Difference between revisions of "Template:LMU-TUM Munich ModelCode"

Latest revision as of 03:52, 20 October 2016

simulation

Setup¶

So first we need to import some libraries

In [1]:

import numpy as np
import matplotlib.pylab as plt
%matplotlib inline

The following library is one that we wrote ourselves. It just contains the basic code that makes up our model of cells and proteins as monomers with binding sites

In [126]:

from monomers import *

Now we define a couple of functions to set up an experiment.

functions to initialize an experiment¶

In [3]:

def init_monomers(n_cells, n_proteins, n_cell_binding = 30, n_protein_binding = 4):
    '''instantiates a certain number of monomers'''
    Cell.n_cells=0
    cells=[]
    for i in range(n_cells):
        cells.append(Cell(n_cell_binding))

    Protein.n_proteins=0
    proteins=[]
    for i in range(n_proteins):
        proteins.append(Protein(n_protein_binding))
    return cells, proteins

After we set our monomers in place we need to modell in some way how they interact with each other. The following "polymerize" function does so in a very basic fashion:

make a list of free binding sites of TP as well as cells
while there are still free binding sites of either kind choose two at random and let them bind together

In [4]:

def polymerize(cells, proteins):
    '''polymerizes cells and proteins in a simple way'''
    free_cell_bindings = []
    for c in cells:
        free_cell_bindings += c.free_bindings

    free_protein_bindings = []
    for p in proteins:
        free_protein_bindings += p.free_bindings

    while len(free_protein_bindings)>0 and len(free_cell_bindings)>0:
        p_binding_idx = np.random.randint(len(free_protein_bindings))
        p_binding = free_protein_bindings.pop(p_binding_idx)
        c_binding_idx = np.random.randint(len(free_cell_bindings))
        c_binding = free_cell_bindings.pop(c_binding_idx)
        p_binding.bind(c_binding)
    return len(free_protein_bindings) , len(free_cell_bindings)

As described in the text above this simulation of polymerization was too simplified. The results we got from this modell were not very surprising and didn't help us much with optimizing our process.

So next we implemented a more sophisticated way of simulating the polymerization process. The following function takes some basic spacial and temporal effects into account.

In [49]:

def polymerize_spacial(cells, proteins, n_protein_binding, concentration=0.01, reactivity=0.2, mobility=0.05, max_time=10.):
    '''simulates polymerization in a more sophisticated way'''
    time = 0.
    position_variance = 1.
    distance_binding_probability = lambda x: np.exp(-x ** 2 / position_variance ** 2) / (
    2 * np.pi * position_variance ** 2)

    free_protein_bindings = []
    for p in proteins:
        free_protein_bindings += p.free_bindings

    while (time < max_time):
        # at each timestep a certain fraction of the free binding sites will have a chance to react
        # this fraction is depending on the defined "reactivity" parameter
        for i in range(int(np.ceil(reactivity * len(free_protein_bindings)))):
            # choose a random NPBS
            p_binding_idx = np.random.randint(len(free_protein_bindings))
            p_binding = free_protein_bindings[p_binding_idx]
            
            # do tests on parent protein
            p = p_binding.parent
            # all monomers get assigned an individual increasing id at creation
            # we use this id to calculate a position by assuming
            # that at creation the cells are put on a line with equal distance to echa other
            
            # the lower to concentration, the higher the distance
            p_pos = float(p.id) / (len(proteins) * concentration)
            # (float) idx of nearest cell
            c_id_mean = p_pos * len(cells) * concentration
            # max distance of reachable cells from nearest cell
            max_range = position_variance * 3.2
            c_id_range = max_range * len(cells) * concentration
            c_id_min = max(int(c_id_mean - c_id_range), 0)
            c_id_max = min(int(c_id_mean + c_id_range), len(cells))
            # now we can calculate the cells in range
            candidate_cells = cells[c_id_min:c_id_max]

            if len(candidate_cells) == 0:
                #if there are no cells in reach we are done here and pic the next random NPBS to try again
                continue
            # otherwise we go on
            # now depending on the individual cells distance to the NP
            # we calculate the probability of each candidate cell to bind as a gaussian pdf of the distance
            min_distance = max(p_pos - position_variance * 3.2, 0) - p_pos
            max_distance = min(-p_pos + position_variance * 3.2,
                               len(proteins) - 1 / len(proteins) / concentration) + p_pos
            probabilities = np.arange(min_distance, max_distance,
                                      (max_distance - min_distance) / len(candidate_cells))[:len(candidate_cells)]
            probabilities = distance_binding_probability(probabilities)
            probabilities /= sum(probabilities) #normalization
            
            # this call picks a random cell based on the calculated probabilities
            cell = np.random.choice(candidate_cells, p=probabilities)
            
            # check if the chosen cell has actually still free binding sites
            try:
                cell.free_bindings.next()
            except StopIteration:
                # no free bindings left in this cell. back to the top.
                continue
                
            # now we find out which cells the TP in question is already bound to
            protein_partners = list(set([b.partner.parent for b in p.bindings if b.partner is not None]))
            #this way we know how many different cells it's bound to
            if len(protein_partners) == 1:
                # if a protein is already attatched to a cell it will most likely not bind to other cells
                # but there is a chance of 10%
                if cell not in protein_partners and np.random.rand()<0.9:
                    continue
            if len(protein_partners)>1 and cell not in protein_partners:
                # if a protein was binding to two cells already, it will not bind to any other
                continue
            # if we made it this far without running into any of the "continue"s we are ready to bind!
            # so the next free binding of the cell will react to our NPBS
            cell.free_bindings.next().bind(p_binding)
            # and the TPBS is removed from our binding sites dating database
            free_protein_bindings.pop(p_binding_idx)
        
        # after all reactive NPBS tired to react we move everything a bit
        # depending on the mobility parameter and increment the time
        position_variance += mobility
        time += 0.01

    # in the end we calculate the number of free CBS. Just to know about it.
    free_cell_bindings = []
    for c in cells:
        free_cell_bindings += c.free_bindings
    return len(free_protein_bindings), len(free_cell_bindings)

Analysis¶

Now for analyzing the generated polymer networks we import another library called graph_tool.

In [11]:

from graph_tool.all import *

from graph_tool import clustering,stats

The following two functions translate the network (or graph) that we build before into graph_tool-graphs. The first one draws a node for each cell. Then it draws a connecting edge betwee two nodes if the respective cells are connected via any NP.

The second one draws a big node for each cell and a small one for each NP. Edges represent a binding between a NP and a connected cell.

We will clarify the difference between the two graphing methods graphically after the two function definitions.

In [127]:

def cell_graph(cells,proteins,draw=False):
    '''vertices are cells, cells connected via a protein are connected in the graph with an edge'''
    g = Graph(directed=False)

    vertices = list(g.add_vertex(len(cells)))

    for c_id in range(len(cells)):
        for c_b in cells[c_id].bindings:
            try:
                for p_b in c_b.partner.parent.bindings:
                    try:
                        c2_id = p_b.partner.parent.id
                        if not c_id==c2_id:
                            g.add_edge(vertices[c_id],vertices[c2_id])
                    except AttributeError:
                        pass
            except AttributeError:
                pass
    if draw:
        graph_draw(g, vertex_text=g.vertex_index, edge_pen_width=2 , vertex_font_size=30, output="/tmp/graph.png",
            output_size=(2000, 2000))
    return g

In [128]:

def pc_graph(cells, proteins, draw=False):
    g = Graph(directed=False)

    v_size = g.new_vertex_property("int")

    for cell in cells:
        cell.vertex = g.add_vertex()
        v_size[cell.vertex] = 120

    for p in proteins:
        p.vertex=g.add_vertex()
        v_size[p.vertex] = 40
        for b in p.bindings:
            #cell connections
            if b.partner is not None:
                cell_vertex = b.partner.parent.vertex
                if g.edge(p.vertex,cell_vertex) is None: #only one connection per pair
                    g.add_edge(p.vertex,cell_vertex)
    if draw:
        pos=fruchterman_reingold_layout(g)
        graph_draw(g, edge_pen_width=2, vertex_text=g.vertex_index, vertex_size=v_size, vertex_font_size=15, output_size=(2000, 2000))
    return g

To make the difference more clear lets just run an experiment and visualize the result in both ways

In [133]:

cells, proteins = init_monomers(n_cells=30, n_proteins=200, n_cell_binding = 300, n_protein_binding = 4)
polymerize_spacial(cells, proteins, n_protein_binding=4, 
                   concentration=0.02, reactivity=0.1, mobility=0.05, max_time=3.0)

Out[133]:

(2, 8202)

The experiment is done. Now let's visualize it

In [141]:

cell_graph(cells,proteins,draw=True)

Out[141]:

<Graph object, undirected, with 30 vertices and 492 edges at 0x7f6ef3edaed0>

And now the same experimental result with the other visualization

In [142]:

pc_graph(cells,proteins,draw=True)

Out[142]:

<Graph object, undirected, with 230 vertices and 276 edges at 0x7f6ef30f4110>

The second graph shows not only how the interconnection between the idnividual cells is but also visualizes how many NP are "lost" by just sticking to a single cell without forming an connection to others. Furthermore one can see how many differnt proteins connect two cells.

