{
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   "source": [
    "# Tutorial 06 — FastRelax\n",
    "\n",
    "[![Open In Colab](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/uw-ipd/tmol/blob/master/docs/tutorial/06_fast_relax.ipynb)\n",
    "\n",
    "TMol `fast_relax()` alternates side-chain repacking and minimization under a changing score-function schedule.\n",
    "\n",
    "## Learning objectives\n",
    "\n",
    "- Prepare a packing palette, move map, and fold forest.\n",
    "- Run one short repeat and inspect the weight schedule.\n",
    "- Compare the input, stage endpoints, and accepted result.\n",
    "\n",
    "## Before you begin\n",
    "\n",
    "- **Prerequisites:** Both [04 — Packing](04_packing_and_mutation_scan.ipynb) and [05 — Minimization](05_minimization_constraints_kinematics.ipynb).\n",
    "- **Curriculum:** This rejoins the two branches after 03 and completes the core 01 → 06 path. Continue with specialized [07 — Ligands](07_ligand_and_params.ipynb) and [08 — Nucleic acids](08_nucleic_acids.ipynb).\n",
    "- **Related:** [Optimization workflow](../user_guide/optimization.md) · [FastRelax API](../api/relax.rst)\n",
    "\n",
    "TMol `fast_relax()` is Rosetta-inspired, but its scoring, search, and acceptance behavior differ. The short CPU run checks that the API works; it does not establish convergence. The larger batch example requires CUDA."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1383b5a",
   "metadata": {},
   "source": [
    "## Setup\n",
    "\n",
    "The main example uses a checked-in six-residue 1UBQ slice, one repeat, and a two-stage schedule so it remains practical on CPU. The larger ensemble cell is tagged `gpu-only` and is executed by the GPU CI lane. Both are pedagogical smoke tests rather than production relaxation schedules."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "1eefc8e2",
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   "outputs": [],
   "source": [
    "try:\n",
    "    import google.colab  # noqa: F401\n",
    "except ImportError:\n",
    "    IN_COLAB = False\n",
    "else:\n",
    "    IN_COLAB = True\n",
    "\n",
    "if IN_COLAB:\n",
    "    from urllib.request import urlopen\n",
    "\n",
    "    exec(\n",
    "        urlopen(\n",
    "            \"https://raw.githubusercontent.com/uw-ipd/tmol/\"\n",
    "            \"master/docs/tutorial/colab_setup.py\"\n",
    "        ).read(),\n",
    "        globals(),\n",
    "    )\n",
    "    setup_colab([\"tmol/tests/data/cif/1UBQ.cif\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "609ab896",
   "metadata": {},
   "outputs": [],
   "source": [
    "from contextlib import redirect_stderr, redirect_stdout\n",
    "from io import StringIO\n",
    "from pathlib import Path\n",
    "import warnings\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import torch\n",
    "from IPython.display import display\n",
    "from biotite.structure.io import load_structure\n",
    "\n",
    "import tmol\n",
    "from tmol.io import pose_stack_from_biotite\n",
    "from tmol.kinematics import CartesianMoveMap, FoldForest, MoveMap\n",
    "from tmol.pack import PackerPalette\n",
    "from tmol.pose import PoseStackBuilder\n",
    "from tmol.score import ScoreType, beta2016_score_function\n",
    "from tmol.score.constraint import create_mainchain_coordinate_constraints\n",
    "\n",
    "SEED = 20260807\n",
    "np.random.seed(SEED)\n",
    "torch.manual_seed(SEED)\n",
    "warnings.filterwarnings(\n",
    "    \"ignore\", message=r\"Sparse invariant checks are implicitly disabled.*\"\n",
    ")\n",
    "device = (\n",
    "    torch.device(\"cuda\", torch.cuda.current_device())\n",
    "    if torch.cuda.is_available()\n",
    "    else torch.device(\"cpu\")\n",
    ")\n",
    "\n",
    "# Strictly a smoke-test budget shared by every minimizer in this tutorial,\n",
    "# including the GPU batch. Finite output is not evidence of convergence.\n",
    "TUTORIAL_MAX_ITER = 10\n",
    "\n",
    "\n",
    "def show_table(frame):\n",
    "    try:\n",
    "        from itables import show\n",
    "    except ImportError:\n",
    "        return display(frame)\n",
    "    return show(frame)\n",
    "\n",
    "\n",
    "def score_components_by_pose(pose_stack, score_function):\n",
    "    scorer = score_function.render_whole_pose_scoring_module(pose_stack)\n",
    "    weighted_terms = scorer(\n",
    "        pose_stack.coords, sum_terms=False, apply_weights=True\n",
    "    )\n",
    "    score_types = score_function.all_score_types()\n",
    "    total_scores = weighted_terms.sum(dim=0)\n",
    "    constraint_index = next(\n",
    "        (\n",
    "            index\n",
    "            for index, score_type in enumerate(score_types)\n",
    "            if score_type == ScoreType.constraint\n",
    "        ),\n",
    "        None,\n",
    "    )\n",
    "    constraint_scores = (\n",
    "        torch.zeros_like(total_scores)\n",
    "        if constraint_index is None\n",
    "        else weighted_terms[constraint_index]\n",
    "    )\n",
    "    non_constraint_scores = total_scores - constraint_scores\n",
    "    return [\n",
    "        {\n",
    "            \"non_constraint_score_units\": float(non_constraint_scores[i].detach().cpu()),\n",
    "            \"constraint_score_units\": float(constraint_scores[i].detach().cpu()),\n",
    "            \"reported_total_score_units\": float(total_scores[i].detach().cpu()),\n",
    "        }\n",
    "        for i in range(pose_stack.n_poses)\n",
    "    ]\n",
    "\n",
    "\n",
    "def score_components(pose_stack, score_function):\n",
    "    if pose_stack.n_poses != 1:\n",
    "        raise ValueError(\"Use score_components_by_pose() for batched PoseStacks.\")\n",
    "    return score_components_by_pose(pose_stack, score_function)[0]\n",
    "\n",
    "\n",
    "def common_atom_mask(reference, mobile):\n",
    "    return torch.isfinite(reference.coords).all(dim=-1) & torch.isfinite(\n",
    "        mobile.coords\n",
    "    ).all(dim=-1)\n",
    "\n",
    "\n",
    "def rms_displacement(reference, mobile):\n",
    "    \"\"\"Raw all-atom RMS displacement in the input coordinate frame.\"\"\"\n",
    "    mask = common_atom_mask(reference, mobile)\n",
    "    delta = mobile.coords[mask] - reference.coords[mask]\n",
    "    return float(torch.sqrt(torch.mean(torch.sum(delta * delta, dim=-1))).cpu())\n",
    "\n",
    "\n",
    "def kabsch_aligned_rmsd(reference, mobile):\n",
    "    \"\"\"All-atom RMSD after least-squares rigid-body superposition.\"\"\"\n",
    "    mask = common_atom_mask(reference, mobile)\n",
    "    reference_xyz = reference.coords[mask]\n",
    "    mobile_xyz = mobile.coords[mask]\n",
    "    reference_centered = reference_xyz - reference_xyz.mean(dim=0)\n",
    "    mobile_centered = mobile_xyz - mobile_xyz.mean(dim=0)\n",
    "    covariance = mobile_centered.T @ reference_centered\n",
    "    u, _, vh = torch.linalg.svd(covariance)\n",
    "    handedness = torch.sign(torch.det(u @ vh))\n",
    "    correction = torch.eye(3, device=mobile_xyz.device, dtype=mobile_xyz.dtype)\n",
    "    correction[-1, -1] = handedness\n",
    "    rotation = u @ correction @ vh\n",
    "    delta = mobile_centered @ rotation - reference_centered\n",
    "    return float(torch.sqrt(torch.mean(torch.sum(delta * delta, dim=-1))).cpu())\n",
    "\n",
    "\n",
    "def declared_mainchain_atom_mask(pose_stack):\n",
    "    \"\"\"Select atoms named in each residue type's TMol polymer declaration.\"\"\"\n",
    "    mask = torch.zeros_like(pose_stack.real_atoms)\n",
    "    atom_names = []\n",
    "    seen_atom_names = set()\n",
    "    for pose_index in range(pose_stack.n_poses):\n",
    "        for block_index in range(pose_stack.max_n_blocks):\n",
    "            block_type_index = int(\n",
    "                pose_stack.block_type_ind64[pose_index, block_index].item()\n",
    "            )\n",
    "            if block_type_index < 0:\n",
    "                continue\n",
    "            block_type = pose_stack.packed_block_types.active_block_types[\n",
    "                block_type_index\n",
    "            ]\n",
    "            polymer = block_type.properties.polymer\n",
    "            if polymer is None:\n",
    "                continue\n",
    "            atom_offset = int(\n",
    "                pose_stack.block_coord_offset64[pose_index, block_index].item()\n",
    "            )\n",
    "            for atom_name in polymer.mainchain_atoms:\n",
    "                atom_index = atom_offset + block_type.atom_to_idx[atom_name]\n",
    "                if bool(pose_stack.real_atoms[pose_index, atom_index]):\n",
    "                    mask[pose_index, atom_index] = True\n",
    "                    if atom_name not in seen_atom_names:\n",
    "                        atom_names.append(atom_name)\n",
    "                        seen_atom_names.add(atom_name)\n",
    "    return mask, tuple(atom_names)\n",
    "\n",
    "\n",
    "def coordinates_equal(first, second):\n",
    "    if first.coords.shape != second.coords.shape:\n",
    "        return False\n",
    "    first_finite = torch.isfinite(first.coords)\n",
    "    second_finite = torch.isfinite(second.coords)\n",
    "    return (\n",
    "        torch.equal(first.block_type_ind64, second.block_type_ind64)\n",
    "        and torch.equal(first_finite, second_finite)\n",
    "        and torch.equal(first.coords[first_finite], second.coords[second_finite])\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33f473af",
   "metadata": {},
   "source": [
    "## Protocol and ramp schedule\n",
    "\n",
    "`tmol.fast_relax()` alternates side-chain repacking and minimization while increasing the `fa_rep` weight. A `CartesianMoveMap` selects Cartesian coordinates. A `MoveMap`, `FoldForest`, and custom minimizer select kinematic degrees of freedom.\n",
    "\n",
    "The default protocol uses four stages and two repeats. This tutorial uses two stages, one repeat, and ten minimizer iterations so it runs as a smoke test. Finite output shows that the workflow executes; it does not establish convergence.\n",
    "\n",
