scoring_mutations_LLR.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Intel MKL WARNING: Support of Intel(R) Streaming SIMD Extensions 4.2 (Intel(R) SSE4.2) enabled only processors has been deprecated. Intel oneAPI Math Kernel Library 2025.0 will require Intel(R) Advanced Vector Extensions (Intel(R) AVX) instructions.\n",
      "Intel MKL WARNING: Support of Intel(R) Streaming SIMD Extensions 4.2 (Intel(R) SSE4.2) enabled only processors has been deprecated. Intel oneAPI Math Kernel Library 2025.0 will require Intel(R) Advanced Vector Extensions (Intel(R) AVX) instructions.\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1500x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from transformers import AutoTokenizer, EsmForMaskedLM\n",
    "import torch\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# Load the model and tokenizer\n",
    "model_name = \"facebook/esm2_t6_8M_UR50D\"\n",
    "tokenizer = AutoTokenizer.from_pretrained(model_name)\n",
    "model = EsmForMaskedLM.from_pretrained(model_name)\n",
    "\n",
    "# Input protein sequence\n",
    "protein_sequence = \"MAPLRKTYVLKLYVAGNTPNSVRALKTLNNILEKEFKGVYALKVIDVLKNPQLAEEDKILATPTLAKVLPPPVRRIIGDLSNREKVLIGLDLLYEEIGDQAEDDLGLE\"\n",
    "\n",
    "# Tokenize the input sequence\n",
    "input_ids = tokenizer.encode(protein_sequence, return_tensors=\"pt\")\n",
    "sequence_length = input_ids.shape[1] - 2  # Excluding the special tokens\n",
    "\n",
    "# List of amino acids\n",
    "amino_acids = list(\"ACDEFGHIKLMNPQRSTVWY\")\n",
    "\n",
    "# Initialize heatmap\n",
    "heatmap = np.zeros((20, sequence_length))\n",
    "\n",
    "# Calculate LLRs for each position and amino acid\n",
    "for position in range(1, sequence_length + 1):\n",
    "    # Mask the target position\n",
    "    masked_input_ids = input_ids.clone()\n",
    "    masked_input_ids[0, position] = tokenizer.mask_token_id\n",
    "    \n",
    "    # Get logits for the masked token\n",
    "    with torch.no_grad():\n",
    "        logits = model(masked_input_ids).logits\n",
    "        \n",
    "    # Calculate log probabilities\n",
    "    probabilities = torch.nn.functional.softmax(logits[0, position], dim=0)\n",
    "    log_probabilities = torch.log(probabilities)\n",
    "    \n",
    "    # Get the log probability of the wild-type residue\n",
    "    wt_residue = input_ids[0, position].item()\n",
    "    log_prob_wt = log_probabilities[wt_residue].item()\n",
    "    \n",
    "    # Calculate LLR for each variant\n",
    "    for i, amino_acid in enumerate(amino_acids):\n",
    "        log_prob_mt = log_probabilities[tokenizer.convert_tokens_to_ids(amino_acid)].item()\n",
    "        heatmap[i, position - 1] = log_prob_mt - log_prob_wt\n",
    "\n",
    "# Visualize the heatmap\n",
    "plt.figure(figsize=(15, 5))\n",
    "plt.imshow(heatmap, cmap=\"viridis\", aspect=\"auto\")\n",
    "plt.xticks(range(sequence_length), list(protein_sequence))\n",
    "plt.yticks(range(20), amino_acids)\n",
    "plt.xlabel(\"Position in Protein Sequence\")\n",
    "plt.ylabel(\"Amino Acid\")\n",
    "plt.title(\"Predicted Effects of Mutations on Protein Sequence (LLR)\")\n",
    "plt.colorbar(label=\"Log Likelihood Ratio (LLR)\")\n",
    "plt.show()\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Abstract:**\n",
    "\n",
    "In this section, we provide a detailed mathematical explanation of the code snippet that utilizes the `transformers` library to assess the effects of amino acid mutations on a given protein sequence. The code employs a pretrained model, specifically the ESM-2 transformer model fine-tuned for masked language modeling tasks. The purpose of this analysis is to compute the Log Likelihood Ratios (LLRs) for amino acid substitutions at different positions along the protein sequence. These LLRs provide insights into the potential impact of mutations on protein stability and function. We present a step-by-step mathematical elucidation of the code's underlying processes, including tokenization, model inference, probability calculations, and the visualization of results in a heatmap format.\n",