More experiments¶

For a first feeling of how the parameters of the polymerization function influence the result it's helpful just to try out a few combinations and look at the visualization of the graph

To make this task a bit easier we defien a small helper function that initializes the monomers, polymerizes them and generates the graph.

In [144]:

def random_graph(graph_method, n_cells, n_proteins, n_cell_binding = 30, n_protein_binding = 4,concentration=0.02,reactivity=0.01,mobility=0.1,max_time=2.):
#    cells,proteins=init_monomers(n_cells, n_proteins, n_cell_binding, n_protein_binding)
#    polymerize(cells,proteins)
    cells,proteins=init_monomers(n_cells, n_proteins, n_cell_binding = n_cell_binding, n_protein_binding = n_protein_binding)
    polymerize_spacial(cells, proteins, n_protein_binding=n_protein_binding, concentration=concentration, reactivity=reactivity, mobility=mobility, max_time=max_time)
    return graph_method(cells,proteins,draw),cells,proteins

As long as we want to see a rendered result we just switch the draw variable to True

In [145]:

draw = True

Now we can build a random graph by plugging in some numbers and runnign a single line of code. (The "_=" just suppresses text output)

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@@ Line 51: / Line 51: @@
 .highlight .err { border: 1px solid #FF0000 } /* Error */
 .highlight .k { color: #008000; font-weight: bold } /* Keyword */
-.highlight .o { color: #666666 } /*  */
+.highlight .o { color: #666666 } /* Operator */
 .highlight .ch { color: #408080; font-style: italic } /* Comment.Hashbang */
 .highlight .cm { color: #408080; font-style: italic } /* Comment.Multiline */
@@ Line 88: / Line 88: @@
 .highlight .nt { color: #008000; font-weight: bold } /* Name.Tag */
 .highlight .nv { color: #19177C } /* Name.Variable */
-.highlight .ow { color: #AA22FF; font-weight: bold } /* .Word */
+.highlight .ow { color: #AA22FF; font-weight: bold } /* Operator.Word */
 .highlight .w { color: #bbbbbb } /* Text.Whitespace */
 .highlight .mb { color: #666666 } /* Literal.Number.Bin */
@@ Line 115: / Line 115: @@
 <style type="text/css">
-/* Overrides of  CSS for static HTML export */
+.input {font-size: 80%}
+.output {font-size: 80%}
+/* Overrides of notebook CSS for static HTML export */
 body {
    overflow: visible;
@@ Line 121: / Line 123: @@
 }
-div# {
+div#notebook {
    overflow: visible;
    border-top: none;
@@ Line 168: / Line 170: @@
      <!-- End of mathjax configuration --></head>
 <body>
-   <div tabindex="-1" id="" class="border-box-sizing">
+   <div tabindex="-1" id="notebook" class="border-box-sizing">
-     <div class="container-fluid" id="-container">
+     <div class="container" id="notebook-container">
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h2 id="Setup">Setup<a class="anchor-link" href="#Setup">&#182;</a></h2>
+</div>
+</div>
+</div>
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<p>So first we need to import some libraries</p>
+</div>
+</div>
+</div>
 <div class="cell border-box-sizing code_cell rendered">
 <div class="input">
@@ Line 185: / Line 206: @@
 </div>
+</div>
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<p>The following library is one that we wrote ourselves. It just contains the basic code that makes up our model of cells and proteins as monomers with binding sites</p>
+</div>
+</div>
 </div>
 <div class="cell border-box-sizing code_cell rendered">
 <div class="input">
-<div class="prompt input_prompt">In&nbsp;[2]:</div>
+<div class="prompt input_prompt">In&nbsp;[126]:</div>
 <div class="inner_cell">
      <div class="input_area">
@@ Line 198: / Line 229: @@
 </div>
+</div>
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<p>Now we define a couple of functions to set up an experiment.</p>
+</div>
+</div>
+</div>
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<h3 id="functions-to-initialize-an-experiment">functions to initialize an experiment<a class="anchor-link" href="#functions-to-initialize-an-experiment">&#182;</a></h3>
+</div>
+</div>
 </div>
 <div class="cell border-box-sizing code_cell rendered">
@@ Line 205: / Line 255: @@
      <div class="input_area">
 <div class=" highlight hl-ipython2"><pre><span></span><span class="k">def</span> <span class="nf">init_monomers</span><span class="p">(</span><span class="n">n_cells</span><span class="p">,</span> <span class="n">n_proteins</span><span class="p">,</span> <span class="n">n_cell_binding</span> <span class="o">=</span> <span class="mi">30</span><span class="p">,</span> <span class="n">n_protein_binding</span> <span class="o">=</span> <span class="mi">4</span><span class="p">):</span>
+    <span class="sd">&#39;&#39;&#39;instantiates a certain number of monomers&#39;&#39;&#39;</span>
      <span class="n">Cell</span><span class="o">.</span><span class="n">n_cells</span><span class="o">=</span><span class="mi">0</span>
      <span class="n">cells</span><span class="o">=</span><span class="p">[]</span>
@@ Line 210: / Line 261: @@
          <span class="n">cells</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">Cell</span><span class="p">(</span><span class="n">n_cell_binding</span><span class="p">))</span>
-     <span class="n"></span><span class="o">.</span><span class="n">n_proteins</span><span class="o">=</span><span class="mi">0</span>
+     <span class="n">Protein</span><span class="o">.</span><span class="n">n_proteins</span><span class="o">=</span><span class="mi">0</span>
-     <span class="n"></span><span class="o">=</span><span class="p">[]</span>
+     <span class="n">proteins</span><span class="o">=</span><span class="p">[]</span>
      <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_proteins</span><span class="p">):</span>
-         <span class="n"></span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n"></span><span class="p">(</span><span class="n">n_protein_binding</span><span class="p">))</span>
+         <span class="n">proteins</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">Protein</span><span class="p">(</span><span class="n">n_protein_binding</span><span class="p">))</span>
-     <span class="k">return</span> <span class="n">cells</span><span class="p">,</span> <span class="n"></span>
+     <span class="k">return</span> <span class="n">cells</span><span class="p">,</span> <span class="n">proteins</span>
 </pre></div>
@@ Line 221: / Line 272: @@
 </div>
+</div>
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<p>After we set our monomers in place we need to modell in some way how they interact with each other. The following "polymerize" function does so in a very basic fashion:</p>
+<ul>
+<li>make a list of free binding sites of TP as well as cells</li>
+<li>while there are still free binding sites of either kind choose two at random and let them bind together</li>
+</ul>
+</div>
+</div>
 </div>
 <div class="cell border-box-sizing code_cell rendered">
@@ Line 227: / Line 292: @@
 <div class="inner_cell">
      <div class="input_area">
-<div class=" highlight hl-ipython2"><pre><span></span><span class="k">def</span> <span class="nf">polymerize</span><span class="p">(</span><span class="n">cells</span><span class="p">,</span> <span class="n"></span><span class="p">):</span>
+<div class=" highlight hl-ipython2"><pre><span></span><span class="k">def</span> <span class="nf">polymerize</span><span class="p">(</span><span class="n">cells</span><span class="p">,</span> <span class="n">proteins</span><span class="p">):</span>
+    <span class="sd">&#39;&#39;&#39;polymerizes cells and proteins in a simple way&#39;&#39;&#39;</span>
      <span class="n">free_cell_bindings</span> <span class="o">=</span> <span class="p">[]</span>
      <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">cells</span><span class="p">:</span>
@@ Line 233: / Line 299: @@
      <span class="n">free_protein_bindings</span> <span class="o">=</span> <span class="p">[]</span>
-     <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n"></span><span class="p">:</span>
+     <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">proteins</span><span class="p">:</span>
          <span class="n">free_protein_bindings</span> <span class="o">+=</span> <span class="n">p</span><span class="o">.</span><span class="n">free_bindings</span>
@@ Line 241: / Line 307: @@
          <span class="n">c_binding_idx</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">free_cell_bindings</span><span class="p">))</span>
          <span class="n">c_binding</span> <span class="o">=</span> <span class="n">free_cell_bindings</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="n">c_binding_idx</span><span class="p">)</span>
-        <span class="c1">#print c_binding.parent.id, p_binding.parent.id</span>
          <span class="n">p_binding</span><span class="o">.</span><span class="n">bind</span><span class="p">(</span><span class="n">c_binding</span><span class="p">)</span>
      <span class="k">return</span> <span class="nb">len</span><span class="p">(</span><span class="n">free_protein_bindings</span><span class="p">)</span> <span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">free_cell_bindings</span><span class="p">)</span>
@@ Line 250: / Line 315: @@
 </div>
+</div>
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
+</div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<p>As described in the text above this simulation of polymerization was too simplified. The results we got from this modell were not very surprising and didn't help us much with optimizing our process.</p>
+<p>So next we implemented a more sophisticated way of simulating the polymerization process. The following function takes some basic spacial and temporal effects into account.</p>
+</div>
+</div>
 </div>
 <div class="cell border-box-sizing code_cell rendered">
@@ Line 256: / Line 332: @@
 <div class="inner_cell">
      <div class="input_area">
