{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Plotly plot of a circular phylogenetic tree
Interactive path marking ##"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A circular phylogenetic tree is defined as the image of a rectangular tree, through a map $g$, that associates\n",
"to each point of cartesian coordinates (x,y), a point of special polar coordinates $(r,\\theta)$, with respect to the `tree.root` as reference point, and the horizontal axis through this point as reference direction.\n",
"\n",
"The Plotly plot generation of a phylogenetic tree with rectangular layout is presented in this [Jupyter Notebook](http://nbviewer.jupyter.org/github/empet/Phylogenetic-trees/blob/master/Plotly-rectangular-phylogram-Zika.ipynb). The cartesian coordinates on the rectangular representation are assigned as in Biopython [https://github.com/biopython/biopython/blob/master/Bio/Phylo/_utils.py](https://github.com/biopython/biopython/blob/master/Bio/Phylo/_utils.py).\n",
"\n",
"\n",
"If `ymin`, `ymax` are the min, max y-coordinates on the rectangular tree, d is the distance between the y-coordinates of two consecutive leafs, then the mapping from cartesian to polar coordinates is defined as follows:\n",
"$$(x,y)\\mapsto (r=x, \\:\\theta=2\\pi (y-ymin+d)/(ymax-ymin+d))$$\n",
"\n",
"\n",
"When the tree has a reduced number of leafs, we can choose to map the rectangular representation onto a circular\n",
"area between some `startangle>=0`, and `endangle`<$2\\pi$. In this case the mapping to polar coordinates is defined\n",
"by:\n",
"$$(x,y)\\mapsto (r=x,\\: \\theta=(endangle-startangle)(y-ymin)/(ymax-ymin))$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let us illustrate this mapping on the basic rectangular tree below, where $x_{left}=x_{right}$:"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
""
],
"text/plain": [
""
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from IPython.display import SVG\n",
"SVG(filename='Data/recttree.svg')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Denoting $\\theta=g(y_{right})$, $\\theta_b=g(y_{bot})$, and $\\theta_t=g(y_{top})$, the circular image of this rectangular tree looks like this one:"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"image/svg+xml": [
""
],
"text/plain": [
""
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"SVG(filename='Data/circtree.svg')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The function `get_circular_tree_data()` computes and returns the lists of x, y-coordinates (with\n",
"$x=r\\cos{\\theta}, y=r\\sin{\\theta}$) of the points on the circular phylogenetic tree."
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Python version: 3.6.4\n",
"Plotly version: 3.3.0\n"
]
}
],
"source": [
"import platform\n",
"print(f'Python version: {platform.python_version()}')\n",
"import plotly\n",
"print(f\"Plotly version: {plotly.__version__}\")"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"from Bio import Phylo\n",
"import numpy as np\n",
"import plotly.graph_objs as go\n",
"import ipywidgets as ipw"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"\n",
"\n",
"def get_circular_tree_data(tree, order='level', dist=1, start_angle=0, end_angle=360, start_leaf='first'):\n",
" \"\"\"Define data needed to get the Plotly plot of a circular tree\n",
" \"\"\"\n",
" # tree: an instance of Bio.Phylo.Newick.Tree or Bio.Phylo.PhyloXML.Phylogeny\n",
" # order: tree traversal method to associate polar coordinates to its nodes\n",
" # dist: the vertical distance between two consecutive leafs in the associated rectangular tree layout\n",
" # start_angle: angle in degrees representing the angle of the first leaf mapped to a circle\n",
" # end_angle: angle in degrees representing the angle of the last leaf\n",
" # the list of leafs mapped in anticlockwise direction onto circles can be tree.get_terminals() \n",
" # or its reversed version tree.get_terminals()[::-1]. \n",
" # start leaf: is a keyword with two possible values\"\n",
" # 'first': to map the leafs in the list tree.get_terminals() onto a circle,\n",