    "Coordinate constraints are attached before relaxation. Each schedule entry scales the starting repulsive and constraint weights, and the final minimization uses full repulsion."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e02638f1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "input: 1UBQ.cif\n",
      "coordinate-restraint atom names: N, CA, C\n",
      "coordinate-restraint count: 18\n",
      "coordinate-restraint sigma: 0.5 Å\n",
      "coordinate-restraint score weight: 1.0\n",
      "O is not TMol-declared main chain here and is not constrained.\n",
      "Weight 1.0 is intentional; Rosetta comparisons commonly use 0.5.\n"
     ]
    },
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   "source": [
    "repo_root = Path.cwd()\n",
    "if not (repo_root / \"tmol/tests/data/cif/1UBQ.cif\").exists():\n",
    "    repo_root = Path(tmol.__file__).resolve().parents[1]\n",
    "cif_path = repo_root / \"tmol\" / \"tests\" / \"data\" / \"cif\" / \"1UBQ.cif\"\n",
    "atom_array = load_structure(str(cif_path), model=1, include_bonds=True)\n",
    "protein_slice = atom_array[(atom_array.chain_id == \"A\") & (atom_array.res_id <= 6)]\n",
    "setup_diagnostics = StringIO()\n",
    "try:\n",
    "    with redirect_stdout(setup_diagnostics), redirect_stderr(setup_diagnostics):\n",
    "        pose = pose_stack_from_biotite(protein_slice, device, no_optH=True)\n",
    "        relax_start = create_mainchain_coordinate_constraints(pose)\n",
    "except Exception:\n",
    "    print(setup_diagnostics.getvalue())\n",
    "    raise\n",
    "\n",
    "score_function = beta2016_score_function(device)\n",
    "score_function.set_weight(ScoreType.constraint, 1.0)\n",
    "fa_rep_start = float(score_function.get_weight(ScoreType.fa_ljrep))\n",
    "constraint_start = float(score_function.get_weight(ScoreType.constraint))\n",
    "mainchain_mask, restrained_atom_names = declared_mainchain_atom_mask(relax_start)\n",
    "CONSTRAINT_SIGMA_A = 0.5\n",
    "\n",
    "palette = PackerPalette()\n",
    "cartesian_move_map = CartesianMoveMap()\n",
    "fold_forest = FoldForest.reasonable_fold_forest(relax_start)\n",
    "tiny_schedule = [\n",
    "    {\"fa_rep_pack_frac\": 0.10, \"fa_rep_min_frac\": 0.20, \"cst_frac\": 1.0},\n",
    "    {\"fa_rep_pack_frac\": 1.00, \"fa_rep_min_frac\": 1.00, \"cst_frac\": 0.0},\n",
    "]\n",
    "\n",
    "schedule_table = pd.DataFrame(tiny_schedule)\n",
    "schedule_table[\"fa_rep_pack_weight\"] = (\n",
    "    schedule_table[\"fa_rep_pack_frac\"] * fa_rep_start\n",
    ")\n",
    "schedule_table[\"fa_rep_min_weight\"] = (\n",
    "    schedule_table[\"fa_rep_min_frac\"] * fa_rep_start\n",
    ")\n",
    "schedule_table[\"constraint_weight\"] = schedule_table[\"cst_frac\"] * constraint_start\n",
    "print(\"input:\", cif_path.name)\n",
    "print(\"coordinate-restraint atom names:\", \", \".join(restrained_atom_names))\n",
    "print(\"coordinate-restraint count:\", int(mainchain_mask.sum().item()))\n",
    "print(f\"coordinate-restraint sigma: {CONSTRAINT_SIGMA_A:.1f} Å\")\n",
    "print(f\"coordinate-restraint score weight: {constraint_start:.1f}\")\n",
    "print(\"O is not TMol-declared main chain here and is not constrained.\")\n",
    "print(\"Weight 1.0 is intentional; Rosetta comparisons commonly use 0.5.\")\n",
    "show_table(schedule_table)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7da9eaf1",
   "metadata": {},
   "source": [
    "## Run one repeat\n",
    "\n",
    "The first stage uses reduced repulsion and the final stage restores full repulsion. The fold forest is passed through the shared protocol API, although the Cartesian minimizer does not use it.\n",
    "\n",
    "The custom minimizer records the score immediately before and after each short minimization. These values help inspect the workflow, but they are not a convergence test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "cb4874b0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "smoke-test optimizer max_iter: 10 (convergence not assessed)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "accepted final source: repeat 1 endpoint (stage 2)\n"
     ]
    },
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    "def tutorial_cart_min(\n",
    "    pose_stack, stage_score_function, *, fold_forest, move_map, verbose\n",
    "):\n",
    "    del fold_forest\n",
    "    coord_mask = move_map.coord_mask if isinstance(move_map, CartesianMoveMap) else None\n",
    "    return tmol.run_cart_min(\n",
    "        pose_stack,\n",
    "        stage_score_function,\n",
    "        coord_mask=coord_mask,\n",
    "        verbose=verbose,\n",
    "        optimizer_kwargs={\n",
    "            \"max_iter\": TUTORIAL_MAX_ITER,\n",
    "            \"verbose\": verbose,\n",
    "        },\n",
    "    )\n",
    "\n",
    "\n",
    "relax_stage_records = []\n",
    "\n",
    "\n",
    "def recording_cart_min(\n",
    "    pose_stack, stage_score_function, *, fold_forest, move_map, verbose\n",
    "):\n",
    "    constraint_weight = float(\n",
    "        stage_score_function.get_weight(ScoreType.constraint)\n",
    "    )\n",
    "    objective_before = score_components(\n",
    "        pose_stack, stage_score_function\n",
    "    )[\"reported_total_score_units\"]\n",
    "    minimized = tutorial_cart_min(\n",
    "        pose_stack,\n",
    "        stage_score_function,\n",
    "        fold_forest=fold_forest,\n",
    "        move_map=move_map,\n",
    "        verbose=verbose,\n",
    "    )\n",
    "    objective_after = score_components(\n",
    "        minimized, stage_score_function\n",
    "    )[\"reported_total_score_units\"]\n",
    "    relax_stage_records.append(\n",
    "        {\n",
    "            \"pose\": minimized.clone(),\n",
    "            \"constraint_weight_at_optimization\": constraint_weight,\n",
    "            \"objective_before_min_units\": objective_before,\n",
    "            \"objective_after_min_units\": objective_after,\n",
    "            \"objective_change_during_min_units\": objective_after - objective_before,\n",
    "        }\n",
    "    )\n",
    "    return minimized\n",
    "\n",
    "\n",
    "print(\n",
    "    f\"smoke-test optimizer max_iter: {TUTORIAL_MAX_ITER} \"\n",
    "    \"(convergence not assessed)\"\n",
    ")\n",
    "before_components = score_components(relax_start, score_function)\n",
    "TUTORIAL_NUM_REPEATS = 1\n",
    "relaxed = tmol.fast_relax(\n",
    "    relax_start,\n",
    "    score_function,\n",
    "    palette,\n",
    "    cartesian_move_map,\n",
    "    fold_forest,\n",
    "    num_repeats=TUTORIAL_NUM_REPEATS,\n",
    "    schedule=tiny_schedule,\n",
    "    ramp_constraints=True,\n",
    "    min_fn=recording_cart_min,\n",
    "    verbose=False,\n",
    ")\n",
    "assert torch.isfinite(relaxed.coords[relaxed.real_atoms]).all()\n",
    "after_components = score_components(relaxed, score_function)\n",
    "\n",
    "if coordinates_equal(relaxed, relax_start):\n",
    "    accepted_from = \"input\"\n",
    "else:\n",
    "    accepted_from = \"unresolved (not an exact recorded repeat endpoint)\"\n",
    "    for repeat_index in range(TUTORIAL_NUM_REPEATS):\n",
    "        record_index = (repeat_index + 1) * len(tiny_schedule) - 1\n",
    "        if coordinates_equal(relaxed, relax_stage_records[record_index][\"pose\"]):\n",
    "            accepted_from = (\n",
    "                f\"repeat {repeat_index + 1} endpoint \"\n",
    "                f\"(stage {record_index + 1})\"\n",
    "            )\n",
    "            break\n",
    "\n",
    "score_frame = pd.DataFrame(\n",
    "    [\n",
    "        {\n",
    "            \"structure\": \"before\",\n",
    "            \"accepted_from\": \"not applicable\",\n",
    "            **before_components,\n",
    "        },\n",
    "        {\n",
    "            \"structure\": \"accepted final\",\n",
    "            \"accepted_from\": accepted_from,\n",
    "            **after_components,\n",
    "        },\n",
    "    ]\n",
    ")\n",
    "for component in (\n",
    "    \"non_constraint_score_units\",\n",
    "    \"constraint_score_units\",\n",
    "    \"reported_total_score_units\",\n",
    "):\n",
    "    score_frame[f\"{component.removesuffix('_units')}_change_units\"] = (\n",
    "        score_frame[component] - before_components[component]\n",
    "    )\n",
    "score_frame[\"finite_smoke_test_output\"] = np.isfinite(\n",
    "    score_frame[\n",
    "        [\n",
    "            \"non_constraint_score_units\",\n",
    "            \"constraint_score_units\",\n",
    "            \"reported_total_score_units\",\n",
    "        ]\n",
    "    ]\n",
    ").all(axis=1)\n",
    "score_frame[\"convergence_status\"] = \"not assessed (10-iteration smoke test)\"\n",
    "print(\"accepted final source:\", accepted_from)\n",
    "show_table(score_frame)"
   ]
  },
  {
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   "execution_count": 5,
   "id": "8e64a6d4",
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       "      <th style=\"border:1px solid #ddd;padding:8px\"><sup><noscript><span title=\"JavaScript not allowed. Please trust this notebook to get interactive tables.\">🔒</span></noscript><a href=https://itables.org/fallbacks/static_preview.html title=\"ITables v2.9.1 static preview\">ⓘ</a></sup>frame</th>\n",
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       "      <th style=\"border:1px solid #ddd;padding:8px\">constraint_weight_at_optimization</th>\n",
       "      <th style=\"border:1px solid #ddd;padding:8px\">objective_before_min_units</th>\n",
       "      <th style=\"border:1px solid #ddd;padding:8px\">objective_after_min_units</th>\n",
       "      <th style=\"border:1px solid #ddd;padding:8px\">objective_change_during_min_units</th>\n",
       "      <th style=\"border:1px solid #ddd;padding:8px\">constraint_weight_for_posthoc_rescore</th>\n",
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       "      <th style=\"border:1px solid #ddd;padding:8px\">Kabsch_RMSD_from_input_A</th>\n",
       "      <th style=\"border:1px solid #ddd;padding:8px\">non_constraint_score_units</th>\n",
       "      <th style=\"border:1px solid #ddd;padding:8px\">constraint_score_units</th>\n",
       "      <th style=\"border:1px solid #ddd;padding:8px\">reported_total_score_units</th>\n",