-<div class=" highlight hl-ipython2"><pre><span></span><span class="k">def</span> <span class="nf">polymerize_spacial</span><span class="p">(</span><span class="n">cells</span><span class="p">,</span> <span class="n"></span><span class="p">,</span> <span class="n">n_protein_binding</span><span class="p">,</span> <span class="n">concentration</span><span class="o">=</span><span class="mf">0.01</span><span class="p">,</span> <span class="n">reactivity</span><span class="o">=</span><span class="mf">0.2</span><span class="p">,</span> <span class="n">mobility</span><span class="o">=</span><span class="mf">0.05</span><span class="p">,</span> <span class="n">max_time</span><span class="o">=</span><span class="mf">10.</span><span class="p">):</span>
+<div class=" highlight hl-ipython2"><pre><span></span><span class="k">def</span> <span class="nf">polymerize_spacial</span><span class="p">(</span><span class="n">cells</span><span class="p">,</span> <span class="n">proteins</span><span class="p">,</span> <span class="n">n_protein_binding</span><span class="p">,</span> <span class="n">concentration</span><span class="o">=</span><span class="mf">0.01</span><span class="p">,</span> <span class="n">reactivity</span><span class="o">=</span><span class="mf">0.2</span><span class="p">,</span> <span class="n">mobility</span><span class="o">=</span><span class="mf">0.05</span><span class="p">,</span> <span class="n">max_time</span><span class="o">=</span><span class="mf">10.</span><span class="p">):</span>
+    <span class="sd">&#39;&#39;&#39;simulates polymerization in a more sophisticated way&#39;&#39;&#39;</span>
      <span class="n">time</span> <span class="o">=</span> <span class="mf">0.</span>
      <span class="n">position_variance</span> <span class="o">=</span> <span class="mf">1.</span>
@@ Line 263: / Line 340: @@
      <span class="n">free_protein_bindings</span> <span class="o">=</span> <span class="p">[]</span>
-     <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n"></span><span class="p">:</span>
+     <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">proteins</span><span class="p">:</span>
          <span class="n">free_protein_bindings</span> <span class="o">+=</span> <span class="n">p</span><span class="o">.</span><span class="n">free_bindings</span>
      <span class="k">while</span> <span class="p">(</span><span class="n">time</span> <span class="o">&lt;</span> <span class="n">max_time</span><span class="p">):</span>
+        <span class="c1"># at each timestep a certain fraction of the free binding sites will have a chance to react</span>
+        <span class="c1"># this fraction is depending on the defined &quot;reactivity&quot; parameter</span>
          <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">int</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">ceil</span><span class="p">(</span><span class="n">reactivity</span> <span class="o">*</span> <span class="nb">len</span><span class="p">(</span><span class="n">free_protein_bindings</span><span class="p">)))):</span>
-             <span class="c1"># choose a random PBS</span>
+             <span class="c1"># choose a random NPBS</span>
              <span class="n">p_binding_idx</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">free_protein_bindings</span><span class="p">))</span>
              <span class="n">p_binding</span> <span class="o">=</span> <span class="n">free_protein_bindings</span><span class="p">[</span><span class="n">p_binding_idx</span><span class="p">]</span>
-             <span class="c1"># do tests on parent </span>
+             <span class="c1"># do tests on parent protein</span>
              <span class="n">p</span> <span class="o">=</span> <span class="n">p_binding</span><span class="o">.</span><span class="n">parent</span>
-             <span class="c1"># position: the liwer to concentration, the higher the distance</span>
+             <span class="c1"># all monomers get assigned an individual increasing id at creation</span>
-             <span class="n">p_pos</span> <span class="o">=</span> <span class="nb">float</span><span class="p">(</span><span class="n">p</span><span class="o">.</span><span class="n">id</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n"></span><span class="p">)</span> <span class="o">*</span> <span class="n">concentration</span><span class="p">)</span>
+            <span class="c1"># we use this id to calculate a position by assuming</span>
+            <span class="c1"># that at creation the cells are put on a line with equal distance to echa other</span>
+            <span class="c1"># the lower to concentration, the higher the distance</span>
+             <span class="n">p_pos</span> <span class="o">=</span> <span class="nb">float</span><span class="p">(</span><span class="n">p</span><span class="o">.</span><span class="n">id</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">proteins</span><span class="p">)</span> <span class="o">*</span> <span class="n">concentration</span><span class="p">)</span>
              <span class="c1"># (float) idx of nearest cell</span>
              <span class="n">c_id_mean</span> <span class="o">=</span> <span class="n">p_pos</span> <span class="o">*</span> <span class="nb">len</span><span class="p">(</span><span class="n">cells</span><span class="p">)</span> <span class="o">*</span> <span class="n">concentration</span>
@@ Line 282: / Line 366: @@
              <span class="n">c_id_min</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="nb">int</span><span class="p">(</span><span class="n">c_id_mean</span> <span class="o">-</span> <span class="n">c_id_range</span><span class="p">),</span> <span class="mi">0</span><span class="p">)</span>
              <span class="n">c_id_max</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="nb">int</span><span class="p">(</span><span class="n">c_id_mean</span> <span class="o">+</span> <span class="n">c_id_range</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">cells</span><span class="p">))</span>
+            <span class="c1"># now we can calculate the cells in range</span>
              <span class="n">candidate_cells</span> <span class="o">=</span> <span class="n">cells</span><span class="p">[</span><span class="n">c_id_min</span><span class="p">:</span><span class="n">c_id_max</span><span class="p">]</span>
-            <span class="c1"># each has a probability according to the distance</span>
              <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">candidate_cells</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+                <span class="c1">#if there are no cells in reach we are done here and pic the next random NPBS to try again</span>
                  <span class="k">continue</span>
+            <span class="c1"># otherwise we go on</span>
+            <span class="c1"># now depending on the individual cells distance to the NP</span>
+            <span class="c1"># we calculate the probability of each candidate cell to bind as a gaussian pdf of the distance</span>
              <span class="n">min_distance</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">p_pos</span> <span class="o">-</span> <span class="n">position_variance</span> <span class="o">*</span> <span class="mf">3.2</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span> <span class="o">-</span> <span class="n">p_pos</span>
              <span class="n">max_distance</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="o">-</span><span class="n">p_pos</span> <span class="o">+</span> <span class="n">position_variance</span> <span class="o">*</span> <span class="mf">3.2</span><span class="p">,</span>
-                                <span class="nb">len</span><span class="p">(</span><span class="n"></span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span> <span class="o">/</span> <span class="nb">len</span><span class="p">(</span><span class="n"></span><span class="p">)</span> <span class="o">/</span> <span class="n">concentration</span><span class="p">)</span> <span class="o">+</span> <span class="n">p_pos</span>
+                                <span class="nb">len</span><span class="p">(</span><span class="n">proteins</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span> <span class="o">/</span> <span class="nb">len</span><span class="p">(</span><span class="n">proteins</span><span class="p">)</span> <span class="o">/</span> <span class="n">concentration</span><span class="p">)</span> <span class="o">+</span> <span class="n">p_pos</span>
              <span class="n">probabilities</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="n">min_distance</span><span class="p">,</span> <span class="n">max_distance</span><span class="p">,</span>
                                        <span class="p">(</span><span class="n">max_distance</span> <span class="o">-</span> <span class="n">min_distance</span><span class="p">)</span> <span class="o">/</span> <span class="nb">len</span><span class="p">(</span><span class="n">candidate_cells</span><span class="p">))[:</span><span class="nb">len</span><span class="p">(</span><span class="n">candidate_cells</span><span class="p">)]</span>
              <span class="n">probabilities</span> <span class="o">=</span> <span class="n">distance_binding_probability</span><span class="p">(</span><span class="n">probabilities</span><span class="p">)</span>
-             <span class="n">probabilities</span> <span class="o">/=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">probabilities</span><span class="p">)</span>
+             <span class="n">probabilities</span> <span class="o">/=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">probabilities</span><span class="p">)</span> <span class="c1">#normalization</span>
-             <span class="c1"># pick one</span>
+             <span class="c1"># this call picks a random cell based on the calculated probabilities</span>
              <span class="n">cell</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">choice</span><span class="p">(</span><span class="n">candidate_cells</span><span class="p">,</span> <span class="n">p</span><span class="o">=</span><span class="n">probabilities</span><span class="p">)</span>
+            <span class="c1"># check if the chosen cell has actually still free binding sites</span>
