Quantifying homologous proteins and proteoforms

Figure 1

a H3K4 Methyl-proteoforms Model

p_{1} - T K Q T A R      x_{1}

\dots

\pagecolorshadecolorYRPGTVALRx2

p2−T\mathclapCH3|KQTARx3

\dots

\pagecolorshadecolorYRPGTVALRx2

p3−T\mathclap(CH3)2|KQTARx4

\dots

\pagecolorshadecolorYRPGTVALRx2

{\to x}_{i} = z_{i} \sum j \in ω_{i} {\to p}_{j}

{\to x}_{i}

–

i^{t h}

peptide levels across

N

conditions

z_{i}

–

i^{t h}

peptide-specific bias (nuisance)

ω_{i}

– Set of proteins containing the

i^{t h}

peptide

{\to p}_{j}

–

j^{t h}

protein levels across

N

conditions

	$     ⇓$
	$\begin{matrix} {\to x}_{2} = z_{2} ({\to p}_{1} + {\to p}_{2} + {\to p}_{3}) & {\to x}_{1} = z_{1} {\to p}_{1} & {\to x}_{3} = z_{3} {\to p}_{2} & {\to x}_{4} = z_{4} {\to p}_{3} \end{matrix}$

⟵% \scriptsize conditions⟶⎛⎜ ⎜⎝x11…x1N⋮⋱⋮xM1…xMN⎞⎟ ⎟⎠ \ann{Peptide levels} \it{\color[rgb]{0,0,1}% Measured (data)}=⟵\scriptsize peptides⟶⎛⎜ ⎜⎝z1…0⋮⋱⋮0…zM⎞⎟ ⎟⎠ \ann{Peptide Biases} \it{\color[rgb]{0,0,1}Unkown}⟵\scriptsize proteins⟶⎛⎜ ⎜⎝s11…s1K⋮⋱⋮sM1…sMK⎞⎟ ⎟⎠ \ann{Design matrix} \it{\color[rgb]{0,0,1}% Kown Proteoforms}⟵\scriptsize conditions⟶⎛⎜ ⎜⎝p11…p1N⋮⋱⋮pK1…pKN⎞⎟ ⎟⎠ \ann{Protein levels} \it{\color[rgb]{0,0,1}% Results}

Figure 1: Model for inferring stoichiometries among proteoforms and paralogous proteins independently from peptide-specific biases. (a) One shared (

x_{2}

) and three unique (

x_{1}

x_{3}

and

x_{4}

) peptides of H3 proteoforms illustrate a very simple case of HIquant. HIquant models the peptide levels measured across conditions (

\to x

) as a supposition of the protein levels (

\to p

), scaled by unknown peptide–specific biases/nuisances (

z

). These coupled equations can be written in a matrix form whose solution infers the methylation stoichiometry independently from the nuisances (

z

). (b) The general form of the model for K proteoforms (or homologous proteins) with M peptides quantified across N conditions can be formulated and solved. In many, albeit not all, cases an optimal and unique solution can be found, even in the absence of unique peptides; see Supplementary Fig. 1 and Supplemental Information.

Figure 2

[width = .99]HIquant_validation_2.pdf

Figure 2: HIquant accurately quantifies ratios across alkylated proteoforms of a spiked-in standard. (a) Schematic diagram of a validation experiment. We prepared a gold standard of proteoforms from the dynamic universal proteomics standard (UPS2) whose cysteines were covalently modified either with iodoacetamide or with vinylpyridine. Upon digestion, these modified UPS proteins generate many shared peptides (peptides not containing cysteine) and a few unique peptides (peptides containing cysteine). The modified UPS2 proteins were mixed with one another at known ratios (

n

), mixed with yeast lysate, digested and quantified by MS. The proteoform ratios that HIquant inferred from the MS data (

^n

) were compared to the mixing ratios. (b) The ratios across the alkylated isoforms of UPS2 inferred by HIquant (

^n

, y-axis) accurately reflect the mixing ratios (

n

, x-axis). (c) Comparison of the error in proteoform ratios inferred by HIquant and ratios inferred from the precursor ion areas and the reporter ion (RI) ratios.

Figure 3

[width = .42]H3K4.pdf

Figure 3: HIquant

accurately infers stoichiometries and confidence intervals across PTM site occupancies of histone 3. (

a) Histone 3 peptides were quantified by SRM across 7 perturbations, and the fractional site occupancies for K4 methylation estimated by two methods: Estimates inferred by HIquant without using external standards are plotted against the corresponding estimates based on MasterMix external standards with known concentrations creech2015building. Each marker shape corresponds to the PTM site(s) shown in the legend; methylation is denoted with “me” and acetylation with “ac” followed by the number of methyl/acetyl groups. (b) The validation method from (a) was extended to another set of more complex fractional site occupancies on K9 methylation and K14 acetylation.