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       "<tr><td style=\"border:1px solid #ddd;padding:8px\">2</td><td style=\"border:1px solid #ddd;padding:8px\">stage 2</td><td style=\"border:1px solid #ddd;padding:8px\"></td><td style=\"border:1px solid #ddd;padding:8px\">0.0</td><td style=\"border:1px solid #ddd;padding:8px\">3.500389</td><td style=\"border:1px solid #ddd;padding:8px\">1.590609</td><td style=\"border:1px solid #ddd;padding:8px\">-1.909780</td><td style=\"border:1px solid #ddd;padding:8px\">0.0</td><td style=\"border:1px solid #ddd;padding:8px\">1.474209</td><td style=\"border:1px solid #ddd;padding:8px\">1.402359e+00</td><td style=\"border:1px solid #ddd;padding:8px\">1.590609</td><td style=\"border:1px solid #ddd;padding:8px\">0.0</td><td style=\"border:1px solid #ddd;padding:8px\">1.590609</td></tr>\n",
       "<tr><td style=\"border:1px solid #ddd;padding:8px\">3</td><td style=\"border:1px solid #ddd;padding:8px\">accepted final</td><td style=\"border:1px solid #ddd;padding:8px\">repeat 1 endpoint (stage 2)</td><td style=\"border:1px solid #ddd;padding:8px\">NaN</td><td style=\"border:1px solid #ddd;padding:8px\">NaN</td><td style=\"border:1px solid #ddd;padding:8px\">NaN</td><td style=\"border:1px solid #ddd;padding:8px\">NaN</td><td style=\"border:1px solid #ddd;padding:8px\">0.0</td><td style=\"border:1px solid #ddd;padding:8px\">1.474209</td><td style=\"border:1px solid #ddd;padding:8px\">1.402359e+00</td><td style=\"border:1px solid #ddd;padding:8px\">1.590609</td><td style=\"border:1px solid #ddd;padding:8px\">0.0</td><td style=\"border:1px solid #ddd;padding:8px\">1.590609</td></tr>\n",
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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
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       "\n",
       "<div class=\"tmol-switchable-view\" id=\"tmol-switch-1c462cb1ab274e28a3dd3c03d545e0f1\" style=\"max-width:720px\">\n",
       "  <label>Structure: <select id=\"tmol-switch-1c462cb1ab274e28a3dd3c03d545e0f1-select\"><option value=\"0\">input</option><option value=\"1\">stage 1</option><option value=\"2\">stage 2</option><option value=\"3\">accepted final</option></select></label>\n",
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       "         style=\"position:absolute;inset:0;visibility:visible\">\n",
       "  <div class=\"tmol-viewer-note\">not a minimization endpoint; post-hoc non-constraint 20.710; constraint 0.000; raw/aligned 0.000/0.000 Å</div>\n",
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       "        </div>\n",
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       "$3Dmolpromise.then(function() {\n",
       "viewer_17885206175711634 = $3Dmol.createViewer(document.getElementById(\"3dmolviewer_17885206175711634\"),{backgroundColor:\"white\"});\n",
       "viewer_17885206175711634.zoomTo();\n",
       "\tviewer_17885206175711634.addModel(\"MODEL 1\\nATOM      1  N   MET A   1      27.340  24.430   2.614  0.00  0.00\\nATOM      2  CA  MET A   1      26.266  25.413   2.842  0.00  0.00\\nATOM      3  C   MET A   1      26.913  26.639   3.531  0.00  0.00\\nATOM      4  O   MET A   1      27.886  26.463   4.263  0.00  0.00\\nATOM      5  CB  MET A   1      25.112  24.880   3.649  0.00  0.00\\nATOM      6  CG  MET A   1      25.353  24.860   5.134  0.00  0.00\\nATOM      7  SD  MET A   1      23.930  23.959   5.904  0.00  0.00\\nATOM      8  CE  MET A   1      24.447  23.984   7.620  0.00  0.00\\nATOM      9  HA  MET A   1      25.864  25.717   1.875  0.00  0.00\\nATOM     10  HB2 MET A   1      24.227  25.486   3.461  0.00  0.00\\nATOM     11  HB3 MET A   1      24.886  23.861   3.332  0.00  0.00\\nATOM     12  HG2 MET A   1      26.298  24.359   5.342  0.00  0.00\\nATOM     13  HG3 MET A   1      25.421  25.882   5.505  0.00  0.00\\nATOM     14  HE1 MET A   1      23.700  23.479   8.233  0.00  0.00\\nATOM     15  HE2 MET A   1      25.405  23.472   7.719  0.00  0.00\\nATOM     16  HE3 MET A   1      24.552  25.017   7.954  0.00  0.00\\nATOM     17  H1  MET A   1      26.961  23.619   2.168  0.00  0.00\\nATOM     18  H2  MET A   1      28.043  24.834   2.029  0.00  0.00\\nATOM     19  H3  MET A   1      27.746  24.169   3.490  0.00  0.00\\nATOM     20  N   GLN A   2      26.335  27.770   3.258  0.00  0.00\\nATOM     21  CA  GLN A   2      26.850  29.021   3.898  0.00  0.00\\nATOM     22  C   GLN A   2      26.100  29.253   5.202  0.00  0.00\\nATOM     23  O   GLN A   2      24.865  29.024   5.330  0.00  0.00\\nATOM     24  CB  GLN A   2      26.733  30.148   2.905  0.00  0.00\\nATOM     25  CG  GLN A   2      26.882  31.546   3.409  0.00  0.00\\nATOM     26  CD  GLN A   2      26.786  32.562   2.270  0.00  0.00\\nATOM     27  OE1 GLN A   2      27.783  33.160   1.870  0.00  0.00\\nATOM     28  NE2 GLN A   2      25.562  32.733   1.806  0.00  0.00\\nATOM     29  H   GLN A   2      25.549  27.828   2.627  0.00  0.00\\nATOM     30  HA  GLN A   2      27.898  28.870   4.158  0.00  0.00\\nATOM     31  HB2 GLN A   2      27.488  30.028   2.128  0.00  0.00\\nATOM     32  HB3 GLN A   2      25.757  30.107   2.422  0.00  0.00\\nATOM     33  HG2 GLN A   2      26.089  31.748   4.128  0.00  0.00\\nATOM     34  HG3 GLN A   2      27.856  31.647   3.889  0.00  0.00\\nATOM     35 HE21 GLN A   2      24.801  32.218   2.200  0.00  0.00\\nATOM     36 HE22 GLN A   2      25.395  33.378   1.059  0.00  0.00\\nATOM     37  N   ILE A   3      26.849  29.656   6.217  0.00  0.00\\nATOM     38  CA  ILE A   3      26.235  30.058   7.497  0.00  0.00\\nATOM     39  C   ILE A   3      26.882  31.428   7.862  0.00  0.00\\nATOM     40  O   ILE A   3      27.906  31.711   7.264  0.00  0.00\\nATOM     41  CB  ILE A   3      26.344  29.050   8.645  0.00  0.00\\nATOM     42  CG1 ILE A   3      27.810  28.748   8.999  0.00  0.00\\nATOM     43  CG2 ILE A   3      25.491  27.771   8.287  0.00  0.00\\nATOM     44  CD1 ILE A   3      27.967  28.087  10.417  0.00  0.00\\nATOM     45  H   ILE A   3      27.854  29.691   6.121  0.00  0.00\\nATOM     46  HA  ILE A   3      25.168  30.210   7.336  0.00  0.00\\nATOM     47  HB  ILE A   3      25.964  29.500   9.562  0.00  0.00\\nATOM     48 HG12 ILE A   3      28.235  28.081   8.250  0.00  0.00\\nATOM     49 HG13 ILE A   3      28.388  29.672   8.977  0.00  0.00\\nATOM     50 HG21 ILE A   3      25.563  27.047   9.098  0.00  0.00\\nATOM     51 HG22 ILE A   3      24.449  28.056   8.147  0.00  0.00\\nATOM     52 HG23 ILE A   3      25.872  27.325   7.368  0.00  0.00\\nATOM     53 HD11 ILE A   3      29.022  27.896  10.615  0.00  0.00\\nATOM     54 HD12 ILE A   3      27.571  28.760  11.178  0.00  0.00\\nATOM     55 HD13 ILE A   3      27.418  27.147  10.443  0.00  0.00\\nATOM     56  N   PHE A   4      26.214  32.097   8.771  0.00  0.00\\nATOM     57  CA  PHE A   4      26.772  33.436   9.197  0.00  0.00\\nATOM     58  C   PHE A   4      27.151  33.362  10.650  0.00  0.00\\nATOM     59  O   PHE A   4      26.350  32.778  11.395  0.00  0.00\\nATOM     60  CB  PHE A   4      25.695  34.498   8.946  0.00  0.00\\nATOM     61  CG  PHE A   4      25.288  34.609   7.499  0.00  0.00\\nATOM     62  CD1 PHE A   4      24.147  33.966   7.038  0.00  0.00\\nATOM     63  CD2 PHE A   4      26.136  35.346   6.640  0.00  0.00\\nATOM     64  CE1 PHE A   4      23.812  34.031   5.677  0.00  0.00\\nATOM     65  CE2 PHE A   4      25.810  35.392   5.267  0.00  0.00\\nATOM     66  CZ  PHE A   4      24.620  34.778   4.853  0.00  0.00\\nATOM     67  H   PHE A   4      25.358  31.764   9.192  0.00  0.00\\nATOM     68  HA  PHE A   4      27.654  33.652   8.592  0.00  0.00\\nATOM     69  HB2 PHE A   4      24.809  34.264   9.535  0.00  0.00\\nATOM     70  HB3 PHE A   4      26.059  35.470   9.276  0.00  0.00\\nATOM     71  HD1 PHE A   4      23.523  33.417   7.744  0.00  0.00\\nATOM     72  HD2 PHE A   4      27.054  35.813   6.998  0.00  0.00\\nATOM     73  HE1 PHE A   4      22.936  33.500   5.306  0.00  0.00\\nATOM     74  HE2 PHE A   4      26.451  35.884   4.536  0.00  0.00\\nATOM     75  HZ  PHE A   4      24.350  34.921   3.808  0.00  0.00\\nATOM     76  N   VAL A   5      28.260  33.943  11.096  0.00  0.00\\nATOM     77  CA  VAL A   5      28.605  33.965  12.503  0.00  0.00\\nATOM     78  C   VAL A   5      28.638  35.461  12.900  0.00  0.00\\nATOM     79  O   VAL A   5      29.522  36.103  12.320  0.00  0.00\\nATOM     80  CB  VAL A   5      29.963  33.317  12.814  0.00  0.00\\nATOM     81  CG1 VAL A   5      30.211  33.394  14.304  0.00  0.00\\nATOM     82  CG2 VAL A   5      29.957  31.838  12.352  0.00  0.00\\nATOM     83  H   VAL A   5      28.880  34.382  10.431  0.00  0.00\\nATOM     84  HA  VAL A   5      27.849  33.405  13.054  0.00  0.00\\nATOM     85  HB  VAL A   5      30.745  33.862  12.284  0.00  0.00\\nATOM     86 HG11 VAL A   5      31.173  32.937  14.537  0.00  0.00\\nATOM     87 HG12 VAL A   5      30.220  34.438  14.618  0.00  0.00\\nATOM     88 HG13 VAL A   5      29.420  32.862  14.832  0.00  0.00\\nATOM     89 HG21 VAL A   5      30.922  31.384  12.574  0.00  0.00\\nATOM     90 HG22 VAL A   5      29.171  31.296  12.877  0.00  0.00\\nATOM     91 HG23 VAL A   5      29.774  31.793  11.278  0.00  0.00\\nATOM     92  N   LYS A   6      27.751  35.867  13.740  0.00  0.00\\nATOM     93  CA  LYS A   6      27.691  37.315  14.143  0.00  0.00\\nATOM     94  C   LYS A   6      28.469  37.475  15.420  0.00  0.00\\nATOM     95  CB  LYS A   6      26.219  37.684  14.307  0.00  0.00\\nATOM     96  CG  LYS A   6      25.884  39.139  14.615  0.00  0.00\\nATOM     97  CD  LYS A   6      24.348  39.296  14.642  0.00  0.00\\nATOM     98  CE  LYS A   6      23.865  40.723  14.749  0.00  0.00\\nATOM     99  NZ  LYS A   6      22.375  40.720  14.907  0.00  0.00\\nATOM    100  H   LYS A   6      27.087  35.218  14.137  0.00  0.00\\nATOM    101  HA  LYS A   6      28.141  37.914  13.350  0.00  0.00\\nATOM    102  HB2 LYS A   6      25.678  37.436  13.394  0.00  0.00\\nATOM    103  HB3 LYS A   6      25.784  37.096  15.115  0.00  0.00\\nATOM    104  HG2 LYS A   6      26.311  39.414  15.580  0.00  0.00\\nATOM    105  HG3 LYS A   6      26.318  39.782  13.850  0.00  0.00\\nATOM    106  HD2 LYS A   6      23.923  38.876  13.729  0.00  0.00\\nATOM    107  HD3 LYS A   6      23.942  38.752  15.495  0.00  0.00\\nATOM    108  HE2 LYS A   6      24.336  41.203  15.605  0.00  0.00\\nATOM    109  HE3 LYS A   6      24.149  41.272  13.851  0.00  0.00\\nATOM    110  HZ1 LYS A   6      22.042  41.671  14.979  0.00  0.00\\nATOM    111  HZ2 LYS A   6      21.952  40.275  14.105  0.00  0.00\\nATOM    112  HZ3 LYS A   6      22.126  40.212  15.744  0.00  0.00\\nATOM    113  O   LYS A   6      28.213  36.753  16.411  0.00  0.00\\nATOM    114  OXT LYS A   6      29.340  38.297  15.493  0.00  0.00\\nTER\\nENDMDL\\n\",\"pdb\");\n",
