{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "ceaf0134",
   "metadata": {
    "language": "markdown"
   },
   "source": [
    "# Precursor frequency, probability mass and expected cells\n",
    "\n",
    "Compare complete human TRB reference sets for GILGFVFTL, NLVPMVATV and LLWNGPMAV. Calculate their probability mass through the published `precursor` CLI, then separate model frequency, expected cells and occupancy.\n",
    "\n",
    "**Before you start**\n",
    "\n",
    "Install `vdjmatch[bench,precursor,notebook]` and `ipykernel`. Open from the repository root or the complete `examples` directory. Set `AIRR_BENCHMARK` if your mirror is elsewhere (default: `~/hf/airr_benchmark`)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "457a4acb",
   "metadata": {
    "language": "markdown"
   },
   "source": [
    "## 1. Define the model assumptions\n",
    "\n",
    "Use a marginal TRB recombination model, radius 1, cognacy retention 0.1 per edit and the existing selection multiplier 9.41. These constants are explicit assumptions, not fits to the plotted epitopes. Expected cells use a 10¹¹-cell pool and compartment fraction 0.3."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cc9d4931",
   "metadata": {
    "language": "python"
   },
   "outputs": [],
   "source": [
    "# Set budgets before numerical imports; every calculation uses a fresh CLI output directory.\n",
    "import os, sys, json, tempfile, platform, subprocess, hashlib\n",
    "from pathlib import Path\n",
    "from importlib.metadata import version\n",
    "THREADS = 4\n",
    "for key in (\"POLARS_MAX_THREADS\", \"OPENBLAS_NUM_THREADS\", \"OMP_NUM_THREADS\", \"MKL_NUM_THREADS\", \"VECLIB_MAXIMUM_THREADS\"):\n",
    "    os.environ[key] = \"1\"\n",
    "os.environ.setdefault(\"MPLCONFIGDIR\", str(Path(tempfile.gettempdir())/\"vdjmatch-matplotlib\"))\n",
    "import numpy as np\n",
    "import polars as pl\n",
    "import matplotlib.pyplot as plt\n",
    "import psutil\n",
    "examples = next(p for p in (Path.cwd()/\"examples\", Path.cwd()) if (p/\"profile_cli.py\").is_file())\n",
    "sys.path.insert(0, str(examples))\n",
    "from profile_cli import profile\n",
    "output = Path(tempfile.mkdtemp(prefix=\"vdjmatch-scientific-example-\"))\n",
    "benchmark = Path(os.environ.get(\"AIRR_BENCHMARK\", Path.home()/\"hf/airr_benchmark\"))\n",
    "reference = benchmark/\"vdjdb/vdjdb-2026-06-11-ZENODO/vdjdb_full.txt.gz\"\n",
    "if not reference.is_file():\n",
    "    raise FileNotFoundError(\"Set AIRR_BENCHMARK to the complete local benchmark mirror\")\n",
    "print(\"Python\", platform.python_version(), platform.machine())\n",
    "for package in (\"vdjmatch\", \"vdjtools\", \"seqtree\", \"polars\", \"matplotlib\", \"scikit-learn\", \"psutil\"):\n",
    "    print(package, version(package))\n",
    "print(\"Logical CPUs:\", psutil.cpu_count(), \"physical cores:\", psutil.cpu_count(logical=False),\n",
    "      \"RAM (GB):\", round(psutil.virtual_memory().total/1e9, 1))\n",
    "print(\"Fresh output directory:\", output)\n",
    "print(\"Reference SHA256:\", hashlib.sha256(reference.read_bytes()).hexdigest())\n",
    "# Consistent final-size typography and colour-blind-safe scientific encodings.\n",
    "plt.rcParams.update({\"font.family\":\"DejaVu Sans\", \"font.size\":8, \"axes.labelsize\":8,\n",
    "                    \"axes.titlesize\":9, \"legend.fontsize\":7, \"xtick.labelsize\":7,\n",
    "                    \"ytick.labelsize\":7, \"axes.spines.top\":False, \"axes.spines.right\":False,\n",
    "                    \"pdf.fonttype\":42, \"svg.fonttype\":\"none\", \"figure.dpi\":150})\n",
    "COLORS = [\"#0072B2\", \"#D55E00\", \"#009E73\", \"#CC79A7\"]\n",