Supplemental Figure 1

a RP L6 Paralogs

p1−x1\pagecolorshadecolorVVYLK

\dots

x_{2}      P H M L K

p2−\pagecolorshadecolorVVYLKx1

\dots

P H L L K      x_{3}

\begin{matrix} {\to x}_{1} = z_{1} ({\to p}_{1} + {\to p}_{2}) & {\to x}_{2} = z_{2} {\to p}_{1} & {\to x}_{3} = z_{3} {\to p}_{2} \end{matrix}      ‖ ⇓

⎛⎜⎝x11x12x21x22x31x32⎞⎟⎠Peptide levels=⎛⎜⎝z1000z2000z3⎞⎟⎠Nuisance⎛⎜⎝111001⎞⎟⎠\normalsize S(p11p12p21p22)Protein levels

b Phospho-proteoforms

p1−x1\pagecolorshadecolorGGCAK

\dots

x_{2}      Y G M G T S V E R

[0.3em]

p2−\pagecolorshadecolorGGCAKx1

\dots

YGMG\textcircledp\bf TSVERx3

[0.3em]

p3−x1\pagecolorshadecolorGGCAK

\dots

x4YGMGT\textcircledp\bf SVER

[0.3em]

p4−\pagecolorshadecolorGGCAKx1

\dots

YGMG\textcircledp\bf T\textcircledp\bf SVERx5

⟵ % conditions ⟶ ⎛ ⎜ ⎜ ⎝ \begin{matrix} x_{11} & \dots & x_{1 N} ⋮ & ⋱ & ⋮ x_{M 1} & \dots & x_{M N} \end{matrix} ⎞ ⎟ ⎟ ⎠      Peptide levels = ⎛ ⎜ ⎜ ⎝ \begin{matrix} z_{1} & \dots & 0 ⋮ & ⋱ & ⋮ 0 & \dots & z_{M} \end{matrix} ⎞ ⎟ ⎟ ⎠      Nuisance ⟵ proteins ⟶ ⎛ ⎜ ⎜ ⎝ \begin{matrix} s_{11} & \dots & s_{1 K} ⋮ & ⋱ & ⋮ s_{M 1} & \dots & s_{M K} \end{matrix} ⎞ ⎟ ⎟ ⎠      Design matrix (S) ⟵ conditions ⟶ ⎛ ⎜ ⎜ ⎝ \begin{matrix} p_{11} & \dots & p_{1 N} ⋮ & ⋱ & ⋮ p_{K 1} & \dots & p_{K N} \end{matrix} ⎞ ⎟ ⎟ ⎠      Protein levels

Figure S1: Model for inferring stoichiometries among proteoforms and paralogous proteins independently from peptide-specific biases. (a) One shared (

x_{1}

) and two unique (

x_{2}

and

x_{3}

) peptides from the two paralogs of ribosomal proteins L6 illustrate the simplest case of HIquant. HIquant models the peptide levels measured across two conditions (

\to x

) as a supposition of the protein levels (

\to p

), scaled by unknown peptide–specific nuisances (

z

). These coupled equations can be written in a matrix form whose solution infers the

p_{1} / p_{2}

stoichiometry independently from the nuisances (

z

). (b) The shared and unique peptides of proteoforms (as illustrated by PDHA1 phospho-proteoforms) can be modeled as in panel (a); (c) The matrix system from (a) generalizes to K proteoforms (and homologous proteins) with M peptides quantified across N conditions. In many, albeit not all, cases an optimal and unique solution can be found, even in the absence of unique peptides. See Supplemental Information for details.

Quantifying homologous proteins and proteoforms

Authors

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Foundations of Inference

DeepIso: A Deep Learning Model for Peptide Feature Detection

Figure 1

Figure 2

Figure 3

Supplemental Figure 1

Quantifying homologous proteins and proteoforms

Authors

Related Research

Automating LC-MS/MS mass chromatogram quantification. Wavelet transform based peak detection and automated estimation of peak boundaries and signal-to-noise ratio using signal

Using Graph Neural Networks for Mass Spectrometry Prediction

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Foundations of Inference

DeepIso: A Deep Learning Model for Peptide Feature Detection

This week in AI

Figure 1

Figure 2

Figure 3

Supplemental Figure 1