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       "\tviewer_17885206175711634.setHoverable({},true,\"function(atom,viewer) {\\n        if(!atom.label) {\\n            atom.label = viewer.addLabel(\\n                atom.chain + ':' + atom.resn + '(' + atom.resi + '):' +\\n                atom.atom + '(idx' + atom.serial + ')',\\n                {position: atom, backgroundColor:\\\"white\\\", fontColor:\\\"black\\\"}\\n            );\\n        }\\n    }\",\"function(atom,viewer) {\\n        if(atom.label) {\\n            viewer.removeLabel(atom.label);\\n            delete atom.label;\\n        }\\n    }\");\n",
       "\tviewer_17885206175711634.zoomTo();\n",
       "viewer_17885206175711634.render();\n",
       "});\n",
       "</script>\n",
       "</section>\n",
       "<section id=\"tmol-switch-1c462cb1ab274e28a3dd3c03d545e0f1-panel-1\" class=\"tmol-switch-panel\"\n",
       "         style=\"position:absolute;inset:0;visibility:hidden\">\n",
       "  <div class=\"tmol-viewer-note\">optimized cst weight 1.000; min objective change -6.765; post-hoc non-constraint 4.383; constraint 0.000; raw/aligned 1.527/1.469 Å</div>\n",
       "  <div id=\"3dmolviewer_17885206175782323\"  style=\"position: relative; width: 720px; height: 420px;\">\n",
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       "        </div>\n",
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       "  $3Dmolpromise = loadScriptAsync('https://cdn.jsdelivr.net/npm/3dmol@2.5.5/build/3Dmol-min.js');\n",
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       "$3Dmolpromise.then(function() {\n",
       "viewer_17885206175782323 = $3Dmol.createViewer(document.getElementById(\"3dmolviewer_17885206175782323\"),{backgroundColor:\"white\"});\n",
       "viewer_17885206175782323.zoomTo();\n",
       "\tviewer_17885206175782323.addModel(\"MODEL 1\\nATOM      1  N   MET A   1      27.328  24.415   2.599  0.00  0.00\\nATOM      2  CA  MET A   1      26.276  25.421   2.859  0.00  0.00\\nATOM      3  C   MET A   1      26.875  26.622   3.566  0.00  0.00\\nATOM      4  O   MET A   1      27.806  26.463   4.371  0.00  0.00\\nATOM      5  CB  MET A   1      25.157  24.828   3.700  0.00  0.00\\nATOM      6  CG  MET A   1      23.956  25.781   3.888  0.00  0.00\\nATOM      7  SD  MET A   1      22.651  25.065   4.877  0.00  0.00\\nATOM      8  CE  MET A   1      23.401  25.117   6.500  0.00  0.00\\nATOM      9  HA  MET A   1      25.877  25.759   1.898  0.00  0.00\\nATOM     10  HB2 MET A   1      24.798  23.905   3.249  0.00  0.00\\nATOM     11  HB3 MET A   1      25.547  24.587   4.685  0.00  0.00\\nATOM     12  HG2 MET A   1      24.278  26.706   4.378  0.00  0.00\\nATOM     13  HG3 MET A   1      23.540  26.038   2.916  0.00  0.00\\nATOM     14  HE1 MET A   1      22.698  24.713   7.228  0.00  0.00\\nATOM     15  HE2 MET A   1      24.312  24.522   6.506  0.00  0.00\\nATOM     16  HE3 MET A   1      23.640  26.150   6.761  0.00  0.00\\nATOM     17  H1  MET A   1      26.922  23.614   2.152  0.00  0.00\\nATOM     18  H2  MET A   1      28.030  24.817   2.005  0.00  0.00\\nATOM     19  H3  MET A   1      27.741  24.142   3.475  0.00  0.00\\nATOM     20  N   GLN A   2      26.364  27.795   3.267  0.00  0.00\\nATOM     21  CA  GLN A   2      26.833  29.026   3.901  0.00  0.00\\nATOM     22  C   GLN A   2      26.114  29.297   5.191  0.00  0.00\\nATOM     23  O   GLN A   2      24.861  29.212   5.248  0.00  0.00\\nATOM     24  CB  GLN A   2      26.692  30.222   2.981  0.00  0.00\\nATOM     25  CG  GLN A   2      27.249  31.533   3.554  0.00  0.00\\nATOM     26  CD  GLN A   2      27.124  32.677   2.603  0.00  0.00\\nATOM     27  OE1 GLN A   2      26.457  32.555   1.575  0.00  0.00\\nATOM     28  NE2 GLN A   2      27.771  33.794   2.916  0.00  0.00\\nATOM     29  H   GLN A   2      25.604  27.862   2.591  0.00  0.00\\nATOM     30  HA  GLN A   2      27.894  28.880   4.142  0.00  0.00\\nATOM     31  HB2 GLN A   2      27.170  30.013   2.031  0.00  0.00\\nATOM     32  HB3 GLN A   2      25.623  30.366   2.786  0.00  0.00\\nATOM     33  HG2 GLN A   2      26.717  31.784   4.484  0.00  0.00\\nATOM     34  HG3 GLN A   2      28.306  31.376   3.776  0.00  0.00\\nATOM     35 HE21 GLN A   2      28.302  33.848   3.766  0.00  0.00\\nATOM     36 HE22 GLN A   2      27.726  34.581   2.307  0.00  0.00\\nATOM     37  N   ILE A   3      26.824  29.678   6.213  0.00  0.00\\nATOM     38  CA  ILE A   3      26.240  30.089   7.482  0.00  0.00\\nATOM     39  C   ILE A   3      26.822  31.441   7.841  0.00  0.00\\nATOM     40  O   ILE A   3      27.888  31.779   7.330  0.00  0.00\\nATOM     41  CB  ILE A   3      26.482  29.067   8.615  0.00  0.00\\nATOM     42  CG1 ILE A   3      27.989  28.910   8.905  0.00  0.00\\nATOM     43  CG2 ILE A   3      25.860  27.715   8.268  0.00  0.00\\nATOM     44  CD1 ILE A   3      28.556  29.927   9.894  0.00  0.00\\nATOM     45  H   ILE A   3      27.839  29.743   6.114  0.00  0.00\\nATOM     46  HA  ILE A   3      25.157  30.195   7.338  0.00  0.00\\nATOM     47  HB  ILE A   3      26.023  29.453   9.533  0.00  0.00\\nATOM     48 HG12 ILE A   3      28.150  27.916   9.313  0.00  0.00\\nATOM     49 HG13 ILE A   3      28.532  28.989   7.967  0.00  0.00\\nATOM     50 HG21 ILE A   3      26.012  27.012   9.088  0.00  0.00\\nATOM     51 HG22 ILE A   3      24.788  27.848   8.105  0.00  0.00\\nATOM     52 HG23 ILE A   3      26.311  27.320   7.358  0.00  0.00\\nATOM     53 HD11 ILE A   3      29.612  29.727  10.049  0.00  0.00\\nATOM     54 HD12 ILE A   3      28.431  30.946   9.518  0.00  0.00\\nATOM     55 HD13 ILE A   3      28.032  29.839  10.849  0.00  0.00\\nATOM     56  N   PHE A   4      26.195  32.125   8.760  0.00  0.00\\nATOM     57  CA  PHE A   4      26.775  33.393   9.212  0.00  0.00\\nATOM     58  C   PHE A   4      27.134  33.326  10.683  0.00  0.00\\nATOM     59  O   PHE A   4      26.366  32.766  11.467  0.00  0.00\\nATOM     60  CB  PHE A   4      25.803  34.531   8.987  0.00  0.00\\nATOM     61  CG  PHE A   4      25.469  34.790   7.534  0.00  0.00\\nATOM     62  CD1 PHE A   4      24.376  34.161   6.932  0.00  0.00\\nATOM     63  CD2 PHE A   4      26.220  35.664   6.772  0.00  0.00\\nATOM     64  CE1 PHE A   4      24.065  34.402   5.607  0.00  0.00\\nATOM     65  CE2 PHE A   4      25.909  35.905   5.450  0.00  0.00\\nATOM     66  CZ  PHE A   4      24.832  35.274   4.869  0.00  0.00\\nATOM     67  H   PHE A   4      25.347  31.793   9.196  0.00  0.00\\nATOM     68  HA  PHE A   4      27.703  33.570   8.663  0.00  0.00\\nATOM     69  HB2 PHE A   4      24.872  34.302   9.504  0.00  0.00\\nATOM     70  HB3 PHE A   4      26.191  35.451   9.414  0.00  0.00\\nATOM     71  HD1 PHE A   4      23.761  33.476   7.514  0.00  0.00\\nATOM     72  HD2 PHE A   4      27.070  36.168   7.229  0.00  0.00\\nATOM     73  HE1 PHE A   4      23.209  33.907   5.148  0.00  0.00\\nATOM     74  HE2 PHE A   4      26.514  36.597   4.866  0.00  0.00\\nATOM     75  HZ  PHE A   4      24.589  35.462   3.825  0.00  0.00\\nATOM     76  N   VAL A   5      28.246  33.938  11.067  0.00  0.00\\nATOM     77  CA  VAL A   5      28.582  33.996  12.479  0.00  0.00\\nATOM     78  C   VAL A   5      28.627  35.474  12.869  0.00  0.00\\nATOM     79  O   VAL A   5      29.447  36.216  12.324  0.00  0.00\\nATOM     80  CB  VAL A   5      29.957  33.340  12.772  0.00  0.00\\nATOM     81  CG1 VAL A   5      30.271  33.425  14.276  0.00  0.00\\nATOM     82  CG2 VAL A   5      29.957  31.900  12.298  0.00  0.00\\nATOM     83  H   VAL A   5      28.828  34.381  10.382  0.00  0.00\\nATOM     84  HA  VAL A   5      27.808  33.511  13.068  0.00  0.00\\nATOM     85  HB  VAL A   5      30.723  33.898  12.247  0.00  0.00\\nATOM     86 HG11 VAL A   5      31.251  32.977  14.472  0.00  0.00\\nATOM     87 HG12 VAL A   5      30.285  34.464  14.596  0.00  0.00\\nATOM     88 HG13 VAL A   5      29.509  32.877  14.835  0.00  0.00\\nATOM     89 HG21 VAL A   5      30.933  31.442  12.496  0.00  0.00\\nATOM     90 HG22 VAL A   5      29.187  31.330  12.822  0.00  0.00\\nATOM     91 HG23 VAL A   5      29.760  31.873  11.231  0.00  0.00\\nATOM     92  N   LYS A   6      27.760  35.865  13.765  0.00  0.00\\nATOM     93  CA  LYS A   6      27.715  37.285  14.150  0.00  0.00\\nATOM     94  C   LYS A   6      28.468  37.478  15.467  0.00  0.00\\nATOM     95  CB  LYS A   6      26.264  37.758  14.328  0.00  0.00\\nATOM     96  CG  LYS A   6      25.426  37.770  13.063  0.00  0.00\\nATOM     97  CD  LYS A   6      24.009  38.289  13.338  0.00  0.00\\nATOM     98  CE  LYS A   6      23.157  38.289  12.073  0.00  0.00\\nATOM     99  NZ  LYS A   6      21.763  38.761  12.333  0.00  0.00\\nATOM    100  H   LYS A   6      27.106  35.223  14.167  0.00  0.00\\nATOM    101  HA  LYS A   6      28.200  37.878  13.389  0.00  0.00\\nATOM    102  HB2 LYS A   6      25.759  37.148  15.066  0.00  0.00\\nATOM    103  HB3 LYS A   6      26.280  38.784  14.708  0.00  0.00\\nATOM    104  HG2 LYS A   6      25.903  38.405  12.318  0.00  0.00\\nATOM    105  HG3 LYS A   6      25.370  36.753  12.657  0.00  0.00\\nATOM    106  HD2 LYS A   6      23.524  37.655  14.091  0.00  0.00\\nATOM    107  HD3 LYS A   6      24.058  39.303  13.728  0.00  0.00\\nATOM    108  HE2 LYS A   6      23.616  38.940  11.337  0.00  0.00\\nATOM    109  HE3 LYS A   6      23.115  37.277  11.673  0.00  0.00\\nATOM    110  HZ1 LYS A   6      21.236  38.744  11.470  0.00  0.00\\nATOM    111  HZ2 LYS A   6      21.318  38.154  13.008  0.00  0.00\\nATOM    112  HZ3 LYS A   6      21.785  39.704  12.695  0.00  0.00\\nATOM    113  O   LYS A   6      28.243  36.743  16.438  0.00  0.00\\nATOM    114  OXT LYS A   6      29.336  38.340  15.528  0.00  0.00\\nTER\\nENDMDL\\n\",\"pdb\");\n",
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       "\tviewer_17885206175782323.zoomTo();\n",
       "viewer_17885206175782323.render();\n",
       "});\n",
       "</script>\n",
