{
"cells": [
{
"cell_type": "markdown",
"id": "responsible-recipient",
"metadata": {},
"source": [
"# Rosetta FoldTree\n",
"\n",
"@Author: 张博文\n",
"@email：bowen.zhang@xtalpi.com\n",
"\n",
"@Proofread: 吴炜坤\n",
"@email：weikun.wu@xtalpi.com"
]
},
{
"cell_type": "markdown",
"id": "alive-analysis",
"metadata": {},
"source": [
"在第一章第五节中，我们学习了有关蛋白质几何构象的处理方式的各种概念及处理方式。在蛋白质构象设计的过程中，我们需要针对这些几何关系对蛋白质结构进行计算。此时，就会涉及到计算过程中坐标的处理方式。这一章将介绍的就是Rosetta中坐标的处理方式。"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "institutional-dividend",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"PyRosetta-4 2021 [Rosetta PyRosetta4.conda.mac.cxx11thread.serialization.python37.Release 2021.26+release.b308454c455dd04f6824cc8b23e54bbb9be2cdd7 2021-07-02T13:01:54] retrieved from: http://www.pyrosetta.org\n",
"(C) Copyright Rosetta Commons Member Institutions. Created in JHU by Sergey Lyskov and PyRosetta Team.\n",
"\u001b[0mcore.init: {0} \u001b[0mChecking for fconfig files in pwd and ./rosetta/flags\n",
"\u001b[0mcore.init: {0} \u001b[0mRosetta version: PyRosetta4.conda.mac.cxx11thread.serialization.python37.Release r288 2021.26+release.b308454c455 b308454c455dd04f6824cc8b23e54bbb9be2cdd7 http://www.pyrosetta.org 2021-07-02T13:01:54\n",
"\u001b[0mcore.init: {0} \u001b[0mcommand: PyRosetta -ex1 -ex2aro -database /opt/miniconda3/lib/python3.7/site-packages/pyrosetta/database\n",
"\u001b[0mbasic.random.init_random_generator: {0} \u001b[0m'RNG device' seed mode, using '/dev/urandom', seed=1689727216 seed_offset=0 real_seed=1689727216 thread_index=0\n",
"\u001b[0mbasic.random.init_random_generator: {0} \u001b[0mRandomGenerator:init: Normal mode, seed=1689727216 RG_type=mt19937\n"
]
}
],
"source": [
"# 初始化pyrosetta，使用pyrosetta必须要做的一件事情\n",
"from pyrosetta import *\n",
"from pyrosetta.rosetta import *\n",
"from pyrosetta.teaching import *\n",
"init()"
]
},
{
"cell_type": "markdown",
"id": "pointed-algebra",
"metadata": {},
"source": [
"### 一、内坐标及减少自由度降低计算复杂度的处理方式"
]
},
{
"cell_type": "markdown",
"id": "molecular-opera",
"metadata": {},
"source": [
"PDB文件中，大多数的表示都是笛卡尔坐标(X,Y,Z)，当改变或设置这3个值时，该原子的位置也就确定了，此时每个原子都具有三个自由度，但三个自由度对于计算来说复杂度过高。"
]
},
{
"cell_type": "markdown",
"id": "weekly-party",
"metadata": {},
"source": [
"**在进行计算的时候，坐标的表示方式是这样的：**"
]
},
{
"cell_type": "markdown",
"id": "surprising-nelson",
"metadata": {},
"source": [
"1 使用了内坐标来进行表示。内坐标定义如下：如下图所示，对于一个原子，其位置坐标通过其与临近原子的键长、键角、二面角来进行表示。此个原子来说，构象的改变是通过改变键长、键角和二面角来完成的，但此时的自由度仍为3。（二面角 dihedral，扭转角 = 180度 - 二面角，互补关系）\n",
"\n",
"举例: 如果想知道原子j的坐标，我们可以通过从原点和原子i的信息来计算，此处已知原点到原子i键长以及原子i到原子j的键长。此时只要再加上原点-原子i-原子j之间的键角。就可以推算出原子j的具体坐标(xyz)，因此内坐标和笛卡尔坐标是可以轻易被转换的。"
]
},
{
"cell_type": "markdown",
"id": "italic-chick",
"metadata": {},
"source": [
"<center><img src=\"./imgs/freedom.jpg\" width = \"700\" height = \"400\" align=center /> </center>\n",
"(图片来源: 晶泰科技团队)"
]
},
{
"cell_type": "markdown",
"id": "demographic-april",
"metadata": {},
"source": [
"2 减少自由度降低计算复杂度:\n",
"\n",
"尽管此时对于一个原子来说自由度仍为3，但这三个自由度在蛋白质设计中的重要程度并不相同。往往在蛋白质建模的过程中，键长、键角的变化相对来说设计很微小的，**这时候若设置将此两者设置为理想值(固定值)，只以二面角的变化来表示构象变化。此时自由度就降为1了！**。同时，对于特定的原子（例如大多数的氢）其二面角受其化学环境的影响是固定的，此时自由度就变为0了。"