              <span class="k">try</span><span class="p">:</span>
                  <span class="n">cell</span><span class="o">.</span><span class="n">free_bindings</span><span class="o">.</span><span class="n">next</span><span class="p">()</span>
              <span class="k">except</span> <span class="ne">StopIteration</span><span class="p">:</span>
-                 <span class="c1"># no free bindings left in this cell</span>
+                 <span class="c1"># no free bindings left in this cell. back to the top.</span>
                  <span class="k">continue</span>
-             <span class="c1"># let react with probability respective to free bindings</span>
+             <span class="c1"># now we find out which cells the TP in question is already bound to</span>
              <span class="n">protein_partners</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="nb">set</span><span class="p">([</span><span class="n">b</span><span class="o">.</span><span class="n">partner</span><span class="o">.</span><span class="n">parent</span> <span class="k">for</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">p</span><span class="o">.</span><span class="n">bindings</span> <span class="k">if</span> <span class="n">b</span><span class="o">.</span><span class="n">partner</span> <span class="ow">is</span> <span class="ow">not</span> <span class="bp">None</span><span class="p">]))</span>
+            <span class="c1">#this way we know how many different cells it&#39;s bound to</span>
              <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">protein_partners</span><span class="p">)</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
-                 <span class="c1"># if a  is already attatched to a cell it will most likely not bind to other cells</span>
+                 <span class="c1"># if a protein is already attatched to a cell it will most likely not bind to other cells</span>
+                <span class="c1"># but there is a chance of 10%</span>
                  <span class="k">if</span> <span class="n">cell</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">protein_partners</span> <span class="ow">and</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">()</span><span class="o">&lt;</span><span class="mf">0.9</span><span class="p">:</span>
                      <span class="k">continue</span>
              <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">protein_partners</span><span class="p">)</span><span class="o">&gt;</span><span class="mi">1</span> <span class="ow">and</span> <span class="n">cell</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">protein_partners</span><span class="p">:</span>
-                 <span class="c1"># if a  was binding to two cells already, it will not bind to any other</span>
+                 <span class="c1"># if a protein was binding to two cells already, it will not bind to any other</span>
                  <span class="k">continue</span>
-<span class="c1">#            if np.random.rand() &lt; float(4 - len(list(p.free_bindings))) / 3.:</span>
+            <span class="c1"># if we made it this far without running into any of the &quot;continue&quot;s we are ready to bind!</span>
-<span class="c1">#                # can only bind to cells it&#39;s already bound to</span>
+            <span class="c1"># so the next free binding of the cell will react to our NPBS</span>
-<span class="c1">#                if cell not in [b.partner.parent for b in p.bindings if b.partner is not None]:</span>
-<span class="c1">#                    continue</span>
              <span class="n">cell</span><span class="o">.</span><span class="n">free_bindings</span><span class="o">.</span><span class="n">next</span><span class="p">()</span><span class="o">.</span><span class="n">bind</span><span class="p">(</span><span class="n">p_binding</span><span class="p">)</span>
+            <span class="c1"># and the TPBS is removed from our binding sites dating database</span>
              <span class="n">free_protein_bindings</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="n">p_binding_idx</span><span class="p">)</span>
+        <span class="c1"># after all reactive NPBS tired to react we move everything a bit</span>
+        <span class="c1"># depending on the mobility parameter and increment the time</span>
          <span class="n">position_variance</span> <span class="o">+=</span> <span class="n">mobility</span>
          <span class="n">time</span> <span class="o">+=</span> <span class="mf">0.01</span>
+    <span class="c1"># in the end we calculate the number of free CBS. Just to know about it.</span>
      <span class="n">free_cell_bindings</span> <span class="o">=</span> <span class="p">[]</span>
      <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">cells</span><span class="p">:</span>
@@ Line 330: / Line 427: @@
 </div>
-<div class="cell border-box-sizing code_cell rendered">
+<div class="cell border-box-sizing text_cell rendered">
-<div class="input">
+<div class="prompt input_prompt">
-<div class="prompt input_prompt">In&nbsp;[89]:</div>
+</div>
 <div class="inner_cell">
-    <div class="input_area">
+<div class="text_cell_render border-box-sizing rendered_html">
-<div class=" highlight hl-ipython2"><pre><span></span><span class="n">draw</span> <span class="o">=</span> <span class="bp">True</span>
+<h2 id="Analysis">Analysis<a class="anchor-link" href="#Analysis">&#182;</a></h2>
-</pre></div>
 </div>
 </div>
 </div>
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
 </div>
-<div class="cell border-box-sizing code_cell rendered">
-<div class="input">
-<div class="prompt input_prompt">In&nbsp;[&nbsp;]:</div>
 <div class="inner_cell">
-    <div class="input_area">
+<div class="text_cell_render border-box-sizing rendered_html">
-<div class=" highlight hl-ipython2"><pre><span></span><span class="n">_</span><span class="p">,</span><span class="n">_</span><span class="p">,</span><span class="n">_</span><span class="o">=</span><span class="n">random_graph</span><span class="p">(</span><span class="n">cell_graph</span><span class="p">,</span> <span class="mi">30</span><span class="p">,</span> <span class="mi">120</span><span class="p">,</span> <span class="n">n_cell_binding</span><span class="o">=</span><span class="mi">400</span><span class="p">,</span> <span class="n">n_protein_binding</span><span class="o">=</span><span class="mi">4</span><span class="p">,</span> <span class="n">concentration</span><span class="o">=</span><span class="mf">0.02</span><span class="p">,</span> <span class="n">reactivity</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span> <span class="n">mobility</span><span class="o">=</span><span class="mf">0.05</span><span class="p">,</span> <span class="n">max_time</span><span class="o">=</span><span class="mf">5.0</span><span class="p">)</span>
+<p>Now for analyzing the generated polymer networks we import another library called graph_tool.</p>
-</pre></div>
 </div>
 </div>
-</div>
 </div>
 <div class="cell border-box-sizing code_cell rendered">
 <div class="input">
-<div class="prompt input_prompt">In&nbsp;[&nbsp;]:</div>
+<div class="prompt input_prompt">In&nbsp;[11]:</div>
 <div class="inner_cell">
      <div class="input_area">
-<div class=" highlight hl-ipython2"><pre><span></span>
+<div class=" highlight hl-ipython2"><pre><span></span><span class="kn">from</span> <span class="nn">graph_tool.all</span> <span class="kn">import</span> <span class="o">*</span>
+<span class="kn">from</span> <span class="nn">graph_tool</span> <span class="kn">import</span> <span class="n">clustering</span><span class="p">,</span><span class="n">stats</span>
 </pre></div>
@@ Line 374: / Line 466: @@
 <div class="inner_cell">
 <div class="text_cell_render border-box-sizing rendered_html">
-<h2 id="Analysis">Analysis<a class="anchor-link" href="#Analysis">&#182;</a></h2>
+<p>The following two functions translate the network (or graph) that we build before into graph_tool-graphs. The first one draws a node for each cell. Then it draws a connecting edge betwee two nodes if the respective cells are connected via any NP.</p>
-</div>
+<p>The second one draws a big node for each cell and a small one for each NP. Edges represent a binding between a NP and a connected cell.</p>
-</div>
+<p>We will clarify the difference between the two graphing methods graphically after the two function definitions.</p>
-</div>
-<div class="cell border-box-sizing code_cell rendered">
-<div class="input">
-<div class="prompt input_prompt">In&nbsp;[&nbsp;]:</div>
-<div class="inner_cell">
-    <div class="input_area">
-<div class=" highlight hl-ipython2"><pre><span></span><span class="n">draw</span> <span class="o">=</span> <span class="bp">False</span>
-</pre></div>
 </div>
 </div>
-</div>
 </div>
 <div class="cell border-box-sizing code_cell rendered">
 <div class="input">
-<div class="prompt input_prompt">In&nbsp;[11]:</div>
+<div class="prompt input_prompt">In&nbsp;[127]:</div>
-<div class="inner_cell">
-    <div class="input_area">
-<div class=" highlight hl-ipython2"><pre><span></span><span class="kn">from</span> <span class="nn">graph_tool.all</span> <span class="kn">import</span> <span class="o">*</span>
-<span class="kn">from</span> <span class="nn">graph_tool</span> <span class="kn">import</span> <span class="n">clustering</span><span class="p">,</span><span class="n">stats</span>
-</pre></div>
-</div>
-</div>
-</div>
-</div>
-<div class="cell border-box-sizing code_cell rendered">
-<div class="input">
-<div class="prompt input_prompt">In&nbsp;[16]:</div>
 <div class="inner_cell">
      <div class="input_area">
-<div class=" highlight hl-ipython2"><pre><span></span><span class="k">def</span> <span class="nf">cell_graph</span><span class="p">(</span><span class="n">cells</span><span class="p">,</span><span class="n"></span><span class="p">,</span><span class="n">draw</span><span class="o">=</span><span class="bp">False</span><span class="p">):</span>