       "</section>\n",
       "<section id=\"tmol-switch-1c462cb1ab274e28a3dd3c03d545e0f1-panel-2\" class=\"tmol-switch-panel\"\n",
       "         style=\"position:absolute;inset:0;visibility:hidden\">\n",
       "  <div class=\"tmol-viewer-note\">optimized cst weight 0.000; min objective change -1.910; post-hoc non-constraint 1.591; constraint 0.000; raw/aligned 1.474/1.402 Å</div>\n",
       "  <div id=\"3dmolviewer_17885206175848207\"  style=\"position: relative; width: 720px; height: 420px;\">\n",
       "        <p id=\"3dmolwarning_17885206175848207\" style=\"background-color:#ffcccc;color:black\">3Dmol.js failed to load for some reason.  Please check your browser console for error messages.<br></p>\n",
       "        </div>\n",
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       "\n",
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       "}\n",
       "\n",
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       "$3Dmolpromise.then(function() {\n",
       "viewer_17885206175848207 = $3Dmol.createViewer(document.getElementById(\"3dmolviewer_17885206175848207\"),{backgroundColor:\"white\"});\n",
       "viewer_17885206175848207.zoomTo();\n",
       "\tviewer_17885206175848207.addModel(\"MODEL 1\\nATOM      1  N   MET A   1      27.318  24.424   2.592  0.00  0.00\\nATOM      2  CA  MET A   1      26.281  25.419   2.862  0.00  0.00\\nATOM      3  C   MET A   1      26.878  26.615   3.587  0.00  0.00\\nATOM      4  O   MET A   1      27.772  26.457   4.418  0.00  0.00\\nATOM      5  CB  MET A   1      25.159  24.821   3.701  0.00  0.00\\nATOM      6  CG  MET A   1      23.951  25.756   3.902  0.00  0.00\\nATOM      7  SD  MET A   1      22.649  25.027   4.889  0.00  0.00\\nATOM      8  CE  MET A   1      23.392  25.119   6.518  0.00  0.00\\nATOM      9  HA  MET A   1      25.876  25.766   1.908  0.00  0.00\\nATOM     10  HB2 MET A   1      24.801  23.904   3.239  0.00  0.00\\nATOM     11  HB3 MET A   1      25.562  24.562   4.673  0.00  0.00\\nATOM     12  HG2 MET A   1      24.256  26.674   4.409  0.00  0.00\\nATOM     13  HG3 MET A   1      23.531  26.029   2.934  0.00  0.00\\nATOM     14  HE1 MET A   1      22.691  24.727   7.254  0.00  0.00\\nATOM     15  HE2 MET A   1      24.306  24.532   6.545  0.00  0.00\\nATOM     16  HE3 MET A   1      23.623  26.158   6.757  0.00  0.00\\nATOM     17  H1  MET A   1      26.913  23.619   2.142  0.00  0.00\\nATOM     18  H2  MET A   1      28.024  24.825   1.993  0.00  0.00\\nATOM     19  H3  MET A   1      27.744  24.141   3.466  0.00  0.00\\nATOM     20  N   GLN A   2      26.391  27.801   3.250  0.00  0.00\\nATOM     21  CA  GLN A   2      26.839  29.035   3.885  0.00  0.00\\nATOM     22  C   GLN A   2      26.080  29.324   5.168  0.00  0.00\\nATOM     23  O   GLN A   2      24.843  29.294   5.196  0.00  0.00\\nATOM     24  CB  GLN A   2      26.667  30.218   2.942  0.00  0.00\\nATOM     25  CG  GLN A   2      27.195  31.546   3.494  0.00  0.00\\nATOM     26  CD  GLN A   2      27.071  32.654   2.503  0.00  0.00\\nATOM     27  OE1 GLN A   2      26.434  32.494   1.459  0.00  0.00\\nATOM     28  NE2 GLN A   2      27.683  33.790   2.799  0.00  0.00\\nATOM     29  H   GLN A   2      25.657  27.854   2.551  0.00  0.00\\nATOM     30  HA  GLN A   2      27.892  28.925   4.137  0.00  0.00\\nATOM     31  HB2 GLN A   2      27.168  30.006   2.000  0.00  0.00\\nATOM     32  HB3 GLN A   2      25.605  30.345   2.727  0.00  0.00\\nATOM     33  HG2 GLN A   2      26.633  31.832   4.385  0.00  0.00\\nATOM     34  HG3 GLN A   2      28.249  31.421   3.741  0.00  0.00\\nATOM     35 HE21 GLN A   2      28.190  33.880   3.660  0.00  0.00\\nATOM     36 HE22 GLN A   2      27.636  34.562   2.167  0.00  0.00\\nATOM     37  N   ILE A   3      26.814  29.682   6.207  0.00  0.00\\nATOM     38  CA  ILE A   3      26.240  30.089   7.482  0.00  0.00\\nATOM     39  C   ILE A   3      26.851  31.433   7.841  0.00  0.00\\nATOM     40  O   ILE A   3      27.916  31.770   7.340  0.00  0.00\\nATOM     41  CB  ILE A   3      26.521  29.082   8.618  0.00  0.00\\nATOM     42  CG1 ILE A   3      28.051  28.980   8.896  0.00  0.00\\nATOM     43  CG2 ILE A   3      25.922  27.711   8.235  0.00  0.00\\nATOM     44  CD1 ILE A   3      28.420  28.196  10.129  0.00  0.00\\nATOM     45  H   ILE A   3      27.818  29.704   6.092  0.00  0.00\\nATOM     46  HA  ILE A   3      25.162  30.210   7.376  0.00  0.00\\nATOM     47  HB  ILE A   3      26.047  29.440   9.532  0.00  0.00\\nATOM     48 HG12 ILE A   3      28.541  28.529   8.033  0.00  0.00\\nATOM     49 HG13 ILE A   3      28.455  29.974   9.045  0.00  0.00\\nATOM     50 HG21 ILE A   3      26.074  26.990   9.046  0.00  0.00\\nATOM     51 HG22 ILE A   3      24.853  27.839   8.059  0.00  0.00\\nATOM     52 HG23 ILE A   3      26.389  27.336   7.331  0.00  0.00\\nATOM     53 HD11 ILE A   3      29.504  28.203  10.245  0.00  0.00\\nATOM     54 HD12 ILE A   3      27.961  28.666  10.998  0.00  0.00\\nATOM     55 HD13 ILE A   3      28.064  27.164  10.049  0.00  0.00\\nATOM     56  N   PHE A   4      26.212  32.140   8.759  0.00  0.00\\nATOM     57  CA  PHE A   4      26.787  33.399   9.212  0.00  0.00\\nATOM     58  C   PHE A   4      27.107  33.318  10.687  0.00  0.00\\nATOM     59  O   PHE A   4      26.338  32.757  11.462  0.00  0.00\\nATOM     60  CB  PHE A   4      25.814  34.547   8.967  0.00  0.00\\nATOM     61  CG  PHE A   4      25.540  34.809   7.513  0.00  0.00\\nATOM     62  CD1 PHE A   4      24.462  34.205   6.873  0.00  0.00\\nATOM     63  CD2 PHE A   4      26.353  35.656   6.780  0.00  0.00\\nATOM     64  CE1 PHE A   4      24.212  34.450   5.538  0.00  0.00\\nATOM     65  CE2 PHE A   4      26.102  35.901   5.449  0.00  0.00\\nATOM     66  CZ  PHE A   4      25.029  35.299   4.828  0.00  0.00\\nATOM     67  H   PHE A   4      25.356  31.802   9.165  0.00  0.00\\nATOM     68  HA  PHE A   4      27.709  33.588   8.670  0.00  0.00\\nATOM     69  HB2 PHE A   4      24.871  34.331   9.462  0.00  0.00\\nATOM     70  HB3 PHE A   4      26.217  35.457   9.414  0.00  0.00\\nATOM     71  HD1 PHE A   4      23.812  33.535   7.433  0.00  0.00\\nATOM     72  HD2 PHE A   4      27.203  36.135   7.267  0.00  0.00\\nATOM     73  HE1 PHE A   4      23.362  33.975   5.048  0.00  0.00\\nATOM     74  HE2 PHE A   4      26.749  36.573   4.886  0.00  0.00\\nATOM     75  HZ  PHE A   4      24.829  35.492   3.777  0.00  0.00\\nATOM     76  N   VAL A   5      28.216  33.932  11.081  0.00  0.00\\nATOM     77  CA  VAL A   5      28.570  34.004  12.487  0.00  0.00\\nATOM     78  C   VAL A   5      28.625  35.478  12.850  0.00  0.00\\nATOM     79  O   VAL A   5      29.419  36.215  12.269  0.00  0.00\\nATOM     80  CB  VAL A   5      29.941  33.346  12.762  0.00  0.00\\nATOM     81  CG1 VAL A   5      30.271  33.441  14.265  0.00  0.00\\nATOM     82  CG2 VAL A   5      29.930  31.887  12.284  0.00  0.00\\nATOM     83  H   VAL A   5      28.797  34.390  10.396  0.00  0.00\\nATOM     84  HA  VAL A   5      27.804  33.513  13.089  0.00  0.00\\nATOM     85  HB  VAL A   5      30.717  33.898  12.229  0.00  0.00\\nATOM     86 HG11 VAL A   5      31.246  32.990  14.453  0.00  0.00\\nATOM     87 HG12 VAL A   5      30.295  34.486  14.589  0.00  0.00\\nATOM     88 HG13 VAL A   5      29.512  32.903  14.835  0.00  0.00\\nATOM     89 HG21 VAL A   5      30.903  31.440  12.480  0.00  0.00\\nATOM     90 HG22 VAL A   5      29.160  31.337  12.817  0.00  0.00\\nATOM     91 HG23 VAL A   5      29.726  31.849  11.212  0.00  0.00\\nATOM     92  N   LYS A   6      27.781  35.889  13.779  0.00  0.00\\nATOM     93  CA  LYS A   6      27.724  37.293  14.169  0.00  0.00\\nATOM     94  C   LYS A   6      28.445  37.493  15.492  0.00  0.00\\nATOM     95  CB  LYS A   6      26.277  37.772  14.295  0.00  0.00\\nATOM     96  CG  LYS A   6      25.488  37.760  12.993  0.00  0.00\\nATOM     97  CD  LYS A   6      24.068  38.286  13.205  0.00  0.00\\nATOM     98  CE  LYS A   6      23.266  38.282  11.909  0.00  0.00\\nATOM     99  NZ  LYS A   6      21.870  38.768  12.114  0.00  0.00\\nATOM    100  H   LYS A   6      27.151  35.228  14.200  0.00  0.00\\nATOM    101  HA  LYS A   6      28.230  37.894  13.408  0.00  0.00\\nATOM    102  HB2 LYS A   6      25.749  37.150  15.020  0.00  0.00\\nATOM    103  HB3 LYS A   6      26.274  38.790  14.676  0.00  0.00\\nATOM    104  HG2 LYS A   6      25.998  38.387  12.262  0.00  0.00\\nATOM    105  HG3 LYS A   6      25.441  36.744  12.602  0.00  0.00\\nATOM    106  HD2 LYS A   6      23.555  37.663  13.942  0.00  0.00\\nATOM    107  HD3 LYS A   6      24.109  39.305  13.588  0.00  0.00\\nATOM    108  HE2 LYS A   6      23.760  38.923  11.183  0.00  0.00\\nATOM    109  HE3 LYS A   6      23.231  37.266  11.516  0.00  0.00\\nATOM    110  HZ1 LYS A   6      21.374  38.749  11.233  0.00  0.00\\nATOM    111  HZ2 LYS A   6      21.397  38.171  12.779  0.00  0.00\\nATOM    112  HZ3 LYS A   6      21.889  39.714  12.468  0.00  0.00\\nATOM    113  O   LYS A   6      28.249  36.724  16.431  0.00  0.00\\nATOM    114  OXT LYS A   6      29.319  38.352  15.575  0.00  0.00\\nTER\\nENDMDL\\n\",\"pdb\");\n",
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       "<section id=\"tmol-switch-1c462cb1ab274e28a3dd3c03d545e0f1-panel-3\" class=\"tmol-switch-panel\"\n",
       "         style=\"position:absolute;inset:0;visibility:hidden\">\n",
       "  <div class=\"tmol-viewer-note\">not a minimization endpoint; post-hoc non-constraint 1.591; constraint 0.000; raw/aligned 1.474/1.402 Å; accepted from repeat 1 endpoint (stage 2)</div>\n",
       "  <div id=\"3dmolviewer_17885206175911195\"  style=\"position: relative; width: 720px; height: 420px;\">\n",
       "        <p id=\"3dmolwarning_17885206175911195\" style=\"background-color:#ffcccc;color:black\">3Dmol.js failed to load for some reason.  Please check your browser console for error messages.<br></p>\n",
       "        </div>\n",