]
},
{
"cell_type": "markdown",
"id": "differential-information",
"metadata": {},
"source": [
"### 二、FoldTree的定义和功能"
]
},
{
"cell_type": "markdown",
"id": "d795ac0e-532f-4a2e-a1c6-4f9a05b6a7f9",
"metadata": {},
"source": [
"#### 2.1 什么是FoldTree？"
]
},
{
"cell_type": "markdown",
"id": "e46edd97-a5ed-475c-9220-23d5fe7aaf6c",
"metadata": {},
"source": [
"**在Rosseta中, FoldTree即对蛋白质主链内部及主链之间表示其上下游关系的方式，它定义了在蛋白质结构中，哪些残基是上游或是母节点、哪些残基是下游或是子节点，并为其贴上了标签，并且约定当内坐标自由度发生变换时，只有FoldTree下游的氨基酸xyz坐标会发生改变，而上游氨基酸的构象保持不变。**"
]
},
{
"cell_type": "markdown",
"id": "265e4c6f-bdea-4e1e-9aa3-2e8213ec4fd5",
"metadata": {},
"source": [
"此处举一个最简单的例子: FoldTree的顺序是从N端到C端，仅有一条链。因此1号残基是此树结构的\"根\"(上游)，8号残基是最末端的\"支\"(下游)。\n",
"\n",
"如果此时对4号残基的骨架的二面角做出改变。只有处于树结构下游（5->6->7->8）的氨基酸会发生坐标变换。"
]
},
{
"cell_type": "markdown",
"id": "96d628d0-0fca-4b88-bb39-1c66761ef708",
"metadata": {},
"source": [
"<center><img src=\"./imgs/simple_foldtree.jpg\" width = \"700\" height = \"300\" align=center /> </center>\n",
"(图片来源: Meiler Lab Rosetta2020教程中的Rosetta_Energy_Function ppt)"
]
},
{
"cell_type": "markdown",
"id": "e23e480d-1c56-4899-9008-c84c370aec48",
"metadata": {},
"source": [
"FoldTree共有四种特性：\n",
"1. 杠杆效应(本节介绍)\n",
"2. 顺序性(本节介绍)\n",
"3. 跳跃性(下一节介绍)\n",
"4. 可切割性(下一节介绍)"
]
},
{
"cell_type": "markdown",
"id": "little-raleigh",
"metadata": {},
"source": [
"#### 2.2 杠杆效应现象"
]
},
{
"cell_type": "markdown",
"id": "741f23a6-0864-41e7-9fac-9db885c501ff",
"metadata": {},
"source": [
"**杠杆效应本质即当遵守如上所说约定时，当内坐标变化时，约定只对处于树下游区域的氨基酸xyz坐标进行变换所产生的现象。**"
]
},
{
"cell_type": "markdown",
"id": "nutritional-helen",
"metadata": {},
"source": [
"举例，首先得到了一个由五个残基组成的多肽。"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "arabic-caution",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\u001b[0mcore.chemical.GlobalResidueTypeSet: {0} \u001b[0mFinished initializing fa_standard residue type set. Created 984 residue types\n",
"\u001b[0mcore.chemical.GlobalResidueTypeSet: {0} \u001b[0mTotal time to initialize 0.695354 seconds.\n"
]
},
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"pose = pose_from_sequence('KPALN') # 根据序列生成一个示例的多肽序列\n",
"pose.dump_pdb('./data/example.pdb') # 保存该pose为pdb文件"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "boxed-exercise",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# 更改示例多肽序列的3号残基的phi角\n",
"pose.set_phi(3,70) # 修改3号ALA残基的phi角\n",
"pose.dump_pdb('./data/example_change.pdb') # 保存修改后的pose为pdb文件"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "5e6965dc-965a-4289-a907-681e0ea1942b",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"FOLD_TREE EDGE 1 5 -1 \n"
]
}
],
"source": [
"# 打印foldtree信息:\n",
"print(pose.fold_tree())"
]
},
{
"cell_type": "markdown",
"id": "eleven-cabin",
"metadata": {},
"source": [
"从foldtree的信息来看，目前的设置是树顺序是1->2->3->4->5，因此当3号氨基酸phi角发生变化时，3，4，5号氨基酸都属于下游区域，理应发生坐标变换。"
]
},
{
"cell_type": "markdown",
"id": "decimal-voltage",
"metadata": {},
"source": [
"<center><img src=\"./imgs/phi_change.jpg\" width = \"800\" height = \"300\" align=center /> </center>\n",
"(图片来源: 知乎，Rosettta研习社)"
]