+<div class=" highlight hl-ipython2"><pre><span></span><span class="k">def</span> <span class="nf">cell_graph</span><span class="p">(</span><span class="n">cells</span><span class="p">,</span><span class="n">proteins</span><span class="p">,</span><span class="n">draw</span><span class="o">=</span><span class="bp">False</span><span class="p">):</span>
-     <span class="sd">&#39;&#39;&#39;vertices are cells, cells connected via a  are connected in the graph with an edge&#39;&#39;&#39;</span>
+     <span class="sd">&#39;&#39;&#39;vertices are cells, cells connected via a protein are connected in the graph with an edge&#39;&#39;&#39;</span>
      <span class="n">g</span> <span class="o">=</span> <span class="n">Graph</span><span class="p">(</span><span class="n">directed</span><span class="o">=</span><span class="bp">False</span><span class="p">)</span>
@@ Line 433: / Line 500: @@
              <span class="n">output_size</span><span class="o">=</span><span class="p">(</span><span class="mi">2000</span><span class="p">,</span> <span class="mi">2000</span><span class="p">))</span>
      <span class="k">return</span> <span class="n">g</span>
-<span class="c1">#graph_draw(g, vertex_text=g.vertex_index, vertex_font_size=18, output=&quot;/tmp/graph.png&quot;,</span>
-<span class="c1">#            output_size=(2000, 2000))</span>
 </pre></div>
@@ Line 445: / Line 509: @@
 <div class="cell border-box-sizing code_cell rendered">
 <div class="input">
-<div class="prompt input_prompt">In&nbsp;[29]:</div>
+<div class="prompt input_prompt">In&nbsp;[128]:</div>
 <div class="inner_cell">
      <div class="input_area">
-<div class=" highlight hl-ipython2"><pre><span></span><span class="k">def</span> <span class="nf">random_graph</span><span class="p">(</span><span class="n">graph_method</span><span class="p">,</span> <span class="n">n_cells</span><span class="p">,</span> <span class="n">n_proteins</span><span class="p">,</span> <span class="n">n_cell_binding</span> <span class="o">=</span> <span class="mi">30</span><span class="p">,</span> <span class="n">n_protein_binding</span> <span class="o">=</span> <span class="mi">4</span><span class="p">,</span><span class="n">concentration</span><span class="o">=</span><span class="mf">0.02</span><span class="p">,</span><span class="n">reactivity</span><span class="o">=</span><span class="mf">0.01</span><span class="p">,</span><span class="n">mobility</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span><span class="n">max_time</span><span class="o">=</span><span class="mf">2.</span><span class="p">):</span>
+<div class=" highlight hl-ipython2"><pre><span></span><span class="k">def</span> <span class="nf">pc_graph</span><span class="p">(</span><span class="n">cells</span><span class="p">,</span> <span class="n">proteins</span><span class="p">,</span> <span class="n">draw</span><span class="o">=</span><span class="bp">False</span><span class="p">):</span>
-<span class="c1">#    cells,=init_monomers(n_cells, n_proteins, n_cell_binding, n_protein_binding)</span>
+     <span class="n">g</span> <span class="o">=</span> <span class="n">Graph</span><span class="p">(</span><span class="n">directed</span><span class="o">=</span><span class="bp">False</span><span class="p">)</span>
-<span class="c1">#    polymerize(cells,)</span>
-     <span class="n">cells</span><span class="p">,</span><span class="n"></span><span class="o">=</span><span class="n">init_monomers</span><span class="p">(</span><span class="n">n_cells</span><span class="p">,</span> <span class="n">n_proteins</span><span class="p">,</span> <span class="n">n_cell_binding</span> <span class="o">=</span> <span class="mi">30</span><span class="p">,</span> <span class="n">n_protein_binding</span> <span class="o">=</span> <span class="mi">4</span><span class="p">)</span>
-    <span class="n">polymerize_spacial</span><span class="p">(</span><span class="n">cells</span><span class="p">,</span> <span class="n"></span><span class="p">,</span> <span class="n">n_protein_binding</span><span class="o">=</span><span class="n">n_protein_binding</span><span class="p">,</span> <span class="n">concentration</span><span class="o">=</span><span class="n">concentration</span><span class="p">,</span> <span class="n">reactivity</span><span class="o">=</span><span class="n">reactivity</span><span class="p">,</span> <span class="n">mobility</span><span class="o">=</span><span class="n">mobility</span><span class="p">,</span> <span class="n">max_time</span><span class="o">=</span><span class="n">max_time</span><span class="p">)</span>
-    <span class="k">return</span> <span class="n">graph_method</span><span class="p">(</span><span class="n">cells</span><span class="p">,</span><span class="n"></span><span class="p">,</span><span class="n">draw</span><span class="p">),</span><span class="n">cells</span><span class="p">,</span><span class="n"></span>
-</pre></div>
-</div>
+    <span class="n">v_size</span> <span class="o">=</span> <span class="n">g</span><span class="o">.</span><span class="n">new_vertex_property</span><span class="p">(</span><span class="s2">&quot;int&quot;</span><span class="p">)</span>
-</div>
-</div>
-</div>
+     <span class="k">for</span> <span class="n">cell</span> <span class="ow">in</span> <span class="n">cells</span><span class="p">:</span>
-<div class="cell border-box-sizing code_cell rendered">
+        <span class="n">cell</span><span class="o">.</span><span class="n">vertex</span> <span class="o">=</span> <span class="n">g</span><span class="o">.</span><span class="n">add_vertex</span><span class="p">()</span>
-<div class="input">
+        <span class="n">v_size</span><span class="p">[</span><span class="n">cell</span><span class="o">.</span><span class="n">vertex</span><span class="p">]</span> <span class="o">=</span> <span class="mi">120</span>
-<div class="prompt input_prompt">In&nbsp;[83]:</div>
-<div class="inner_cell">
-     <div class="input_area">
-<div class=" highlight hl-ipython2"><pre><span></span><span class="n">results</span><span class="o">=</span><span class="p">[]</span>
-<span class="n">draw</span><span class="o">=</span><span class="bp">False</span>
-<span class="k">for</span> <span class="n">n_proteins</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="o">-</span><span class="mf">1.5</span><span class="p">,</span><span class="mf">1.5</span><span class="p">,</span><span class="mf">0.1</span><span class="p">):</span>
-    <span class="n">n_proteins</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">cells</span><span class="p">)</span><span class="o">*</span><span class="mi">10</span><span class="o">**</span><span class="n">n_proteins</span><span class="p">)</span>
-    <span class="n">g</span><span class="p">,</span><span class="n">cells</span><span class="p">,</span><span class="n"></span> <span class="o">=</span> <span class="n">random_graph</span><span class="p">(</span><span class="n">cell_graph</span><span class="p">,</span> <span class="mi">30</span><span class="p">,</span> <span class="n">n_proteins</span><span class="p">,</span> <span class="n">n_cell_binding</span><span class="o">=</span><span class="mi">400</span><span class="p">,</span> <span class="n">n_protein_binding</span><span class="o">=</span><span class="mi">4</span><span class="p">,</span> <span class="n">concentration</span><span class="o">=</span><span class="mf">0.02</span><span class="p">,</span> <span class="n">reactivity</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span> <span class="n">mobility</span><span class="o">=</span><span class="mf">0.05</span><span class="p">,</span> <span class="n">max_time</span><span class="o">=</span><span class="mf">5.0</span><span class="p">)</span>
-    <span class="n">global_clustering</span> <span class="o">=</span> <span class="n">clustering</span><span class="o">.</span><span class="n">global_clustering</span><span class="p">(</span><span class="n">g</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
-    <span class="n">tmp</span><span class="o">=</span><span class="n">graph_tool</span><span class="o">.</span><span class="n">topology</span><span class="o">.</span><span class="n">max_cardinality_matching</span><span class="p">(</span><span class="n">g</span><span class="p">)</span>
-    <span class="n">n_max_matching</span> <span class="o">=</span> <span class="n">tmp</span><span class="o">.</span><span class="n">count</span><span class="p">(</span><span class="n">tmp</span><span class="p">)</span>
-    <span class="n">max_shortest_path</span> <span class="o">=</span> <span class="n">graph_tool</span><span class="o">.</span><span class="n">topology</span><span class="o">.</span><span class="n">pseudo_diameter</span><span class="p">(</span><span class="n">g</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
-    <span class="n">tmp</span><span class="o">=</span><span class="n">graph_tool</span><span class="o">.</span><span class="n">topology</span><span class="o">.</span><span class="n">label_largest_component</span><span class="p">(</span><span class="n">g</span><span class="p">)</span>
-    <span class="n">biggest_cluster</span> <span class="o">=</span> <span class="n">tmp</span><span class="o">.</span><span class="n">get_array</span><span class="p">()</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
-    <span class="n">tmp</span> <span class="o">=</span> <span class="n">graph_tool</span><span class="o">.</span><span class="n">topology</span><span class="o">.</span><span class="n">label_components</span><span class="p">(</span><span class="n">g</span><span class="p">)[</span><span class="mi">1</span><span class="p">]</span>
-    <span class="n">tmp</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sort</span><span class="p">(</span><span class="n">tmp</span><span class="p">)[::</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
-    <span class="n">n_clusters</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">tmp</span><span class="p">)</span>
-    <span class="n">biggest_cluster</span> <span class="o">=</span> <span class="n">tmp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
