide mass calculation for 12C and 13C

Script 1:

  • 1. Reduction of dataset (ChemScore, Modification etc.)

2 a. Peptide mass calculation Molecular formula of AA Sum of C, H, N, O for each sequence Sequence in DB + Why? Calculation of percentage 13C incorporation

GAG G=C2H6NO2 A=C3H8NO2 C7 H20 N3 O6 315,579 90,637

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Peptide mass calculation for 12C and 13C

  • 2b. Peptide mass calculation

Sum of C, H, N, O of each sequence Molecular weights of sequences (with decimal residuals)

+ Atomic weights

12C = 12.000000 Da 13C = 13.003355 Da

N = 14.003074 Da O = 15.994915 Da H = 1.007825 Da

C7 H20 N3 O6

12C=242.135212 Da 13C=249.158697 Da

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+ +

C C O H

1R

NH3

+

OH

C C O H

1R

NH3

+

C C O H

2R

N OH H

C C O H

2R

NH3

+

OH

H3O+

Peptide mass calculation for 12C and 13C

  • 2a. Peptide mass calculation

Molecular weights of sequences (with decimal residuals)

+

Count sum of C, H, N, O, S for each sequence

MW(H3O+) = 19.01839 Da

Atomic weights

12C = 12.000000 Da 13C = 13,003355 Da

N = 14.003074 Da O = 15.994915 Da H = 1.007825 Da S = 31.972071 Da

Molecular Masses of 12C and 13C peptides

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Flowchart Script 2

Peptide sequence masses

Transformation

  • Transf. Peptide

sequence masses

k-means clustering

Groupings

  • Transf. Decimal

Residuals m/z – DR plot Slope 0%/100% 13C

Linear fitting

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1000 2000 3000 4000 5000 6000 0.0 0.2 0.4 0.6 0.8 1.0

m/z Decimal residuals

Estimation of 12C and 13C slopes

Script 2: m/zTemp = m/z - 1800 * DR

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1000 2000 3000 4000 5000 6000 0.0 0.2 0.4 0.6 0.8 1.0

m/zTemp Decimal residuals

Estimation of 12C and 13C slopes

k-means clustering

using kmeans()

Hartigan & Wong (1979)

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Estimation of 12C and 13C slopes

Hartigan & Wong (1979)

1000 2000 3000 4000 5000 6000 0.0 0.2 0.4 0.6 0.8 1.0

m/zTemp Decimal residuals

1 2 3 Add k-means clustering

using kmeans()

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Estimation of 12C and 13C slopes

m/z Decimal residuals

1000 2000 3000 4000 5000 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

100% slope = 0.000633 0% slope = 0.000514

lm() function Stats package

0% 100%

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Flowchart Script 3

Slope 0% + 100% 13C User data

Robust linear fitting

Slope user data Estimation of relative

13C incorporation rates

calculation reference k-means clustering

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Estimation of relative 13C incorporation rates

Script 3:

1000 2000 3000 4000 5000 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 100% slope = 0.000633 0% slope = 0.000514

m/z Decimal residuals

m/z b DR ∗ =

(with a=0)

‘outliers‘

Influence on slope estimation 100% 0%

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Estimation of relative 13C incorporation rates

1000 2000 3000 4000 5000 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

m/z Decimal residuals

Linear fitting: minimizing the error sum of the squares

∑

∗ − =

2

) ( min m/z b DR SSE

Breakdown point value = 0

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Estimation of relative 13C incorporation rates

1000 2000 3000 4000 5000 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

m/z Decimal residuals

Robust linear model (Huber 1973) M-estimator type Iterative re-weighted least squares (IWLS; Huber 1981, Hampel et al 1986) rlm() function

MASS package (Venable & Ripley 2002)

Breakdown point value set = 0.5 >50% of datapoints must change

robust linear fitting

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Estimation of relative 13C incorporation rates

1000 2000 3000 4000 5000 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 100% slope = 0.000633 0% slope = 0.000514

m/z Decimal residuals

100 %

12 13 12 13

∗ − − =

C C C user User

b b b b C

m/z b DR ∗ =

(with a=0) 100% 0%

Your incorporation rate is 98.3%

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User data input

+ R Script 3

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User data output

+ R Script 3

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Sensitivity of Method

Dataset Pseudomonas putida

  • 1. Calculated 50% and 100% 13C incorporation
  • 2. Randomly sampled 100 times each

10-100 (steps by 10), 150, 200, 300, 500, 1000 sequences (0%,50% and 100%)

  • 3. Statistics on estimated incorporation rate for 0%,

50% and 100%

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50% 0%

Incorporation [%]

10 20 30 40 50 60 70 80 90 100

Number of peptides

10 50 100 150 200 300 500 1000

  • 50
  • 40
  • 30
  • 20
  • 10

10 20 30 40 50

100%

50 60 70 80 90 100 110 120 130 140 150

Sensitivity of Method

~100 samples

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Conclusion

  • 1. ‚Half-decimal place rule‘ useful for

the estimation of 13C incorporation rates

  • 3. >100 measurements needed for

prescision <5% incorporation estimation

  • 2. Robust linear models better suited

for fitting of highly variable user data than MinSSE fitting

http://s3.amazonaws.com/readers/2008/08/14/draddalybig_1.jpg

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Outlook

  • 1. Application of HPDR on DNA
  • 3. Include N-isotope

incoorporation

  • 2. Backcalculation to 12C-peaks

function identification

http://www.sharp.co.jp/plasmacluster-tech/en/release/images/041117_3.gif

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Acknowledgement

Nico Jemlich (UFZ) Frank Schmidt (Uni Greifwald) Hauke Harms (UFZ) Martin von Bergen (UFZ) Jens Mattow (MPI Berlin) Carsten Vogt (UFZ) Bernd Thiede (Uni Oslo) Hans-Hermann Richnow (UFZ) R development team

http://cache.gawker.com/assets/images/gizmodo/2009/01/bactsunsuet_01.jpg