" # in the counter-clockwise direction\n",
" # 'last': to map the leafs in the list, tree.get_terminals()[::-1] \n",
" \n",
" start_angle *= np.pi/180 # conversion to radians\n",
" end_angle *= np.pi/180\n",
" \n",
" def get_radius(tree):\n",
" \"\"\"\n",
" Associates to each clade root its radius, equal to the distance from that clade to the tree root\n",
" returns dict {clade: node_radius}\n",
" \"\"\"\n",
" node_radius = tree.depths()\n",
" \n",
" # If the tree did not record the branch lengths assign the unit branch length\n",
" # (ex: the case of a newick tree \"(A, (B, C), (D, E))\")\n",
" if not np.count_nonzero(node_radius.values()):\n",
" node_radius = tree.depths(unit_branch_lengths=True)\n",
" return node_radius\n",
" \n",
" \n",
" def get_vertical_position(tree):\n",
" \"\"\"\n",
" returns a dict {clade: ycoord}, where y-coord is the cartesian y-coordinate \n",
" of a clade root in a rectangular phylogram\n",
" \n",
" \"\"\"\n",
" n_leafs = tree.count_terminals() # Counts the number of tree leafs.\n",
" \n",
" # Assign y-coordinates to the tree leafs\n",
" if start_leaf == 'first':\n",
" node_ycoord = dict((leaf, k) for k, leaf in enumerate(tree.get_terminals()))\n",
" elif start_leaf == 'last':\n",
" node_ycoord = dict((leaf, k) for k, leaf in enumerate(reversed(tree.get_terminals())))\n",
" else:\n",
" raise ValueError(\"start leaf can be only 'first' or 'last'\")\n",
" \n",
" def assign_ycoord(clade):#compute the y-coord for the root of this clade\n",
" for subclade in clade:\n",
" if subclade not in node_ycoord: # if the subclade root hasn't a y-coord yet\n",
" assign_ycoord(subclade)\n",
" node_ycoord[clade] = 0.5 * (node_ycoord[clade.clades[0]] + node_ycoord[clade.clades[-1]])\n",
"\n",
" if tree.root.clades:\n",
" assign_ycoord(tree.root)\n",
" return node_ycoord\n",
"\n",
" node_radius = get_radius(tree)\n",
" node_ycoord = get_vertical_position(tree)\n",
" y_vals = node_ycoord.values()\n",
" ymin, ymax = min(y_vals), max(y_vals)\n",
" ymin -= dist # this dist subtraction is necessary to avoid coincidence of the first and last leaf angle\n",
" # when the interval [ymin, ymax] is mapped onto [0, 2pi],\n",
" \n",
" def ycoord2theta(y):\n",
" # maps an y in the interval [ymin-dist, ymax] to the interval [radian(start_angle), radian(end_angle)]\n",
" \n",
" return start_angle + (end_angle - start_angle) * (y-ymin) / float(ymax-ymin)\n",
"\n",
" \n",
" \n",
"\n",
" def get_points_on_lines(linetype='radial', x_left=0, x_right=0, y_right=0, y_bot=0, y_top=0):\n",
" \"\"\"\n",
" - define the points that generate a radial branch and the circular arcs, perpendicular to that branch\n",
" \n",
" - a circular arc (angular linetype) is defined by 10 points on the segment of ends\n",
" (x_bot, y_bot), (x_top, y_top) in the rectangular layout,\n",
" mapped by the polar transformation into 10 points that are spline interpolated\n",
" - returns for each linetype the lists X, Y, containing the x-coords, resp y-coords of the\n",
" line representative points\n",
" \"\"\"\n",
" \n",
" if linetype == 'radial':\n",
" theta = ycoord2theta(y_right) \n",
" X = [x_left*np.cos(theta), x_right*np.cos(theta), None]\n",
" Y = [x_left*np.sin(theta), x_right*np.sin(theta), None]\n",
" \n",
" elif linetype == 'angular':\n",
" theta_b = ycoord2theta(y_bot)\n",
" theta_t = ycoord2theta(y_top)\n",
" t = np.linspace(0,1, 10)# 10 points that span the circular arc \n",
" theta = (1-t) * theta_b + t * theta_t\n",
" X = list(x_right * np.cos(theta)) + [None]\n",
" Y = list(x_right * np.sin(theta)) + [None]\n",
" \n",
" else:\n",
" raise ValueError(\"linetype can be only 'radial' or 'angular'\")\n",
" \n",
" return X,Y \n",
" \n",
" \n",
"\n",
" def get_line_lists(clade, x_left, xlines, ylines, xarc, yarc):\n",
" \"\"\"Recursively compute the lists of points that span the tree branches\"\"\"\n",
" \n",
" # xlines, ylines - the lists of x-coords, resp y-coords of radial edge ends\n",
" # xarc, yarc - the lists of points generating arc segments for tree branches\n",