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       "\tviewer_17885206175911195.addModel(\"MODEL 1\\nATOM      1  N   MET A   1      27.318  24.424   2.592  0.00  0.00\\nATOM      2  CA  MET A   1      26.281  25.419   2.862  0.00  0.00\\nATOM      3  C   MET A   1      26.878  26.615   3.587  0.00  0.00\\nATOM      4  O   MET A   1      27.772  26.457   4.418  0.00  0.00\\nATOM      5  CB  MET A   1      25.159  24.821   3.701  0.00  0.00\\nATOM      6  CG  MET A   1      23.951  25.756   3.902  0.00  0.00\\nATOM      7  SD  MET A   1      22.649  25.027   4.889  0.00  0.00\\nATOM      8  CE  MET A   1      23.392  25.119   6.518  0.00  0.00\\nATOM      9  HA  MET A   1      25.876  25.766   1.908  0.00  0.00\\nATOM     10  HB2 MET A   1      24.801  23.904   3.239  0.00  0.00\\nATOM     11  HB3 MET A   1      25.562  24.562   4.673  0.00  0.00\\nATOM     12  HG2 MET A   1      24.256  26.674   4.409  0.00  0.00\\nATOM     13  HG3 MET A   1      23.531  26.029   2.934  0.00  0.00\\nATOM     14  HE1 MET A   1      22.691  24.727   7.254  0.00  0.00\\nATOM     15  HE2 MET A   1      24.306  24.532   6.545  0.00  0.00\\nATOM     16  HE3 MET A   1      23.623  26.158   6.757  0.00  0.00\\nATOM     17  H1  MET A   1      26.913  23.619   2.142  0.00  0.00\\nATOM     18  H2  MET A   1      28.024  24.825   1.993  0.00  0.00\\nATOM     19  H3  MET A   1      27.744  24.141   3.466  0.00  0.00\\nATOM     20  N   GLN A   2      26.391  27.801   3.250  0.00  0.00\\nATOM     21  CA  GLN A   2      26.839  29.035   3.885  0.00  0.00\\nATOM     22  C   GLN A   2      26.080  29.324   5.168  0.00  0.00\\nATOM     23  O   GLN A   2      24.843  29.294   5.196  0.00  0.00\\nATOM     24  CB  GLN A   2      26.667  30.218   2.942  0.00  0.00\\nATOM     25  CG  GLN A   2      27.195  31.546   3.494  0.00  0.00\\nATOM     26  CD  GLN A   2      27.071  32.654   2.503  0.00  0.00\\nATOM     27  OE1 GLN A   2      26.434  32.494   1.459  0.00  0.00\\nATOM     28  NE2 GLN A   2      27.683  33.790   2.799  0.00  0.00\\nATOM     29  H   GLN A   2      25.657  27.854   2.551  0.00  0.00\\nATOM     30  HA  GLN A   2      27.892  28.925   4.137  0.00  0.00\\nATOM     31  HB2 GLN A   2      27.168  30.006   2.000  0.00  0.00\\nATOM     32  HB3 GLN A   2      25.605  30.345   2.727  0.00  0.00\\nATOM     33  HG2 GLN A   2      26.633  31.832   4.385  0.00  0.00\\nATOM     34  HG3 GLN A   2      28.249  31.421   3.741  0.00  0.00\\nATOM     35 HE21 GLN A   2      28.190  33.880   3.660  0.00  0.00\\nATOM     36 HE22 GLN A   2      27.636  34.562   2.167  0.00  0.00\\nATOM     37  N   ILE A   3      26.814  29.682   6.207  0.00  0.00\\nATOM     38  CA  ILE A   3      26.240  30.089   7.482  0.00  0.00\\nATOM     39  C   ILE A   3      26.851  31.433   7.841  0.00  0.00\\nATOM     40  O   ILE A   3      27.916  31.770   7.340  0.00  0.00\\nATOM     41  CB  ILE A   3      26.521  29.082   8.618  0.00  0.00\\nATOM     42  CG1 ILE A   3      28.051  28.980   8.896  0.00  0.00\\nATOM     43  CG2 ILE A   3      25.922  27.711   8.235  0.00  0.00\\nATOM     44  CD1 ILE A   3      28.420  28.196  10.129  0.00  0.00\\nATOM     45  H   ILE A   3      27.818  29.704   6.092  0.00  0.00\\nATOM     46  HA  ILE A   3      25.162  30.210   7.376  0.00  0.00\\nATOM     47  HB  ILE A   3      26.047  29.440   9.532  0.00  0.00\\nATOM     48 HG12 ILE A   3      28.541  28.529   8.033  0.00  0.00\\nATOM     49 HG13 ILE A   3      28.455  29.974   9.045  0.00  0.00\\nATOM     50 HG21 ILE A   3      26.074  26.990   9.046  0.00  0.00\\nATOM     51 HG22 ILE A   3      24.853  27.839   8.059  0.00  0.00\\nATOM     52 HG23 ILE A   3      26.389  27.336   7.331  0.00  0.00\\nATOM     53 HD11 ILE A   3      29.504  28.203  10.245  0.00  0.00\\nATOM     54 HD12 ILE A   3      27.961  28.666  10.998  0.00  0.00\\nATOM     55 HD13 ILE A   3      28.064  27.164  10.049  0.00  0.00\\nATOM     56  N   PHE A   4      26.212  32.140   8.759  0.00  0.00\\nATOM     57  CA  PHE A   4      26.787  33.399   9.212  0.00  0.00\\nATOM     58  C   PHE A   4      27.107  33.318  10.687  0.00  0.00\\nATOM     59  O   PHE A   4      26.338  32.757  11.462  0.00  0.00\\nATOM     60  CB  PHE A   4      25.814  34.547   8.967  0.00  0.00\\nATOM     61  CG  PHE A   4      25.540  34.809   7.513  0.00  0.00\\nATOM     62  CD1 PHE A   4      24.462  34.205   6.873  0.00  0.00\\nATOM     63  CD2 PHE A   4      26.353  35.656   6.780  0.00  0.00\\nATOM     64  CE1 PHE A   4      24.212  34.450   5.538  0.00  0.00\\nATOM     65  CE2 PHE A   4      26.102  35.901   5.449  0.00  0.00\\nATOM     66  CZ  PHE A   4      25.029  35.299   4.828  0.00  0.00\\nATOM     67  H   PHE A   4      25.356  31.802   9.165  0.00  0.00\\nATOM     68  HA  PHE A   4      27.709  33.588   8.670  0.00  0.00\\nATOM     69  HB2 PHE A   4      24.871  34.331   9.462  0.00  0.00\\nATOM     70  HB3 PHE A   4      26.217  35.457   9.414  0.00  0.00\\nATOM     71  HD1 PHE A   4      23.812  33.535   7.433  0.00  0.00\\nATOM     72  HD2 PHE A   4      27.203  36.135   7.267  0.00  0.00\\nATOM     73  HE1 PHE A   4      23.362  33.975   5.048  0.00  0.00\\nATOM     74  HE2 PHE A   4      26.749  36.573   4.886  0.00  0.00\\nATOM     75  HZ  PHE A   4      24.829  35.492   3.777  0.00  0.00\\nATOM     76  N   VAL A   5      28.216  33.932  11.081  0.00  0.00\\nATOM     77  CA  VAL A   5      28.570  34.004  12.487  0.00  0.00\\nATOM     78  C   VAL A   5      28.625  35.478  12.850  0.00  0.00\\nATOM     79  O   VAL A   5      29.419  36.215  12.269  0.00  0.00\\nATOM     80  CB  VAL A   5      29.941  33.346  12.762  0.00  0.00\\nATOM     81  CG1 VAL A   5      30.271  33.441  14.265  0.00  0.00\\nATOM     82  CG2 VAL A   5      29.930  31.887  12.284  0.00  0.00\\nATOM     83  H   VAL A   5      28.797  34.390  10.396  0.00  0.00\\nATOM     84  HA  VAL A   5      27.804  33.513  13.089  0.00  0.00\\nATOM     85  HB  VAL A   5      30.717  33.898  12.229  0.00  0.00\\nATOM     86 HG11 VAL A   5      31.246  32.990  14.453  0.00  0.00\\nATOM     87 HG12 VAL A   5      30.295  34.486  14.589  0.00  0.00\\nATOM     88 HG13 VAL A   5      29.512  32.903  14.835  0.00  0.00\\nATOM     89 HG21 VAL A   5      30.903  31.440  12.480  0.00  0.00\\nATOM     90 HG22 VAL A   5      29.160  31.337  12.817  0.00  0.00\\nATOM     91 HG23 VAL A   5      29.726  31.849  11.212  0.00  0.00\\nATOM     92  N   LYS A   6      27.781  35.889  13.779  0.00  0.00\\nATOM     93  CA  LYS A   6      27.724  37.293  14.169  0.00  0.00\\nATOM     94  C   LYS A   6      28.445  37.493  15.492  0.00  0.00\\nATOM     95  CB  LYS A   6      26.277  37.772  14.295  0.00  0.00\\nATOM     96  CG  LYS A   6      25.488  37.760  12.993  0.00  0.00\\nATOM     97  CD  LYS A   6      24.068  38.286  13.205  0.00  0.00\\nATOM     98  CE  LYS A   6      23.266  38.282  11.909  0.00  0.00\\nATOM     99  NZ  LYS A   6      21.870  38.768  12.114  0.00  0.00\\nATOM    100  H   LYS A   6      27.151  35.228  14.200  0.00  0.00\\nATOM    101  HA  LYS A   6      28.230  37.894  13.408  0.00  0.00\\nATOM    102  HB2 LYS A   6      25.749  37.150  15.020  0.00  0.00\\nATOM    103  HB3 LYS A   6      26.274  38.790  14.676  0.00  0.00\\nATOM    104  HG2 LYS A   6      25.998  38.387  12.262  0.00  0.00\\nATOM    105  HG3 LYS A   6      25.441  36.744  12.602  0.00  0.00\\nATOM    106  HD2 LYS A   6      23.555  37.663  13.942  0.00  0.00\\nATOM    107  HD3 LYS A   6      24.109  39.305  13.588  0.00  0.00\\nATOM    108  HE2 LYS A   6      23.760  38.923  11.183  0.00  0.00\\nATOM    109  HE3 LYS A   6      23.231  37.266  11.516  0.00  0.00\\nATOM    110  HZ1 LYS A   6      21.374  38.749  11.233  0.00  0.00\\nATOM    111  HZ2 LYS A   6      21.397  38.171  12.779  0.00  0.00\\nATOM    112  HZ3 LYS A   6      21.889  39.714  12.468  0.00  0.00\\nATOM    113  O   LYS A   6      28.249  36.724  16.431  0.00  0.00\\nATOM    114  OXT LYS A   6      29.319  38.352  15.575  0.00  0.00\\nTER\\nENDMDL\\n\",\"pdb\");\n",
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       "  </div>\n",
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   ],
   "source": [
    "trajectory_structures = {\"input\": relax_start}\n",
    "stage_metadata = {\n",
    "    \"input\": {\n",
    "        \"constraint_weight_at_optimization\": np.nan,\n",
    "        \"objective_before_min_units\": np.nan,\n",
    "        \"objective_after_min_units\": np.nan,\n",
    "        \"objective_change_during_min_units\": np.nan,\n",
    "    }\n",
    "}\n",
    "for stage_index, record in enumerate(relax_stage_records):\n",
    "    label = f\"stage {stage_index + 1}\"\n",
    "    trajectory_structures[label] = record[\"pose\"]\n",
    "    stage_metadata[label] = record\n",
    "trajectory_structures[\"accepted final\"] = relaxed\n",
    "stage_metadata[\"accepted final\"] = {\n",
    "    \"constraint_weight_at_optimization\": np.nan,\n",
    "    \"objective_before_min_units\": np.nan,\n",
    "    \"objective_after_min_units\": np.nan,\n",
    "    \"objective_change_during_min_units\": np.nan,\n",
    "}\n",
    "\n",
    "# fast_relax restores the starting constraint weight before returning. These\n",
    "# scores are therefore a common post-hoc decomposition, not each stage's\n",
    "# historical optimization objective.\n",
    "posthoc_constraint_weight = float(\n",
    "    score_function.get_weight(ScoreType.constraint)\n",
    ")\n",
    "trajectory_rows = []\n",
    "trajectory_notes = {}\n",
    "for frame_index, (label, frame_pose) in enumerate(trajectory_structures.items()):\n",
    "    components = score_components(frame_pose, score_function)\n",
    "    metadata = stage_metadata[label]\n",
    "    raw_displacement = rms_displacement(relax_start, frame_pose)\n",
    "    aligned_rmsd = kabsch_aligned_rmsd(relax_start, frame_pose)\n",
    "    trajectory_rows.append(\n",
    "        {\n",
    "            \"frame\": frame_index,\n",
    "            \"label\": label,\n",
    "            \"accepted_from\": accepted_from if label == \"accepted final\" else \"\",\n",
    "            \"constraint_weight_at_optimization\": metadata[\n",
    "                \"constraint_weight_at_optimization\"\n",
    "            ],\n",
    "            \"objective_before_min_units\": metadata[\n",
    "                \"objective_before_min_units\"\n",
    "            ],\n",
    "            \"objective_after_min_units\": metadata[\n",
    "                \"objective_after_min_units\"\n",
    "            ],\n",
    "            \"objective_change_during_min_units\": metadata[\n",
    "                \"objective_change_during_min_units\"\n",
    "            ],\n",
    "            \"constraint_weight_for_posthoc_rescore\": posthoc_constraint_weight,\n",