-    <span class="n">mean_cluster</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">tmp</span><span class="p">)</span>
-    <span class="n">n_free_protein_bindings</span> <span class="o">=</span> <span class="mi">0</span>
-    <span class="n">n_free_proteins</span> <span class="o">=</span> <span class="mi">0</span>
-    <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n"></span><span class="p">:</span>
-        <span class="n">p_free</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">p</span><span class="o">.</span><span class="n">free_bindings</span><span class="p">))</span>
-        <span class="n">n_free_protein_bindings</span> <span class="o">+=</span> <span class="n">p_free</span>
-        <span class="k">if</span> <span class="n">p_free</span> <span class="o">==</span> <span class="nb">len</span><span class="p">(</span><span class="n">p</span><span class="o">.</span><span class="n">bindings</span><span class="p">):</span>
-            <span class="n">n_free_proteins</span> <span class="o">+=</span> <span class="mi">1</span>
-    <span class="n">n_free_cell_bindings</span> <span class="o">=</span> <span class="mi">0</span>
-    <span class="n">n_free_cells</span> <span class="o">=</span> <span class="mi">0</span>
-    <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">cells</span><span class="p">:</span>
-        <span class="n">c_free</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">c</span><span class="o">.</span><span class="n">free_bindings</span><span class="p">))</span>
-        <span class="n">n_free_cell_bindings</span> <span class="o">+=</span> <span class="n">c_free</span>
-        <span class="k">if</span> <span class="n">c_free</span> <span class="o">==</span> <span class="nb">len</span><span class="p">(</span><span class="n">c</span><span class="o">.</span><span class="n">bindings</span><span class="p">):</span>
-            <span class="n">n_free_cells</span> <span class="o">+=</span> <span class="mi">1</span>
-    <span class="k">print</span> <span class="n">n_proteins</span><span class="p">,</span> <span class="n">n_free_cells</span><span class="p">,</span> <span class="n">n_free_cell_bindings</span><span class="p">,</span> <span class="n">n_free_proteins</span><span class="p">,</span> <span class="n">n_free_protein_bindings</span><span class="p">,</span> <span class="n">n_clusters</span><span class="p">,</span> <span class="n">mean_cluster</span><span class="p">,</span> <span class="n">biggest_cluster</span><span class="p">,</span> <span class="n">global_clustering</span><span class="p">,</span> <span class="n">max_shortest_path</span><span class="c1">#, n_max_matching, biggest_cluster</span>
-    <span class="n">results</span><span class="o">.</span><span class="n">append</span><span class="p">([</span><span class="n">n_proteins</span><span class="p">,</span> <span class="n">n_free_cells</span><span class="p">,</span> <span class="n">n_free_cell_bindings</span><span class="p">,</span> <span class="n">n_free_proteins</span><span class="p">,</span> <span class="n">n_free_protein_bindings</span><span class="p">,</span> <span class="n">n_clusters</span><span class="p">,</span> <span class="n">mean_cluster</span><span class="p">,</span> <span class="n">biggest_cluster</span><span class="p">,</span> <span class="n">global_clustering</span><span class="p">,</span> <span class="n">max_shortest_path</span><span class="p">])</span>
-</pre></div>
-</div>
+    <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">proteins</span><span class="p">:</span>
-</div>
+        <span class="n">p</span><span class="o">.</span><span class="n">vertex</span><span class="o">=</span><span class="n">g</span><span class="o">.</span><span class="n">add_vertex</span><span class="p">()</span>
-</div>
+        <span class="n">v_size</span><span class="p">[</span><span class="n">p</span><span class="o">.</span><span class="n">vertex</span><span class="p">]</span> <span class="o">=</span> <span class="mi">40</span>
+        <span class="k">for</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">p</span><span class="o">.</span><span class="n">bindings</span><span class="p">:</span>
-<div class="output_wrapper">
+            <span class="c1">#cell connections</span>
-<div class="output">
+            <span class="k">if</span> <span class="n">b</span><span class="o">.</span><span class="n">partner</span> <span class="ow">is</span> <span class="ow">not</span> <span class="bp">None</span><span class="p">:</span>
+                <span class="n">cell_vertex</span> <span class="o">=</span> <span class="n">b</span><span class="o">.</span><span class="n">partner</span><span class="o">.</span><span class="n">parent</span><span class="o">.</span><span class="n">vertex</span>
+                <span class="k">if</span> <span class="n">g</span><span class="o">.</span><span class="n">edge</span><span class="p">(</span><span class="n">p</span><span class="o">.</span><span class="n">vertex</span><span class="p">,</span><span class="n">cell_vertex</span><span class="p">)</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span> <span class="c1">#only one connection per pair</span>
-<div class="output_area"><div class="prompt"></div>
+                    <span class="n">g</span><span class="o">.</span><span class="n">add_edge</span><span class="p">(</span><span class="n">p</span><span class="o">.</span><span class="n">vertex</span><span class="p">,</span><span class="n">cell_vertex</span><span class="p">)</span>
-<div class="output_subarea output_stream output_stdout output_text">
+    <span class="k">if</span> <span class="n">draw</span><span class="p">:</span>
-<pre>0 30 900 0 0 30 1.0 1 nan 0
+        <span class="n">pos</span><span class="o">=</span><span class="n">fruchterman_reingold_layout</span><span class="p">(</span><span class="n">g</span><span class="p">)</span>
-29 896 0 0 30 1.0 1 nan 0
+        <span class="n">graph_draw</span><span class="p">(</span><span class="n">g</span><span class="p">,</span> <span class="n">edge_pen_width</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">vertex_text</span><span class="o">=</span><span class="n">g</span><span class="o">.</span><span class="n">vertex_index</span><span class="p">,</span> <span class="n">vertex_size</span><span class="o">=</span><span class="n">v_size</span><span class="p">,</span> <span class="n">vertex_font_size</span><span class="o">=</span><span class="mi">15</span><span class="p">,</span> <span class="n">output_size</span><span class="o">=</span><span class="p">(</span><span class="mi">2000</span><span class="p">,</span> <span class="mi">2000</span><span class="p">))</span>
-29 896 0 0 30 1.0 1 nan 0
+    <span class="k">return</span> <span class="n">g</span>
-29 896 0 0 30 1.0 1 nan 0
-27 892 0 0 29 1.03448275862 2 0.0 1.0
-27 888 0 0 30 1.0 1 nan 0
-27 888 0 0 30 1.0 1 nan 0
-25 884 0 0 29 1.03448275862 2 0.0 0
-23 880 0 0 28 1.07142857143 2 0.0 0
-21 872 0 0 28 1.07142857143 2 0.0 0
-17 864 0 0 26 1.15384615385 2 0.0 0
-18 856 0 0 29 1.03448275862 2 0.0 0
-11 840 0 0 24 1.25 2 0.0 0
-7 828 0 0 22 1.36363636364 3 0.0 0
-7 808 0 0 25 1.2 3 0.0 0
-7 780 0 0 21 1.42857142857 4 0.0 3.0
-4 752 0 0 23 1.30434782609 3 0.0 1.0
-0 712 0 0 14 2.14285714286 6 0.0 0
-1 664 0 0 13 2.30769230769 5 0.0 0
-0 600 0 0 12 2.5 10 0.0 3.0
-0 524 0 0 9 3.33333333333 8 0.164890633763 1.0
-0 424 0 0 7 4.28571428571 9 0.165856155618 1.0
-0 304 0 4 2 15.0 17 0.229697260932 8.0
-0 150 0 6 2 15.0 28 0.238134206219 1.0
-0 24 0 76 1 30.0 30 0.273657289003 15.0
-0 22 1 322 4 7.5 14 0.215702479339 8.0
-0 11 4 619 6 5.0 16 0.0472049689441 3.0
-0 0 17 1000 11 2.72727272727 7 0.0336605890603 1.0
-0 9 61 1501 16 1.875 4 0.0 2.0
-0 0 152 2112 22 1.36363636364 3 0.0 0
-</pre>
-</div>
-</div>
-</div>
-</div>
-</div>
-<div class="cell border-box-sizing code_cell rendered">
-<div class="input">
-<div class="prompt input_prompt">In&nbsp;[84]:</div>
-<div class="inner_cell">
-    <div class="input_area">
-<div class=" highlight hl-ipython2"><pre><span></span><span class="n">tmp_res</span><span class="o">=</span><span class="n">results</span>
 </pre></div>
@@ Line 572: / Line 541: @@
 </div>
-<div class="cell border-box-sizing code_cell rendered">
+<div class="cell border-box-sizing text_cell rendered">
-<div class="input">
+<div class="prompt input_prompt">
-<div class="prompt input_prompt">In&nbsp;[85]:</div>
-<div class="inner_cell">
-    <div class="input_area">
-<div class=" highlight hl-ipython2"><pre><span></span><span class="n">results</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">results</span><span class="p">)</span><span class="o">.</span><span class="n">T</span>
-<span class="n">n_proteins</span><span class="o">=</span><span class="n">results</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
-</pre></div>
 </div>
-</div>
-</div>
-</div>
-<div class="cell border-box-sizing code_cell rendered">
-<div class="input">
-<div class="prompt input_prompt">In&nbsp;[86]:</div>
 <div class="inner_cell">
-    <div class="input_area">
+<div class="text_cell_render border-box-sizing rendered_html">
-<div class=" highlight hl-ipython2"><pre><span></span><span class="n">results</span><span class="o">=</span><span class="n">results</span><span class="p">[</span><span class="mi">1</span><span class="p">:]</span>
+<p>To make the difference more clear lets just run an experiment and visualize the result in both ways</p>
-</pre></div>
 </div>
 </div>
-</div>
 </div>
 <div class="cell border-box-sizing code_cell rendered">
 <div class="input">
-<div class="prompt input_prompt">In&nbsp;[&nbsp;]:</div>
+<div class="prompt input_prompt">In&nbsp;[133]:</div>
 <div class="inner_cell">
      <div class="input_area">
