afcn A tool to fit, predict, and perform TWAS using phased genotype data

The afcn program applies a mechanistic model of gene expression regulation by cis-regulatory elements developed by Mohammadi et al. 2017 (1) and Ehsan et al. 2024 (2). Here, we provide submodules

• afcn fit to infer model parameters from data
• afcn predict to generate gene expression predictions from phased genotypes.
• afcn twas to perform transcriptome wide association analysis, TWAS (3) / prediXcan (4), 🚧 under construction 🚧

Installation

The package requires Python >= 3.9 and can be installed directly from the GitHub repo using pip

python -m pip install git+https://github.com/PejLab/haptwas.git

Alternatively, clone this repository then install from local source code using pip.

Examples

Examples and ficticious data can be found in the example directory of this repository. These examples demonstrate the enumerate options and how to use each submodule. (afcn fit is under construction).

Method description

Mohammadi et al. 2017 (1) defined allele fold change (aFC) as the ratio in the number of gene transcripts under the alternative allele with respect to that of the reference allele. Consequently, it is a parameter that quantifies the effect of any one regulatory variant with its target gene. The authors of (1) showed mathematically how to combine individual phased genotypes and aFC values to predict observed gene expression. While this definition and model is general, the authors used it to specifically study cis-regulatory effects of gene regulation.

This software package for the Python programming language can be used as:

afcn fit 🚧 under construction 🚧

Infers model parameters ($\alpha$, $\beta$) values by least squares. As an example consider the cis-regulation of an arbitrary gene. Let $i = 1,2,\dots, N$ be an index identifying one of $N$ samples, $j = 1,2, \dots, J$ be an index identifying one of $J$ cis-regulatory loci, and $h=1,2$ be an index identifying one of 2 phased haplotypes. For each $i$, we have RNA Sequencing derived gene counts $y_i$ and $J$ length vectors of phased haplotypes $x_i^{(1)}$ and $x_i^{(2)}$. An allele at locus $j$ for haplotype $h$ sample $i$, $x_{ij}^{(h)}$, takes values 0 and 1 representing the presence of either reference or alternative allele, respectively. Let's denote the model predicted expression of our arbitrary gene by haplotype $h$, defined by Mohammadi et al. 2017 (1),

$$ g\big(x_i^{(h)}, \alpha, \beta\big) = 2^{\alpha + x_{i}^{(h) T}\beta} $$

then the total expression of the gene in sample $i$ is

$$ f\big(x_i^{(1)}, x_i^{(2)},\alpha, \beta\big) = g\big(x_i^{(1)}, \alpha, \beta\big) + g\big(x_i^{(2)}, \alpha, \beta\big) $$

Where $\alpha$ is a scalar represents the log2 reference expression and $\beta$ is a $J$ length vector the log2 fold change per locus. Inference of these parameters will be computed by least squares

$$ \hat{\alpha},\hat{\beta} = \underset{\alpha,\beta}{\text{argmin}} \sum_{i=1}^N \left( \log_2\big(y_i + 1\big) - \log_2\big( f(x_i^{(1)},x_i^{(2)}, \alpha,\beta)\big) \right)^2 $$

afcn predict

Estimate the gene count of sample $i$ attributed to haplotype $h$ is $g(x_{i}^{(h)},\alpha=0,\beta)$, and the total gene count $f(x_{i}^{(1)},x_{i}^{(2)},\alpha=0,\beta)$.

References

(1)

@article{Mohammadi2017GenomeResearch,
  title={Quantifying the regulatory effect size of cis-acting genetic variation using allelic fold change},
  author={Mohammadi, Pejman and Castel, Stephane E and Brown, Andrew A and Lappalainen, Tuuli},
  journal={Genome research},
  volume={27},
  number={11},
  pages={1872--1884},
  year={2017},
  publisher={Cold Spring Harbor Lab}
}

(2)

@article{Ehsan2024NatureCommunications,
  title={Haplotype-aware modeling of cis-regulatory effects highlights the gaps remaining in eQTL data},
  author={Ehsan, Nava and Kotis, Bence M and Castel, Stephane E and Song, Eric J and Mancuso, Nicholas and Mohammadi, Pejman},
  journal={Nature Communications},
  volume={15},
  number={1},
  pages={522},
  year={2024},
  publisher={Nature Publishing Group UK London}
}

(3)

@article{Gusev2016NatureGenetics,
  title={Integrative approaches for large-scale transcriptome-wide association studies},
  author={Gusev, Alexander and Ko, Arthur and Shi, Huwenbo and Bhatia, Gaurav and Chung, Wonil and Penninx, Brenda WJH and Jansen, Rick and De Geus, Eco JC and Boomsma, Dorret I and Wright, Fred A and others},
  journal={Nature Genetics},
  volume={48},
  number={3},
  pages={245--252},
  year={2016},
  publisher={Nature Publishing Group US New York}
}

(4)

@article{Gamazon2015NatureGenetics,
  title={A gene-based association method for mapping traits using reference transcriptome data},
  author={Gamazon, Eric R and Wheeler, Heather E and Shah, Kaanan P and Mozaffari, Sahar V and Aquino-Michaels, Keston and Carroll, Robert J and Eyler, Anne E and Denny, Joshua C and GTEx Consortium and Nicolae, Dan L and others},
  journal={Nature Genetics},
  volume={47},
  number={9},
  pages={1091--1098},
  year={2015},
  publisher={Nature Publishing Group US New York}
}