    "            \"raw_RMS_displacement_from_input_A\": raw_displacement,\n",
    "            \"Kabsch_RMSD_from_input_A\": aligned_rmsd,\n",
    "            **components,\n",
    "        }\n",
    "    )\n",
    "    optimized_weight = metadata[\"constraint_weight_at_optimization\"]\n",
    "    optimized_text = (\n",
    "        \"not a minimization endpoint\"\n",
    "        if np.isnan(optimized_weight)\n",
    "        else (\n",
    "            f\"optimized cst weight {optimized_weight:.3f}; min objective change \"\n",
    "            f\"{metadata['objective_change_during_min_units']:+.3f}\"\n",
    "        )\n",
    "    )\n",
    "    acceptance_text = (\n",
    "        f\"; accepted from {accepted_from}\" if label == \"accepted final\" else \"\"\n",
    "    )\n",
    "    trajectory_notes[label] = (\n",
    "        f\"{optimized_text}; post-hoc non-constraint \"\n",
    "        f\"{components['non_constraint_score_units']:.3f}; \"\n",
    "        f\"constraint {components['constraint_score_units']:.3f}; \"\n",
    "        f\"raw/aligned {raw_displacement:.3f}/{aligned_rmsd:.3f} Å\"\n",
    "        f\"{acceptance_text}\"\n",
    "    )\n",
    "trajectory_frame = pd.DataFrame(trajectory_rows)\n",
    "show_table(trajectory_frame)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 4))\n",
    "ax.plot(\n",
    "    trajectory_frame[\"frame\"],\n",
    "    trajectory_frame[\"non_constraint_score_units\"],\n",
    "    marker=\"o\",\n",
    "    label=\"post-hoc non-constraint score\",\n",
    ")\n",
    "ax.plot(\n",
    "    trajectory_frame[\"frame\"],\n",
    "    trajectory_frame[\"constraint_score_units\"],\n",
    "    marker=\"o\",\n",
    "    label=\"post-hoc constraint score\",\n",
    ")\n",
    "ax.set(\n",
    "    xticks=trajectory_frame[\"frame\"],\n",
    "    xticklabels=trajectory_frame[\"label\"],\n",
    "    ylabel=\"weighted score units\",\n",
    "    title=\"FastRelax endpoints rescored at restored constraint weight\",\n",
    ")\n",
    "ax.tick_params(axis=\"x\", rotation=20)\n",
    "ax.grid(alpha=0.3)\n",
    "ax.legend()\n",
    "plt.tight_layout()\n",
    "plt.show()\n",
    "\n",
    "display(\n",
    "    tmol.switchable_view(\n",
    "        trajectory_structures,\n",
    "        notes=trajectory_notes,\n",
    "    )\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59eda836",
   "metadata": {},
   "source": [
    "**Expected observations.** The non-constraint and constraint components, score changes, and structural metrics must be finite. “Non-constraint” is the exact description: it includes every weighted beta2016 term except the coordinate-constraint term, including empirical/statistical contributions. All reported values are weighted TMol score units, not kcal/mol. The raw metric retains coordinate-frame motion; Kabsch RMSD removes the best rigid-body superposition.\n",
    "\n",
    "`fast_relax()` restores the starting constraint weight before returning. The table records the weight and objective change present during each stage's minimization separately from the restored weight used for the common post-hoc score decomposition. In particular, the final stage is optimized with `cst_frac=0`, but its displayed constraint penalty is recalculated afterward at full starting weight; it diagnoses restraint violation and is not part of that stage's optimization objective. The structure switcher records minimization endpoints for each pack/min stage and the final accept-to-best result; it does not contain LBFGS line-search evaluations or internal packing trajectories.\n",
    "\n",
    "TMol's accept-best pool is **input-inclusive**: it initializes the best pose from the unrelaxed input and, after each complete schedule repeat, accepts that repeat endpoint only when its score is strictly lower. It does not accept among every intermediate stage. Consequently, a one-repeat run can legitimately return the exact input, and `accepted_from` explicitly distinguishes that case from the recorded repeat endpoint. This differs from Rosetta's usual FastRelax comparison among relaxed repeat outputs, where the unrelaxed input is not normally retained as an accept-best candidate.\n",
    "\n",
    "There is an important custom-schedule caveat: the initial best score is captured with the weights present at protocol start, whereas `accept_best` scores a repeat endpoint with the weights left by the final schedule step. The tiny schedule here ends at full repulsion and zero constraint weight, and its restraints are built from the input coordinates, which masks that mismatch for this demonstration. For a custom schedule or initially violated restraints, rescore the input and repeat endpoints under one fixed weight set before interpreting which structure is better.\n",
    "\n",
    "The `score_frame` and trajectory decomposition above are **matched-weight rescoring**: input, stage endpoints, and the accepted result are all evaluated after `fast_relax()` restores the same starting score-function weights. Historical per-stage objectives remain separate columns because those stages used different ramp weights. Compare structures only within one declared weight set; never subtract a low-repulsion stage objective from a full-repulsion endpoint and call the result an improvement.\n",
    "\n",
    "A tiny pedagogical schedule is not guaranteed to improve every input. Large distortions, NaNs, or a missing ligand/residue are failures, not expected stochastic variation. Conversely, finite output or a favorable objective change under `max_iter=10` is only smoke-test evidence; convergence is not assessed.\n",
    "\n",
    "## Convenience minimizers and precision boundary\n",
    "\n",
    "`fast_relax` calls a custom minimizer as `min_fn(pose_stack, sfxn, *, fold_forest, move_map, verbose)`. The adapter below uses the supported top-level `tmol.run_kin_min(pose_stack, sfxn, ff, mm, ...)` signature and the same tutorial iteration limit. To use it, supply a `MoveMap` (not a `CartesianMoveMap`) and pass `min_fn=kinematic_min_fn` to `fast_relax`.\n",
    "\n",
    "Direct packing operates on float32 coordinates. The FastRelax wrappers make the precision boundary explicit: when given a float64 pose, each packing stage receives a temporary float32 view, then the packed coordinates are converted back to float64 before minimization and the returned pose preserves float64. The main run above asserts this behavior. For direct `pack_rotamers()` calls, keep float32 coordinates unless that API's contract changes.\n",
    "\n",
    "`kin_dtype=torch.float64` promotes the kinematic DOFs and inverse/forward-kinematics calculation. Reconstructed coordinates use the pose's coordinate dtype for scoring, so pass a float64 pose as well when the intended kinematic minimization path is double precision.\n",
    "\n",
    "The kinematic adapter is defined but not invoked because doing so would duplicate the full packing schedule with a different minimizer. Notebook 05 executes both Cartesian and kinematic minimization directly; use that comparison before enabling the more expensive FastRelax variant here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0c2cb59a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "FastRelax input/output dtype: torch.float32 → torch.float32\n"
     ]
    }
   ],
   "source": [
    "def kinematic_min_fn(\n",
    "    pose_stack, score_function, *, fold_forest, move_map, verbose\n",
    "):\n",
    "    return tmol.run_kin_min(\n",
    "        pose_stack,\n",
    "        score_function,\n",
    "        fold_forest,\n",
    "        move_map,\n",
    "        optimizer_kwargs={\n",
    "            \"max_iter\": TUTORIAL_MAX_ITER,\n",
    "            \"verbose\": verbose,\n",
    "        },\n",
    "        verbose=verbose,\n",
    "        kin_dtype=torch.float64,\n",
    "    )\n",
    "\n",
    "\n",
    "kinematic_move_map = MoveMap.from_pose_stack(relax_start)\n",
    "kinematic_move_map.move_all_named_torsions = True\n",
    "kinematic_move_map.move_all_jumps = False\n",
    "kinematic_move_map.move_all_root_jumps = False\n",
    "print(\n",
    "    \"FastRelax input/output dtype:\",\n",
    "    relax_start.coords.dtype,\n",
    "    \"→\",\n",
    "    relaxed.coords.dtype,\n",
    ")\n",
    "\n",
    "# Optional kinematic form using the same public protocol (not run here):\n",
    "# kin_relaxed = tmol.fast_relax(\n",
    "#     relax_start,\n",
    "#     score_function,\n",
    "#     palette,\n",
    "#     kinematic_move_map,\n",
    "#     fold_forest,\n",
    "#     num_repeats=1,\n",
    "#     schedule=tiny_schedule,\n",
    "#     min_fn=kinematic_min_fn,\n",
    "# )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7a51e7d",
   "metadata": {},
   "source": [
    "## Relax an ensemble in one GPU batch\n",
    "\n",
    "The single-structure call above and the batched call below use the same constrained protocol: each perturbed input receives main-chain coordinate constraints, the ensemble score function starts with the same nonzero constraint weight, the same two-stage schedule is used, and every minimization uses `TUTORIAL_MAX_ITER`. Four reproducibly perturbed conformations are assembled into one `PoseStack`, relaxed together, scored with the same constraint/non-constraint decomposition, and split after the batched protocol for per-member metrics and the labeled structure switcher. This exposes the batch dimension to GPU kernels; measure it against four serial calls on the target GPU before choosing a production batch size.\n",
    "\n",
    "Constraints are constructed after perturbation, so each ensemble member is restrained to its own starting TMol-declared N/CA/C coordinates, exactly as the single structure is restrained to its own start; O is not constrained. The results report per-member score changes, raw displacement, Kabsch-aligned RMSD, and whether accept-best retained that member's input or the recorded repeat endpoint. The cell is marked `gpu-only`: the GPU CI lane executes it, while the hosted CPU docs build preserves its checked-in output. The Colab button remains the way to rerun it on another GPU."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "11ebd429",
   "metadata": {
    "tags": [
     "gpu-only"
    ]
   },
   "outputs": [],