    "def export(fig, name):\n",
    "    for extension in (\"pdf\", \"svg\", \"png\"):\n",
    "        fig.savefig(output/f\"{name}.{extension}\", dpi=300, bbox_inches=\"tight\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec8a577a",
   "metadata": {
    "language": "markdown"
   },
   "source": [
    "## 2. Load complete reference sets\n",
    "\n",
    "Keep independent source records; the CLI deduplicates junction search keys. Legacy VDJdb `cdr3` contains conserved anchors and therefore represents a junction. These peptide-level marginal estimates pool MHC restrictions explicitly; retain MHC metadata in the input table."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "94ce9456",
   "metadata": {
    "language": "python"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "shape: (3, 4)\n",
      "┌───────────┬────────────────┬────────────────────┬────────────────────────┐\n",
      "│ epitope   ┆ source_records ┆ distinct_junctions ┆ distinct_reference_ids │\n",
      "│ ---       ┆ ---            ┆ ---                ┆ ---                    │\n",
      "│ str       ┆ u32            ┆ u32                ┆ u32                    │\n",
      "╞═══════════╪════════════════╪════════════════════╪════════════════════════╡\n",
      "│ GILGFVFTL ┆ 12798          ┆ 6637               ┆ 30                     │\n",
      "│ LLWNGPMAV ┆ 2239           ┆ 2143               ┆ 8                      │\n",
      "│ NLVPMVATV ┆ 19125          ┆ 13391              ┆ 57                     │\n",
      "└───────────┴────────────────┴────────────────────┴────────────────────────┘\n"
     ]
    }
   ],
   "source": [
    "# Read the pinned reference and export all target source observations for the precursor CLI.\n",
    "from vdjmatch import db\n",
    "EPITOPES=[\"GILGFVFTL\",\"NLVPMVATV\",\"LLWNGPMAV\"]\n",
    "reference_rows=db.load(reference,species=\"HomoSapiens\",gene=\"TRB\")\n",
    "cognate=reference_rows.filter(pl.col(\"epitope\").is_in(EPITOPES))\n",
    "assert set(cognate[\"epitope\"].unique())==set(EPITOPES)\n",
    "cognate.write_csv(output/\"cognate-source.tsv\",separator=\"\\t\")\n",
    "counts=cognate.group_by(\"epitope\").agg(pl.len().alias(\"source_records\"),\n",
    "          pl.col(\"cdr3\").n_unique().alias(\"distinct_junctions\"),\n",
    "          pl.col(\"reference_id\").n_unique().alias(\"distinct_reference_ids\")).sort(\"epitope\")\n",
    "print(counts)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3c0ba18",
   "metadata": {
    "language": "markdown"
   },
   "source": [
    "## 3. Calculate neighbourhood mass\n",
    "\n",
    "The union estimator counts mass once where one-substitution neighbourhoods overlap. Cognacy retention discounts the added shell. The CLI writes one fresh flat TSV; `--no-unseen` keeps this lesson focused on observed sets and neighbourhood mass."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bddc4e9b",
   "metadata": {
    "language": "python"
   },
   "outputs": [],
   "source": [
    "# Run the established estimator with explicit assumptions and measure the complete process tree.\n",
    "command=[sys.executable,\"-m\",\"vdjmatch.cli\",\"precursor\",str(output/\"cognate-source.tsv\"),\n",
    "         \"--junction-col\",\"cdr3\",\"--group-by\",\"epitope\",\"--locus\",\"TRB\",\n",
    "         \"--source\",\"olga\",\"--organism\",\"human\",\"--radius\",\"1\",\"--alpha\",\"0.1\",\n",
    "         \"--q\",\"9.41\",\"--n-cells\",\"1e11\",\"--compartment\",\"0.3\",\"--n-eff\",\"1e8\",\n",
    "         \"--no-unseen\",\"--threads\",str(THREADS),\"--output\",str(output/\"precursor.tsv\")]\n",
    "usage=profile(command,output/\"precursor.log\",timeout=300)\n",