" \n",
" x_right = node_radius[clade]\n",
" y_right = node_ycoord[clade]\n",
" \n",
" X,Y = get_points_on_lines(linetype='radial', x_left=x_left, x_right=x_right, y_right=y_right)\n",
" \n",
" xlines.extend(X)\n",
" ylines.extend(Y)\n",
" \n",
" if clade.clades:\n",
" \n",
" y_top = node_ycoord[clade.clades[0]]\n",
" y_bot = node_ycoord[clade.clades[-1]]\n",
" \n",
" X,Y = get_points_on_lines(linetype='angular', x_right=x_right, y_bot=y_bot, y_top=y_top)\n",
" xarc.extend(X)\n",
" yarc.extend(Y)\n",
" \n",
" # get and append the lists of points representing the branches of the descedants\n",
" for child in clade:\n",
" get_line_lists(child, x_right, xlines, ylines, xarc, yarc)\n",
"\n",
" xlines = []\n",
" ylines = []\n",
" xarc = []\n",
" yarc = []\n",
" get_line_lists(tree.root, 0, xlines, ylines, xarc, yarc) \n",
" xnodes = []\n",
" ynodes = []\n",
"\n",
" for clade in tree.find_clades(order='preorder'): #it was 'level'\n",
" theta = ycoord2theta(node_ycoord[clade])\n",
" xnodes.append(node_radius[clade]*np.cos(theta))\n",
" ynodes.append(node_radius[clade]*np.sin(theta))\n",
" \n",
" return xnodes, ynodes, xlines, ylines, xarc, yarc "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### A circular phylogram from a `'phyloxml'` file"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Read a phylogenetic tree from a [phyloxml file](http://phyloxml.org/) "
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"tree = Phylo.read('Data/bcl_2.xml', 'phyloxml')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Assign an id to each tree node: "
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"traverse_order = 'preorder'\n",
"\n",
"all_clades=list(tree.find_clades(order=traverse_order))\n",
"for k in range(len((all_clades))):\n",
" all_clades[k].id=k"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Get the coordinates for the nodes and links, as linear and circular lines, that define the Plotly traces\n",
"representing the phylogram:"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"xnodes, ynodes, xlines, ylines, xarc, yarc = get_circular_tree_data(tree, order=traverse_order, start_leaf='last')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the next cell we are performing a particular processing that is dictated by the type of data provided for each tree node \n",
"in the `phyloxml` file.\n",
"\n",
"More precisely, we are extracting the text to be displayed on hover over the tree nodes, and the confidence values to be mapped to a colorscale. \n"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [],
"source": [
"tooltip=[]\n",
"color=[]\n",
"for clade in tree.find_clades(order=traverse_order):\n",
" if clade.name and clade.confidence and clade.branch_length:\n",
" tooltip.append(f\"id: {clade.id}
name: {clade.name}
branch-length: {clade.branch_length}\\\n",
"
confidence: {int(clade.confidence.value)}\")\n",
" color.append[clade.confidence.value]\n",
" elif clade.name is None and clade.branch_length is not None and clade.confidence is not None: \n",
" color.append(clade.confidence.value)\n",
" tooltip.append(f\"id: {clade.id}
branch-length: {clade.branch_length}\\\n",
"
confidence: {int(clade.confidence.value)}\")\n",
" elif clade.name and clade.branch_length and clade.confidence is None:\n",
" tooltip.append(f\"id: {clade.id}
name: {clade.name}
branch-length: {clade.branch_length}\")\n",
" color.append(-1)\n",
" else: \n",
" tooltip.append('')\n",
" color.append(-1)\n",
"\n",
"size=[9 if c!=-1 else 7 for c in color]"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"pl_colorscale=[[0.0, 'rgb(10,10,150)'],#color for leafs that haven't associated a confidence\n",
" [0.001, 'rgb(10,10,150)'],\n",
" [0.001, 'rgb(214, 47, 38)'], # in fact the colorscale starts here \n",
" [0.1, 'rgb(214, 47, 38)'],\n",
" [0.2, 'rgb(244, 109, 67)'],\n",
" [0.3, 'rgb(252, 172, 96)'],\n",
" [0.4, 'rgb(254, 224, 139)'],\n",
" [0.5, 'rgb(254, 254, 189)'],\n",
" [0.6, 'rgb(217, 239, 139)'],\n",
" [0.7, 'rgb(164, 216, 105)'],\n",
" [0.8, 'rgb(102, 189, 99)'],\n",