-<div class=" highlight hl-ipython2"><pre><span></span><span class="n">titles</span><span class="o">=</span><span class="p">[</span><span class="s2">&quot;n_free_cells&quot;</span><span class="p">,</span> <span class="s2">&quot;n_free_cell_bindings&quot;</span><span class="p">,</span> <span class="s2">&quot;n_free_proteins&quot;</span><span class="p">,</span> <span class="s2">&quot;n_free_protein_bindings&quot;</span><span class="p">,</span> <span class="s2">&quot;n_clusters&quot;</span><span class="p">,</span> <span class="s2">&quot;mean_cluster&quot;</span><span class="p">,</span> <span class="s2">&quot;biggest_cluster&quot;</span><span class="p">,</span> <span class="s2">&quot;global_clustering&quot;</span><span class="p">,</span> <span class="s2">&quot;max_shortest_path&quot;</span><span class="p">]</span>
+<div class=" highlight hl-ipython2"><pre><span></span><span class="n">cells</span><span class="p">,</span> <span class="n">proteins</span> <span class="o">=</span> <span class="n">init_monomers</span><span class="p">(</span><span class="n">n_cells</span><span class="o">=</span><span class="mi">30</span><span class="p">,</span> <span class="n">n_proteins</span><span class="o">=</span><span class="mi">200</span><span class="p">,</span> <span class="n">n_cell_binding</span> <span class="o">=</span> <span class="mi">300</span><span class="p">,</span> <span class="n">n_protein_binding</span> <span class="o">=</span> <span class="mi">4</span><span class="p">)</span>
-<span class="n">f</span><span class="p">,</span> <span class="n">axes</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">titles</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="o">+</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span> <span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">16</span><span class="p">,</span><span class="mi">8</span><span class="o">*</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">titles</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="o">+</span><span class="mi">1</span><span class="p">)))</span>
+<span class="n">polymerize_spacial</span><span class="p">(</span><span class="n">cells</span><span class="p">,</span> <span class="n">proteins</span><span class="p">,</span> <span class="n">n_protein_binding</span><span class="o">=</span><span class="mi">4</span><span class="p">,</span>
-<span class="k">for</span> <span class="n">i</span><span class="p">,</span><span class="n">result</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">results</span><span class="p">):</span>
+                   <span class="n">concentration</span><span class="o">=</span><span class="mf">0.02</span><span class="p">,</span> <span class="n">reactivity</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span> <span class="n">mobility</span><span class="o">=</span><span class="mf">0.05</span><span class="p">,</span> <span class="n">max_time</span><span class="o">=</span><span class="mf">3.0</span><span class="p">)</span>
-    <span class="n">ax</span> <span class="o">=</span> <span class="n">axes</span><span class="p">[</span><span class="n">i</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span><span class="n">i</span><span class="o">%</span><span class="k">2</span>]
-    <span class="n">ax</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="n">titles</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
-    <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">n_proteins</span><span class="p">,</span><span class="n">result</span><span class="o">.</span><span class="n">T</span><span class="p">,</span><span class="s2">&quot;-x&quot;</span><span class="p">)</span>
-    <span class="n">ax</span><span class="o">.</span><span class="n">set_xscale</span><span class="p">(</span><span class="s2">&quot;log&quot;</span><span class="p">)</span>
-</pre></div>
-</div>
-</div>
-</div>
-</div>
-<div class="cell border-box-sizing code_cell rendered">
-<div class="input">
-<div class="prompt input_prompt">In&nbsp;[26]:</div>
-<div class="inner_cell">
-    <div class="input_area">
-<div class=" highlight hl-ipython2"><pre><span></span><span class="n">clustering</span><span class="o">.</span><span class="n">global_clustering</span><span class="p">(</span><span class="n">g</span><span class="p">)</span>
 </pre></div>
@@ Line 634: / Line 569: @@
-<div class="output_area"><div class="prompt output_prompt">Out[26]:</div>
+<div class="output_area"><div class="prompt output_prompt">Out[133]:</div>
 <div class="output_text output_subarea output_execute_result">
-<pre>(0.4555753617923612, 0.0034127709652872246)</pre>
+<pre>(2, 8202)</pre>
 </div>
@@ Line 647: / Line 582: @@
 </div>
-<div class="cell border-box-sizing code_cell rendered">
+<div class="cell border-box-sizing text_cell rendered">
-<div class="input">
+<div class="prompt input_prompt">
-<div class="prompt input_prompt">In&nbsp;[37]:</div>
+</div>
 <div class="inner_cell">
-    <div class="input_area">
+<div class="text_cell_render border-box-sizing rendered_html">
-<div class=" highlight hl-ipython2"><pre><span></span><span class="n">stats</span><span class="o">.</span><span class="n">distance_histogram</span><span class="p">(</span><span class="n">g</span><span class="p">)</span>
+<p>The experiment is done. Now let's visualize it</p>
-</pre></div>
 </div>
 </div>
-</div>
-<div class="output_wrapper">
-<div class="output">
-<div class="output_area"><div class="prompt output_prompt">Out[37]:</div>
-<div class="output_text output_subarea output_execute_result">
-<pre>[array([    0.,  4534.,  5366.]), array([0, 1, 2, 3], dtype=uint64)]</pre>
-</div>
-</div>
-</div>
-</div>
 </div>
 <div class="cell border-box-sizing code_cell rendered">
 <div class="input">
-<div class="prompt input_prompt">In&nbsp;[46]:</div>
+<div class="prompt input_prompt">In&nbsp;[141]:</div>
 <div class="inner_cell">
      <div class="input_area">
-<div class=" highlight hl-ipython2"><pre><span></span><span class="n">tmp</span><span class="o">=</span><span class="n">graph_tool</span><span class="o">.</span><span class="n">topology</span><span class="o">.</span><span class="n">max_cardinality_matching</span><span class="p">(</span><span class="n">g</span><span class="p">)</span>
+<div class=" highlight hl-ipython2"><pre><span></span><span class="n">cell_graph</span><span class="p">(</span><span class="n">cells</span><span class="p">,</span><span class="n">proteins</span><span class="p">,</span><span class="n">draw</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
-<span class="n">tmp</span><span class="o">.</span><span class="n">count</span><span class="p">(</span><span class="n">tmp</span><span class="p">)</span>
 </pre></div>
@@ Line 693: / Line 608: @@
-<div class="output_area"><div class="prompt output_prompt">Out[46]:</div>
+<div class="output_area"><div class="prompt"></div>
-<div class="output_text output_subarea output_execute_result">
+<div class="output_png output_subarea ">
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+>
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-</div>
+<div class="output_area"><div class="prompt output_prompt">Out[141]:</div>
+<div class="output_text output_subarea output_execute_result">
+<pre>&lt;Graph object, undirected, with 30 vertices and 492 edges at 0x7f6ef3edaed0&gt;</pre>
 </div>
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-<div class="cell border-box-sizing code_cell rendered">
-<div class="input">
-<div class="prompt input_prompt">In&nbsp;[48]:</div>
-<div class="inner_cell">
-    <div class="input_area">
-<div class=" highlight hl-ipython2"><pre><span></span><span class="n">graph_tool</span><span class="o">.</span><span class="n">topology</span><span class="o">.</span><span class="n">max_independent_vertex_set</span><span class="p">(</span><span class="n">g</span><span class="p">)</span>
-</pre></div>
-</div>
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-<div class="output_wrapper">
-<div class="output">
-<div class="output_area"><div class="prompt output_prompt">Out[48]:</div>
-<div class="output_text output_subarea output_execute_result">
-<pre>&lt;PropertyMap object with key type &apos;Vertex&apos; and value type &apos;bool&apos;, for Graph 0x7f5770624b10, at 0x7f5775aac210&gt;</pre>
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+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
 </div>
+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<p>And now the same experimental result with the other visualization</p>
 </div>
 </div>
 </div>
 <div class="cell border-box-sizing code_cell rendered">
 <div class="input">
-<div class="prompt input_prompt">In&nbsp;[49]:</div>
+<div class="prompt input_prompt">In&nbsp;[142]:</div>
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      <div class="input_area">
-<div class=" highlight hl-ipython2"><pre><span></span><span class="n">graph_tool</span><span class="o">.</span><span class="n">topology</span><span class="o">.</span><span class="n">pseudo_diameter</span><span class="p">(</span><span class="n">g</span><span class="p">)</span>
+<div class=" highlight hl-ipython2"><pre><span></span><span class="n">pc_graph</span><span class="p">(</span><span class="n">cells</span><span class="p">,</span><span class="n">proteins</span><span class="p">,</span><span class="n">draw</span><span class="o">=</span><span class="bp">True</span><span class="p">)</span>
 </pre></div>
@@ Line 751: / Line 6,949: @@
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+<div class="output_area"><div class="prompt"></div>
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+<div class="output_png output_subarea ">
-<pre>(2.0,
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+>
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-</div>
+<div class="output_area"><div class="prompt output_prompt">Out[142]:</div>
-</div>
-</div>
-<div class="cell border-box-sizing code_cell rendered">
-<div class="input">
-<div class="prompt input_prompt">In&nbsp;[54]:</div>
-<div class="inner_cell">
-    <div class="input_area">
-<div class=" highlight hl-ipython2"><pre><span></span><span class="n">tmp</span><span class="o">=</span><span class="n">graph_tool</span><span class="o">.</span><span class="n">topology</span><span class="o">.</span><span class="n">label_largest_component</span><span class="p">(</span><span class="n">g</span><span class="p">)</span>
-<span class="n">tmp</span><span class="o">.</span><span class="n">get_array</span><span class="p">()</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