},
{
"cell_type": "markdown",
"id": "154bfead-b2ae-439a-8a93-58cb30760ca2",
"metadata": {},
"source": [
"因此在内坐标体系中，通过内坐标和笛卡尔坐标的换算，可以高效地表示由于杠杠效应带来的3N*atom_number个自由度的变化。"
]
},
{
"cell_type": "markdown",
"id": "indoor-correspondence",
"metadata": {},
"source": [
"#### 2.3 FoldTree的表示方式"
]
},
{
"cell_type": "markdown",
"id": "handled-illinois",
"metadata": {},
"source": [
"Edge是FoldTree的基本组成部分，一个FoldTree是由1个或多个Edge组成。在Pyrosetta中Fold_Tree通过fold_tree方法来进行调用"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "understanding-mortality",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\u001b[0mcore.import_pose.import_pose: {0} \u001b[0mFile './data/1v74.pdb' automatically determined to be of type PDB\n",
"\u001b[0mcore.conformation.Conformation: {0} \u001b[0m\u001b[1m[ WARNING ]\u001b[0m missing heavyatom: OXT on residue LEU:CtermProteinFull 107\n",
"\u001b[0mcore.conformation.Conformation: {0} \u001b[0m\u001b[1m[ WARNING ]\u001b[0m missing heavyatom: OXT on residue LEU:CtermProteinFull 194\n"
]
}
],
"source": [
"# PDB:1v74的例子\n",
"pose_1v74 = pose_from_pdb('./data/1v74.pdb') #读入蛋白质的pdb文件\n",
"pose_1v74_foldtree = pose_1v74.fold_tree() #得到该pose的foldtree实例"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "removed-dynamics",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"PDB file name: ./data/1v74.pdb\n",
" Pose Range Chain PDB Range | #Residues #Atoms\n",
"\n",
"0001 -- 0107 A 0591 -- 0697 | 0107 residues; 01728 atoms\n",
"0108 -- 0194 B 0001 -- 0087 | 0087 residues; 01425 atoms\n",
" TOTAL | 0194 residues; 03153 atoms\n",
"\n"
]
}
],
"source": [
"# 输出PDB:1V74的信息\n",
"print(pose_1v74.pdb_info())"
]
},
{
"cell_type": "markdown",
"id": "scheduled-harvest",
"metadata": {},
"source": [
"如同上面的输出所示，示例pose具有2条多肽链，分别是1-107号残基，以及108-194号残基的肽链。"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "artificial-portugal",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1v74 Fold Tree:\n",
" FOLD_TREE EDGE 1 107 -1 EDGE 1 108 1 EDGE 108 194 -1 \n"
]
}
],
"source": [
"# 输出PDB:1V74的fold tree表示\n",
"print(\"1v74 Fold Tree:\\n\", pose_1v74_foldtree)"
]
},
{
"cell_type": "markdown",
"id": "included-economics",
"metadata": {},
"source": [
"FoldTree的表示方式一般如下。有四个字段组成：**EDGE、Start、End、Define**\n",
"如上面输出所示：\n",
"- **当Define字段是-1时**，代表着这一段多肽区域按照从start到end位的顺序通过共价键进行延伸。如上所示，表示1到107残基、108到194残基是以共价相连。如\"EDGE 1 107 -1\", \"EDGE 108 194 -1\"。\n",
"- **当Define字段是正整数时**，代表着会在start和end位氨基酸建立虚拟链接,代表这个是一个Jump点，表示在FoldTree中，第Start号氨基酸和第End号氨基酸之间将建立**“虚拟的共价链接”**，Jump点会直接改变不同多肽链之间的上下游的关系。如上所示，分别在1和108号残基有1个jump点。如\"EDGE 1 108 1\", 1代表Jump的id序号，第一个Jump点。"
]
},
{
"cell_type": "markdown",
"id": "asian-ranch",
"metadata": {},
"source": [
"对于FoldTree的Jump，我们可以通过foldtree实例的一些方法得到他的信息。（**关于Jump点的信息我们将在3.2章节中进行介绍**）"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "necessary-section",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The size of the foldtree (number of edges) is 3\n",
"The number of the jump is 1\n"
]
}
],
"source": [
"print(f\"The size of the foldtree (number of edges) is {pose_1v74_foldtree.size()}\") #Foldtree 的尺寸（edge的个数）\n",