" [0.9, 'rgb(63, 170, 89)'], \n",
" [1.0, 'rgb(25, 151, 79)']]\n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Define data and layout for the Plotly plot of our circular phylogram:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"trace_nodes=dict(type='scatter',\n",
" x=xnodes,\n",
" y= ynodes, \n",
" mode='markers',\n",
" marker=dict(color=color,\n",
" size=size, colorscale=pl_colorscale, \n",
" colorbar=dict(thickness=20, dtick=10, ticklen=4, title='confidence')),\n",
" text=tooltip, \n",
" hoverinfo='text',\n",
" opacity=1)\n",
"\n",
"trace_radial_lines=dict(type='scatter',\n",
" x=xlines,\n",
" y=ylines, \n",
" mode='lines',\n",
" line=dict(color='rgb(20,20,20)', width=1),\n",
" hoverinfo='none')\n",
"\n",
"trace_arcs=dict(type='scatter',\n",
" x=xarc,\n",
" y=yarc,\n",
" mode='lines',\n",
" line=dict(color='rgb(20,20,20)', width=1, shape='spline'),\n",
" hoverinfo='none')"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"layout=dict(title='Bcl-2 gene family tree',\n",
" font=dict(family='Balto',size=14),\n",
" width=700,\n",
" height=750,\n",
" autosize=False,\n",
" showlegend=False,\n",
" xaxis=dict(visible=False),\n",
" yaxis=dict(visible=False), \n",
" hovermode='closest',\n",
" plot_bgcolor='rgb(245,245,245)',\n",
" margin=dict(t=75)\n",
" )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 1. Plotly plot of the circular phylogram"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"fig=go.FigureWidget(data=[trace_radial_lines, trace_arcs, trace_nodes], layout=layout)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
""
],
"text/plain": [
""
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import plotly.plotly as py\n",
"py.sign_in('empet', '')\n",
"py.iplot(fig, filename='bcl2-phyloxml')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 2. Interactive path marking from root to an arbitrary tree node"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"fw=go.FigureWidget(fig)\n",
"with fw.batch_update():\n",
" fw.data[2].marker.showscale=False\n",
" fw.layout.title='Path marking from root to a tree node by clicking that node'"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"textarea_box = ipw.Textarea(value='',\n",
" description='',\n",
" disabled=False,\n",
" continuous_update=True)\n",
"\n",
"textarea_box.layout = dict(margin='-70px 10px 10px 80px', width='540px') "
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [],
"source": [
"def select_path_nodes(trace, points, state):\n",
" \n",
" if not points.point_inds:\n",
" return\n",
" ind = points.point_inds[0] \n",
" new_color = np.array(['rgb(150, 160, 150)']*len(trace.x)) \n",
" path=tree.get_path(id=ind)\n",
" path_ids=[0]+[path[k].id for k in range(len(path))]\n",
" new_color[path_ids] = 'magenta'\n",
" trace.marker.color = new_color \n",
" target_node=list(tree.find_elements(id=ind))[0]\n",
" path_to=target_node.name if target_node.name else 'noname'\n",
" textarea_box.value = ' '.join(f\" {x} ->\" for x in path_ids[:-1])+ f\"{path_ids[-1]} ({path_to})\" "
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "55cfdb04a59349fbbf400a87f9361e78",
"version_major": 2,
"version_minor": 0
},
"text/plain": [
"VBox(children=(FigureWidget({\n",
" 'data': [{'hoverinfo': 'none',\n",
" 'line': {'color': 'rgb(20,20,20…"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fw.data[2].on_click(select_path_nodes) \n",
"ipw.VBox([fw, textarea_box])"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n"
],
"text/plain": [
""
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from IPython.core.display import HTML\n",
"def css_styling():\n",
" styles = open(\"./custom.css\", \"r\").read()\n",
" return HTML(styles)\n",
"css_styling()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.4"
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"layout": "IPY_MODEL_08c0800f5ac14b4490a542dc696b0b92"
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"value": " 0 -> 60 -> 61 -> 62 -> 144 -> 180 -> 181 -> 185 -> 186 ->187 (55_BOVIN)"
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