    "estimates=pl.read_csv(output/\"precursor.tsv\",separator=\"\\t\").rename({\"group\":\"epitope\"}).sort(\"epitope\")\n",
    "print(estimates)\n",
    "print(\"Elapsed seconds:\",round(usage[\"seconds\"],2),\"peak tree GB:\",round(usage[\"peak_tree_rss_GB\"],3))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "accd092d",
   "metadata": {
    "language": "markdown"
   },
   "source": [
    "## 4. Check the estimates\n",
    "\n",
    "Verify that observed mass ≤ retained mass ≤ unweighted union ≤ naive sum. Keep source-record and distinct-junction counts beside the estimates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "78aa2c64",
   "metadata": {
    "language": "python"
   },
   "outputs": [],
   "source": [
    "# Inspect the authoritative columns and retain exact counts beside all estimates.\n",
    "print(estimates.columns)\n",
    "assert estimates.height==len(EPITOPES)\n",
    "combined=counts.join(estimates,on=\"epitope\",validate=\"1:1\")\n",
    "combined.write_csv(output/\"precursor-with-counts.tsv\",separator=\"\\t\")\n",
    "\n",
    "assert (estimates[\"observed_mass\"] <= estimates[\"retained\"]).all()\n",
    "assert (estimates[\"retained\"] <= estimates[\"union\"]).all()\n",
    "assert (estimates[\"union\"] <= estimates[\"naive_sum\"] * (1 + 1e-10)).all()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba4a22de",
   "metadata": {
    "language": "markdown"
   },
   "source": [
    "## 5. Compare frequency and expected cells\n",
    "\n",
    "Both panels use the same epitope order and logarithmic axes. Expected cells are the model frequency multiplied by 10¹¹ × 0.3, an explicit unit conversion rather than independent validation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6d225f1f",
   "metadata": {
    "language": "python"
   },
   "outputs": [
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot frequency and expected cells directly from the CLI output, with a common epitope order.\n",
    "labels=combined[\"epitope\"].to_list(); y=np.arange(len(labels))\n",
    "fig,axes=plt.subplots(1,2,figsize=(7.09,2.5),sharey=True,layout=\"constrained\")\n",
    "for ax,col,label,title in zip(axes,[\"F\",\"cells\"],[\"Model frequency (fraction)\",\"Expected cells in specified compartment\"],\n",
    "                            [\"a  Retained precursor frequency\",\"b  Expected cell count\"]):\n",
    "    ax.scatter(combined[col],y,color=\"#0072B2\",s=25)\n",
    "    ax.set(xscale=\"log\",xlabel=label,title=title)\n",
    "    ax.set_yticks(y,labels)\n",
    "    ax.grid(axis=\"x\",ls=\":\",lw=.5,color=\"0.85\")\n",
    "export(fig,\"precursor-frequency-cells\");plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11264ce7",
   "metadata": {
    "language": "markdown"
   },
   "source": [
    "**Figure 1 | Marginal TRB precursor estimates under explicit model assumptions.** **a**, Model frequency for the complete cognate junction sets of three peptides, calculated with radius 1, per-edit retention 0.1 and selection multiplier 9.41. **b**, Expected cells after multiplying each frequency by 10¹¹ × 0.3. Points are deterministic model estimates; no empirical uncertainty interval or significance test is introduced. Source-record, distinct-junction and reference-ID counts accompany the flat table; distinct source IDs need not represent independent assays."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "428b106c",
   "metadata": {
    "language": "markdown"
   },
   "source": [
    "## 6. Separate observed and added mass\n",
    "\n",
    "Observed junctions provide a lower bound. Cognacy retention discounts the added shell; the unweighted union includes its full probability. The three marks distinguish these quantities directly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2cf1c367",