"print(f\"The number of the jump is {pose_1v74_foldtree.num_jump()}\") #Foldtree 的jump点的个数"
]
},
{
"cell_type": "markdown",
"id": "interesting-format",
"metadata": {},
"source": [
"#### 2.4 自定义一个FoldTree"
]
},
{
"cell_type": "markdown",
"id": "opening-duplicate",
"metadata": {},
"source": [
"基本的操作方式:\n",
"1. 实例化一个FoldTree对象; \n",
"2. 使用该对象的add_edge、delete_edge进行FoldTree的编辑; \n",
"3. pose的fold_tree读回创建的FoldTree对象。"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "capable-hello",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"FOLD_TREE EDGE 1 7 -1 \n"
]
}
],
"source": [
"# 从序列创建一个Pose对象\n",
"seq_pose = pose_from_sequence('AAAAAAA') #读入PDB文件\n",
"print(seq_pose.fold_tree())"
]
},
{
"cell_type": "markdown",
"id": "broken-blond",
"metadata": {},
"source": [
"可见，在创建Pose的同时FoldTree也会同时被自动创建，但这个foldtree默认是从N到C端的顺序进行创建。"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "stainless-messenger",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"FOLD_TREE \n"
]
},
{
"data": {
"text/plain": [
"False"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# 设置一个foldtree对象的实例，并将它读回pose中更新foldtree\n",
"ft = FoldTree() #设置一个空的foldtree对象\n",
"print(ft)\n",
"ft.check_fold_tree() # 检查foldtree的有效性;"
]
},
{
"cell_type": "markdown",
"id": "molecular-colorado",
"metadata": {},
"source": [
"可见，通过check_fold_tree函数，可以快速检测你的foldtree是否有效。"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "given-statement",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"#增加一个5号残基到1号残基的共价连接的edge\n",
"ft.add_edge(start=5, stop=1, label=-1) # label代表egde类型，-1=多肽链，1=jump\n",
"ft.check_fold_tree() # 检查foldtree的有效性;"
]
},
{
"cell_type": "markdown",
"id": "vulnerable-bracket",
"metadata": {},
"source": [
"上面我们仅定义了1-5号氨基酸的foldtree，但是我们创建的pose却有7个氨基酸。此时将这个foldtree加载到pose中会发生什么？"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "delayed-electricity",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\u001b[0mcore.conformation.Conformation: {0} \u001b[0m\u001b[31m\u001b[1m[ ERROR ]\u001b[0m Error in assigning a FoldTree to a Conformation - size mismatch.\n",
"\u001b[0mcore.conformation.Conformation: {0} \u001b[0m\u001b[31m\u001b[1m[ ERROR ]\u001b[0m Conformation of length 7: A[ALA:NtermProteinFull]AAAAAA[ALA:CtermProteinFull]\n",
"\u001b[0mcore.conformation.Conformation: {0} \u001b[0m\u001b[31m\u001b[1m[ ERROR ]\u001b[0m FoldTree of length 5: FOLD_TREE EDGE 5 1 -1\n"
]
},
{
"ename": "RuntimeError",
"evalue": "\n\nFile: /Volumes/MacintoshHD3/benchmark/W.fujii.release/rosetta.Fujii.release/_commits_/main/source/src/core/conformation/Conformation.cc:829\n[ ERROR ] UtilityExitException\nERROR: Conformation: fold_tree nres should match conformation nres. conformation nres: 7 fold_tree nres: 5\n\n",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
"\u001b[0;31mRuntimeError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m<ipython-input-12-cb53977f0fef>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mseq_pose\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfold_tree\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mft\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;31m#更新pose的fold_tree\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