    "\n",
    "**Introduction:**\n",
    "\n",
    "Understanding the effects of mutations in protein sequences is crucial for elucidating the molecular basis of various biological processes. The code snippet provided aims to predict the potential consequences of amino acid substitutions at different positions within a protein sequence. It utilizes a pretrained transformer model to estimate Log Likelihood Ratios (LLRs) for amino acid variants, which are indicative of the likelihood of a given mutation being deleterious or neutral.\n",
    "\n",
    "**Methods:**\n",
    "\n",
    "**1. Tokenization:**\n",
    "\n",
    "The code begins by importing necessary libraries, loading the pretrained ESM-2.0 model and tokenizer, and specifying the input protein sequence. The sequence is tokenized using the tokenizer, resulting in a sequence of token IDs. Each amino acid in the protein sequence is mapped to a corresponding token using the tokenizer's vocabulary.\n",
    "\n",
    "**2. LLR Calculation:**\n",
    "\n",
    "For each position `p` along the protein sequence, LLRs are calculated for each of the 20 standard amino acids. Let `i` represent the index of an amino acid variant in the list of amino acids. The LLR for amino acid substitution `i` at position `p` is given by:\n",
    "\n",
    "$$\n",
    "LLR_{i,p} = \\log\\left(\\frac{P_{i,p}}{P_{\\text{wt},p}}\\right)\n",
    "$$\n",
    "\n",
    "where:\n",
    "- $P_{i,p}$ is the probability of observing amino acid `i` at position `p`.\n",
    "- $P_{\\text{wt},p}$ is the probability of observing the wild-type amino acid at position `p`.\n",
    "\n",
    "**3. Model Inference:**\n",
    "\n",
    "At each position `p`, the target amino acid is masked, and the model is used to predict the probability distribution of amino acid tokens at that position. The logits output by the model for each amino acid token are transformed into probabilities using the softmax function:\n",
    "\n",
    "$$\n",
    "P_{i,p} = \\text{softmax}\\left(\\text{logits}_{i,p}\\right)\n",
    "$$\n",
    "\n",
    "**4. Log Probability Calculation:**\n",
    "\n",
    "The predicted probabilities are then used to calculate the log probabilities:\n",
    "\n",
    "$$\n",
    "\\log P_{i,p} = \\log\\left(\\text{softmax}\\left(\\text{logits}_{i,p}\\right)\\right)\n",
    "$$\n",
    "\n",
    "**5. LLR Calculation for Wild-Type:**\n",
    "\n",
    "The log probability of the wild-type amino acid at position `p`, denoted as $\\log P_{\\text{wt},p}$, is retrieved from the log probability tensor.\n",
    "\n",
    "**6. LLR Calculation for Variant Amino Acids:**\n",
    "\n",
    "The log probability of amino acid variant `i` at position `p`, denoted as $\\log P_{i,p}$, is calculated similarly.\n",
    "\n",
    "**Results:**\n",
    "\n",
    "The LLRs for all amino acid substitutions at each position are calculated and stored in a heatmap, where rows correspond to amino acid variants and columns correspond to positions along the protein sequence. The LLR value represents the relative impact of substituting the wild-type amino acid with the corresponding variant at a particular position.\n",
    "\n",
    "**Conclusion:**\n",
    "\n",
    "The code snippet exemplifies the computational assessment of amino acid mutations' effects on protein sequences using pretrained transformer models. The resulting LLRs provide insights into the potential functional consequences of mutations, aiding in protein engineering and structural biology studies.\n",
    "\n",
    "Please note that while this explanation strives for mathematical rigor, some practical implementation details may have been simplified or omitted for clarity."
   ]
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