   "metadata": {
    "language": "python"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compare the CLI's observed, retained and unweighted union masses on a common log axis.\n",
    "fig,ax=plt.subplots(figsize=(5.2,2.8),layout=\"constrained\")\n",
    "for i,(col,label,color,marker) in enumerate([(\"observed_mass\",\"Observed junctions\",\"#0072B2\",\"o\"),\n",
    "    (\"retained\",\"Cognacy-retained mass\",\"#D55E00\",\"s\"),(\"union\",\"Unweighted union\",\"#009E73\",\"^\")]):\n",
    "    ax.scatter(combined[col],y+(i-1)*.12,color=color,marker=marker,s=25,label=label)\n",
    "ax.set(yticks=y,yticklabels=labels,xscale=\"log\",xlabel=\"Recombination probability mass (fraction)\")\n",
    "ax.legend(frameon=False,loc=\"upper center\",bbox_to_anchor=(.5,-.25),ncol=3)\n",
    "export(fig,\"precursor-mass-decomposition\");plt.show()\n",
    "# Occupancy is saturated for these sets at the specified rearrangement count; keep exact values in a table.\n",
    "print(combined.select(\"epitope\",\"lambda\",\"p_ge_1\",\"p_ge_10\"))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d2aa52c",
   "metadata": {
    "language": "markdown"
   },
   "source": [
    "**Figure 2 | Observed and added neighbourhood mass.** Circles, squares and triangles identify the observed-junction mass, cognacy-retained mass and unweighted union, respectively. All are fractions under the same marginal TRB recombination model and complete reference sets. The retained value lies between the observed set and the radius-1 union. Marker separation reflects the explicitly assumed shell-retention weight; it is not an uncertainty interval.\n",
    "\n",
    "At the assumed 10⁸ independent rearrangements, the CLI reports the Poisson mean and the probability of at least one or ten precursors in the accompanying table. Near-one occupancy means model-supported precursors are expected to exist at that repertoire size; it is not a probability of mounting a detectable immune response."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "86883262",
   "metadata": {
    "language": "markdown"
   },
   "source": [
    "## 7. Export resource measurements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "017d998a",
   "metadata": {
    "language": "python"
   },
   "outputs": [],
   "source": [
    "# Save whole-invocation measurements with complete source-record and junction counts.\n",
    "pl.DataFrame([{\"workflow\":\"Three complete TRB precursor sets\",\"source_records\":cognate.height,\n",
    "               \"native_threads\":THREADS,**usage}]).write_csv(output/\"resources.tsv\",separator=\"\\t\")\n",
    "print({k:round(v,3) if isinstance(v,float) else v for k,v in usage.items()})\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ac264f1",
   "metadata": {
    "language": "markdown"
   },
   "source": [
    "## Interpretation and limits\n",
    "\n",
    "The calculation separates neighbourhood mass → retained mass → assumed selected frequency → expected cells → occupancy.\n",
    "\n",
    "- Reference-set sizes differ and influence neighbourhood mass.\n",
    "- The model is marginal human TRB. MHC restrictions are pooled explicitly; it is not a paired binding model.\n",
    "- Selection, retention and pool parameters are assumptions. The estimates are deterministic; no empirical uncertainty or response probability is inferred.\n",
    "- Measured precursor frequencies in the literature compendium are validation observations, not substitutes for these model estimates.\n",
    "\n",
    "Fresh CLI TSVs and editable PDF/SVG plus 300-dpi PNG figures are in the output directory."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}