"\u001b[0;31mRuntimeError\u001b[0m: \n\nFile: /Volumes/MacintoshHD3/benchmark/W.fujii.release/rosetta.Fujii.release/_commits_/main/source/src/core/conformation/Conformation.cc:829\n[ ERROR ] UtilityExitException\nERROR: Conformation: fold_tree nres should match conformation nres. conformation nres: 7 fold_tree nres: 5\n\n"
]
}
],
"source": [
"seq_pose.fold_tree(ft) #更新pose的fold_tree"
]
},
{
"cell_type": "markdown",
"id": "governmental-migration",
"metadata": {},
"source": [
"运行结果表示，foldtree中必须完整定义整个pose的所有氨基酸上下游关系时，才是一个完整的tree！"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "written-graphics",
"metadata": {},
"outputs": [],
"source": [
"# 完整定义试试:\n",
"ft = FoldTree() #设置一个空的foldtree对象\n",
"ft.add_edge(start=5, stop=1, label=-1)\n",
"ft.add_edge(start=5, stop=7, label=-1)\n",
"ft.check_fold_tree() # 检查foldtree的有效性;"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "familiar-qatar",
"metadata": {},
"outputs": [],
"source": [
"seq_pose.fold_tree(ft) #更新pose的fold_tree\n",
"print(seq_pose.fold_tree())"
]
},
{
"cell_type": "markdown",
"id": "proof-surgery",
"metadata": {},
"source": [
"#### 2.5 FoldTree的顺序性"
]
},
{
"cell_type": "markdown",
"id": "legislative-testimony",
"metadata": {},
"source": [
"在FoldTree中,Start和End字段是顺序敏感的，包括N->C顺序以及C->N顺序。不同顺序，代表EDGE内氨基酸所对应的上下游关系不同。"
]
},
{
"cell_type": "markdown",
"id": "after-growing",
"metadata": {},
"source": [
"还是以原本的的五肽为例，原本是以N->C的顺序来进行排列的。我们将其人为修改为C->N后，由于FoldTree上下游关系的改变，修改二面角后构象造成的变化也不再相同。"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "positive-settlement",
"metadata": {},
"outputs": [],
"source": [
"#观察原本五肽的FoldTree\n",
"pose = pose_from_sequence('KPALN') # 根据一个序列得到一个五肽序列的pose\n",
"pose.dump_pdb('./data/example_5_1.pdb') #保存五肽的构象\n",
"print(\"The Fold Tree of the pose:\\n\", pose.fold_tree()) # 输出该pose的FoldTree"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "loving-fiction",
"metadata": {},
"outputs": [],
"source": [
"# 设置一个foldtree对象的实例，并将它读回pose中更新foldtree\n",
"ft = FoldTree() #设置一个空的foldtree对象\n",
"ft.add_edge(start=5, stop=1, label=-1) #增加一个5号残基到1号残基的共价连接的edge\n",
"pose.fold_tree(ft) #更新pose的fold_tree\n",
"print(pose.fold_tree()) #输出foldtree"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "authentic-patient",
"metadata": {},
"outputs": [],
"source": [
"pose.set_phi(3,70) #更改肽链的3号残基的phi角\n",
"pose.dump_pdb('./data/example_5_1_change.pdb') #保存更改后的五肽的构象"
]
},
{
"cell_type": "markdown",
"id": "simplified-search",
"metadata": {},
"source": [
"<img src=\"./imgs/foldtree_sequence.png\" width = \"600\" height = \"300\" align=center /> \n",
"(图片来源: 晶泰科技团队)"
]
},
{
"cell_type": "markdown",
"id": "premier-front",
"metadata": {},
"source": [
"如图，黄色的是初始的五肽，蓝色的是原本的多肽在修改3号残基的phi角后的多肽构象，可以发现出现构象改变的是4、5号残基；而在修改该多肽的FoldTree为从5到1的顺序后，发生构象变化的就是1、2号残基。而这，就是foldtree的顺序性，即在改变选定残基的构象时，随之而改变的只有选定残基下游的氨基酸的构象"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "blank-sewing",
"metadata": {},
"outputs": [],
"source": []
}
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