   "source": [
    "#| tags: [gpu-only]\n",
    "if device.type != \"cuda\":\n",
    "    print(\"Skipped: open this notebook in a Colab GPU runtime to run batch relax.\")\n",
    "else:\n",
    "    ensemble_members = {}\n",
    "    for member_index, noise_scale in enumerate((0.00, 0.01, 0.02, 0.03)):\n",
    "        member = pose.clone()\n",
    "        generator = torch.Generator(device=device).manual_seed(SEED + member_index)\n",
    "        noise = torch.randn(\n",
    "            member.coords.shape,\n",
    "            generator=generator,\n",
    "            device=device,\n",
    "            dtype=member.coords.dtype,\n",
    "        )\n",
    "        member.coords[member.real_atoms] += noise[member.real_atoms] * noise_scale\n",
    "        ensemble_members[f\"input {member_index}\"] = member\n",
    "\n",
    "    ensemble = PoseStackBuilder.from_poses(\n",
    "        list(ensemble_members.values()), device\n",
    "    )\n",
    "    ensemble = create_mainchain_coordinate_constraints(ensemble)\n",
    "    ensemble_sfxn = beta2016_score_function(device)\n",
    "    ensemble_sfxn.set_weight(ScoreType.constraint, constraint_start)\n",
    "    ensemble_before = score_components_by_pose(ensemble, ensemble_sfxn)\n",
    "    ensemble_stage_records = []\n",
    "\n",
    "    def recording_ensemble_cart_min(\n",
    "        pose_stack, stage_score_function, *, fold_forest, move_map, verbose\n",
    "    ):\n",
    "        minimized = tutorial_cart_min(\n",
    "            pose_stack,\n",
    "            stage_score_function,\n",
    "            fold_forest=fold_forest,\n",
    "            move_map=move_map,\n",
    "            verbose=verbose,\n",
    "        )\n",
    "        ensemble_stage_records.append(minimized.clone())\n",
    "        return minimized\n",
    "\n",
    "    relaxed_ensemble = tmol.fast_relax(\n",
    "        ensemble,\n",
    "        ensemble_sfxn,\n",
    "        PackerPalette(),\n",
    "        CartesianMoveMap(),\n",
    "        FoldForest.reasonable_fold_forest(ensemble),\n",
    "        num_repeats=1,\n",
    "        schedule=tiny_schedule,\n",
    "        ramp_constraints=True,\n",
    "        min_fn=recording_ensemble_cart_min,\n",
    "        verbose=False,\n",
    "    )\n",
    "    ensemble_after = score_components_by_pose(\n",
    "        relaxed_ensemble, ensemble_sfxn\n",
    "    )\n",
    "\n",
    "    ensemble_rows = []\n",
    "    ensemble_accepted_from = {}\n",
    "    for member_index in range(ensemble.n_poses):\n",
    "        before_pose = ensemble.split(member_index)\n",
    "        after_pose = relaxed_ensemble.split(member_index)\n",
    "        endpoint_pose = ensemble_stage_records[-1].split(member_index)\n",
    "        if coordinates_equal(after_pose, before_pose):\n",
    "            member_accepted_from = \"input\"\n",
    "        elif coordinates_equal(after_pose, endpoint_pose):\n",
    "            member_accepted_from = \"repeat 1 endpoint (stage 2)\"\n",
    "        else:\n",
    "            member_accepted_from = \"unresolved\"\n",
    "        ensemble_accepted_from[member_index] = member_accepted_from\n",
    "        raw_after = rms_displacement(before_pose, after_pose)\n",
    "        aligned_after = kabsch_aligned_rmsd(before_pose, after_pose)\n",
    "        before = ensemble_before[member_index]\n",
    "        after = ensemble_after[member_index]\n",
    "        ensemble_rows.extend(\n",
    "            [\n",
    "                {\n",
    "                    \"member\": member_index,\n",
    "                    \"structure\": \"before\",\n",
    "                    \"accepted_from\": \"not applicable\",\n",
    "                    \"raw_RMS_displacement_A\": 0.0,\n",
    "                    \"Kabsch_RMSD_A\": 0.0,\n",
    "                    \"non_constraint_score_change_units\": 0.0,\n",
    "                    \"constraint_score_change_units\": 0.0,\n",
    "                    \"objective_change_units\": 0.0,\n",
    "                    **before,\n",
    "                },\n",
    "                {\n",
    "                    \"member\": member_index,\n",
    "                    \"structure\": \"accepted final\",\n",
    "                    \"accepted_from\": member_accepted_from,\n",
    "                    \"raw_RMS_displacement_A\": raw_after,\n",
    "                    \"Kabsch_RMSD_A\": aligned_after,\n",
    "                    \"non_constraint_score_change_units\": (\n",
    "                        after[\"non_constraint_score_units\"]\n",
    "                        - before[\"non_constraint_score_units\"]\n",
    "                    ),\n",
    "                    \"constraint_score_change_units\": (\n",
    "                        after[\"constraint_score_units\"]\n",
    "                        - before[\"constraint_score_units\"]\n",
    "                    ),\n",
    "                    \"objective_change_units\": (\n",
    "                        after[\"reported_total_score_units\"]\n",
    "                        - before[\"reported_total_score_units\"]\n",
    "                    ),\n",
    "                    **after,\n",
    "                },\n",
    "            ]\n",
    "        )\n",
    "    ensemble_frame = pd.DataFrame(ensemble_rows)\n",
    "    ensemble_frame[\"finite_smoke_test_output\"] = np.isfinite(\n",
    "        ensemble_frame[\n",
    "            [\n",
    "                \"reported_total_score_units\",\n",
    "                \"raw_RMS_displacement_A\",\n",
    "                \"Kabsch_RMSD_A\",\n",
    "            ]\n",
    "        ]\n",
    "    ).all(axis=1)\n",
    "    ensemble_frame[\"convergence_status\"] = (\n",
    "        \"not assessed (10-iteration smoke test)\"\n",
    "    )\n",
    "    show_table(ensemble_frame)\n",
    "\n",
    "    comparison_structures = {}\n",
    "    comparison_notes = {}\n",
    "    for member_index in range(ensemble.n_poses):\n",
    "        before_label = f\"member {member_index} — before\"\n",
    "        after_label = f\"member {member_index} — after\"\n",
    "        comparison_structures[before_label] = ensemble.split(member_index)\n",
    "        comparison_structures[after_label] = relaxed_ensemble.split(member_index)\n",
    "        before = ensemble_before[member_index]\n",
    "        after = ensemble_after[member_index]\n",
    "        comparison_notes[before_label] = (\n",
    "            f\"non-constraint {before['non_constraint_score_units']:.3f}; \"\n",
    "            f\"constraint {before['constraint_score_units']:.3f} score units; \"\n",
    "            \"raw/aligned 0.000/0.000 Å\"\n",
    "        )\n",
    "        comparison_notes[after_label] = (\n",
    "            f\"non-constraint {after['non_constraint_score_units']:.3f}; \"\n",
    "            f\"constraint {after['constraint_score_units']:.3f}; \"\n",
    "            f\"raw/aligned \"\n",
    "            f\"{rms_displacement(ensemble.split(member_index), relaxed_ensemble.split(member_index)):.3f}/\"\n",
    "            f\"{kabsch_aligned_rmsd(ensemble.split(member_index), relaxed_ensemble.split(member_index)):.3f} Å; \"\n",
    "            f\"accepted from {ensemble_accepted_from[member_index]}\"\n",
    "        )\n",
    "    display(\n",
    "        tmol.switchable_view(\n",
    "            comparison_structures,\n",
    "            notes=comparison_notes,\n",
    "        )\n",
    "    )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d1e153e3",
   "metadata": {},
   "source": [
    "## Rosetta comparison\n",
    "\n",
    "TMol `fast_relax()` is a Rosetta-inspired, batched refinement subset—not an exact Rosetta FastRelax port. Both repeat packing and minimization under a changing score-function schedule, but their score functions, sampling, minimizers, acceptance behavior, trajectories, and outputs differ.\n",
    "\n",
    "TMol defaults to Cartesian minimization, whereas Rosetta FastRelax commonly uses torsional movement unless configured otherwise. TMol's accept-best pool also includes the unrelaxed input; Rosetta repeat selection does not normally retain that input as a candidate. Use this notebook to learn the TMol API, and consult the [Rosetta FastRelax mover documentation](https://docs.rosettacommons.org/docs/latest/scripting_documentation/RosettaScripts/Movers/movers_pages/FastRelaxMover) for Rosetta protocol options and production guidance.\n",
    "\n",
    "## Next: add noncanonical chemistry\n",
    "\n",
    "Continue to [07 — Ligands and parameter files](07_ligand_and_params.ipynb) to prepare ligand chemistry and refine a local pocket."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c0f57fb1",
   "metadata": {},
   "source": [
    "## Exercises\n",
    "\n",
    "1. Replace the tiny schedule with `DEFAULT_RELAX_SCHEDULE` and compare runtime and score.\n",
    "2. Keep constraints active in the final step and compare Cα displacement.\n",
    "3. Pass `kinematic_min_fn` with the prepared `kinematic_move_map` and compare Cartesian and kinematic results.\n",
    "4. Restrict packing with a `PackerTask` block mask, such as `disable_packing_by_block_mask()`.\n",
    "5. Batch two small poses, then rescore the input and repeat endpoints under one fixed weight set before interpreting accept-to-best behavior per pose."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "624597cb",
   "metadata": {},
   "source": [
    "## References\n",
    "\n",
    "- [Rosetta-to-TMol crosswalk](rosetta_crosswalk.md)\n",
    "- [Rosetta Relax tutorial](https://docs.rosettacommons.org/demos/latest/tutorials/Relax_Tutorial/Relax)\n",
    "- [Rosetta FastRelax implementation](https://github.com/RosettaCommons/rosetta/blob/main/source/src/protocols/relax/FastRelax.cc)\n",
    "- [PyRosetta packing, design, and regional relax](https://nbviewer.org/github/RosettaCommons/PyRosetta.notebooks/blob/master/notebooks/06.02-Packing-design-and-regional-relax.ipynb)\n",
    "- [Current PyRosetta notebook curriculum](https://rosettacommons.github.io/PyRosetta.notebooks/)"
   ]
  }
 ],
 "metadata": {
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  "language_info": {
   "name": "python"
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 "nbformat": 4,
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