-</pre></div>
-</div>
-</div>
-</div>
-<div class="output_wrapper">
-<div class="output">
-<div class="output_area"><div class="prompt output_prompt">Out[54]:</div>
 <div class="output_text output_subarea output_execute_result">
-<pre>(100,)</pre>
+<pre>&lt;Graph object, undirected, with 230 vertices and 276 edges at 0x7f6ef30f4110&gt;</pre>
 </div>
@@ Line 801: / Line 19,915: @@
 <div class="inner_cell">
 <div class="text_cell_render border-box-sizing rendered_html">
-<h3 id="Cells-and--bindings-vertices">Cells and  bindings vertices<a class="anchor-link" href="#Cells-and--bindings-vertices">&#182;</a></h3>
+<p>The second graph shows not only how the interconnection between the idnividual cells is but also visualizes how many NP are "lost" by just sticking to a single cell without forming an connection to others. Furthermore one can see how many differnt proteins connect two cells.</p>
-</div>
-</div>
-</div>
-<div class="cell border-box-sizing code_cell rendered">
-<div class="input">
-<div class="prompt input_prompt">In&nbsp;[&nbsp;]:</div>
-<div class="inner_cell">
-    <div class="input_area">
-<div class=" highlight hl-ipython2"><pre><span></span><span class="n">g</span> <span class="o">=</span> <span class="n">Graph</span><span class="p">(</span><span class="n">directed</span><span class="o">=</span><span class="bp">False</span><span class="p">)</span>
-<span class="n">v_size</span> <span class="o">=</span> <span class="n">g</span><span class="o">.</span><span class="n">new_vertex_property</span><span class="p">(</span><span class="s2">&quot;int&quot;</span><span class="p">,</span><span class="n">val</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span>
-<span class="n">v_group</span> <span class="o">=</span> <span class="n">g</span><span class="o">.</span><span class="n">new_vertex_property</span><span class="p">(</span><span class="s2">&quot;int32_t&quot;</span><span class="p">)</span>
-<span class="c1">#v_color = vprop_vint = g.new_vertex_property(&quot;&lt;int&gt;&quot;, vals=[])</span>
-<span class="c1">#cell_vertices = list(g.add_vertex(n_cells))</span>
-<span class="k">for</span> <span class="n">cell</span> <span class="ow">in</span> <span class="n">cells</span><span class="p">:</span>
-    <span class="n">cell</span><span class="o">.</span><span class="n">vertex</span> <span class="o">=</span> <span class="n">g</span><span class="o">.</span><span class="n">add_vertex</span><span class="p">()</span>
-    <span class="n">v_size</span><span class="p">[</span><span class="n">cell</span><span class="o">.</span><span class="n">vertex</span><span class="p">]</span> <span class="o">=</span> <span class="mi">100</span>
-<span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n"></span><span class="p">:</span>
-    <span class="n">last_vertex</span> <span class="o">=</span> <span class="bp">None</span>
-    <span class="k">for</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">p</span><span class="o">.</span><span class="n">bindings</span><span class="p">:</span>
-        <span class="n">b</span><span class="o">.</span><span class="n">vertex</span><span class="o">=</span><span class="n">g</span><span class="o">.</span><span class="n">add_vertex</span><span class="p">()</span>
-        <span class="n">v_size</span><span class="p">[</span><span class="n">b</span><span class="o">.</span><span class="n">vertex</span><span class="p">]</span> <span class="o">=</span> <span class="mi">10</span>
-        <span class="n">v_group</span><span class="p">[</span><span class="n">cell</span><span class="o">.</span><span class="n">vertex</span><span class="p">]</span> <span class="o">=</span> <span class="n">p</span><span class="o">.</span><span class="n">id</span>
-        <span class="c1">#intraprotein connections</span>
-        <span class="k">if</span> <span class="n">last_vertex</span> <span class="ow">is</span> <span class="ow">not</span> <span class="bp">None</span><span class="p">:</span>
-            <span class="n">g</span><span class="o">.</span><span class="n">add_edge</span><span class="p">(</span><span class="n">b</span><span class="o">.</span><span class="n">vertex</span><span class="p">,</span><span class="n">last_vertex</span><span class="p">)</span>
-        <span class="n">last_vertex</span><span class="o">=</span><span class="n">b</span><span class="o">.</span><span class="n">vertex</span>
-        <span class="c1">#cell connections</span>
-        <span class="k">if</span> <span class="n">b</span><span class="o">.</span><span class="n">partner</span> <span class="ow">is</span> <span class="ow">not</span> <span class="bp">None</span><span class="p">:</span>
-            <span class="n">cell_vertex</span> <span class="o">=</span> <span class="n">b</span><span class="o">.</span><span class="n">partner</span><span class="o">.</span><span class="n">parent</span><span class="o">.</span><span class="n">vertex</span>
-            <span class="n">g</span><span class="o">.</span><span class="n">add_edge</span><span class="p">(</span><span class="n">b</span><span class="o">.</span><span class="n">vertex</span><span class="p">,</span><span class="n">cell_vertex</span><span class="p">)</span>
-<span class="n">pos</span><span class="o">=</span><span class="n">sfdp_layout</span><span class="p">(</span><span class="n">g</span><span class="p">,</span><span class="n">groups</span><span class="o">=</span><span class="n">v_group</span><span class="p">)</span>
-<span class="c1">#graph_draw(g, vertex_text=g.vertex_index, vertex_font_size=18, output=&quot;/tmp/graph.png&quot;,</span>
-<span class="c1">#            output_size=(2000, 2000))</span>
-<span class="n">graph_draw</span><span class="p">(</span><span class="n">g</span><span class="p">,</span> <span class="n">pos</span><span class="o">=</span><span class="n">pos</span><span class="p">,</span><span class="n">edge_pen_width</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">vertex_text</span><span class="o">=</span><span class="n">g</span><span class="o">.</span><span class="n">vertex_index</span><span class="p">,</span> <span class="n">vertex_size</span><span class="o">=</span><span class="n">v_size</span><span class="p">,</span> <span class="n">vertex_font_size</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">output_size</span><span class="o">=</span><span class="p">(</span><span class="mi">2000</span><span class="p">,</span> <span class="mi">2000</span><span class="p">))</span>
-<span class="c1">#graphviz_draw(g, elen=100, vsize=v_size, size=(2000, 2000))</span>
-</pre></div>
 </div>
 </div>
-</div>
 </div>
 <div class="cell border-box-sizing text_cell rendered">
@@ Line 856: / Line 19,925: @@
 <div class="inner_cell">
 <div class="text_cell_render border-box-sizing rendered_html">
-<h3 id="-vertices-and-cell-vertices"> vertices and cell vertices<a class="anchor-link" href="#-vertices-and-cell-vertices">&#182;</a></h3>
+<h3 id="More-experiments">More experiments<a class="anchor-link" href="#More-experiments">&#182;</a></h3>
 </div>
 </div>
 </div>
-<div class="cell border-box-sizing code_cell rendered">
+<div class="cell border-box-sizing text_cell rendered">
-<div class="input">
+<div class="prompt input_prompt">
-<div class="prompt input_prompt">In&nbsp;[48]:</div>
+</div>
 <div class="inner_cell">
-    <div class="input_area">
+<div class="text_cell_render border-box-sizing rendered_html">
-<div class=" highlight hl-ipython2"><pre><span></span><span class="k">def</span> <span class="nf">pc_graph</span><span class="p">(</span><span class="n">cells</span><span class="p">,</span> <span class="n"></span><span class="p">,</span> <span class="n">draw</span><span class="o">=</span><span class="bp">False</span><span class="p">):</span>
+<p>For a first feeling of how the parameters of the polymerization function influence the result it's helpful just to try out a few combinations and look at the visualization of the graph</p>
-    <span class="n">g</span> <span class="o">=</span> <span class="n">Graph</span><span class="p">(</span><span class="n">directed</span><span class="o">=</span><span class="bp">False</span><span class="p">)</span>
+<p>To make this task a bit easier we defien a small helper function that initializes the monomers, polymerizes them and generates the graph.</p>
-    <span class="n">v_size</span> <span class="o">=</span> <span class="n">g</span><span class="o">.</span><span class="n">new_vertex_property</span><span class="p">(</span><span class="s2">&quot;int&quot;</span><span class="p">)</span>
-    <span class="c1">#v_group = g.new_vertex_property(&quot;i&#39;nt32_t&quot;)</span>
-    <span class="c1">#v_color = vprop_vint = g.new_vertex_property(&quot;&lt;int&gt;&quot;, vals=[])</span>
-    <span class="k">for</span> <span class="n">cell</span> <span class="ow">in</span> <span class="n">cells</span><span class="p">:</span>
-        <span class="n">cell</span><span class="o">.</span><span class="n">vertex</span> <span class="o">=</span> <span class="n">g</span><span class="o">.</span><span class="n">add_vertex</span><span class="p">()</span>
-        <span class="n">v_size</span><span class="p">[</span><span class="n">cell</span><span class="o">.</span><span class="n">vertex</span><span class="p">]</span> <span class="o">=</span> <span class="mi">120</span>
-    <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n"></span><span class="p">:</span>
-        <span class="n">p</span><span class="o">.</span><span class="n">vertex</span><span class="o">=</span><span class="n">g</span><span class="o">.</span><span class="n">add_vertex</span><span class="p">()</span>
-        <span class="n">v_size</span><span class="p">[</span><span class="n">p</span><span class="o">.</span><span class="n">vertex</span><span class="p">]</span> <span class="o">=</span> <span class="mi">40</span>
-        <span class="k">for</span> <span class="n">b</span> <span class="ow">in</span> <span class="n">p</span><span class="o">.</span><span class="n">bindings</span><span class="p">:</span>
-            <span class="c1">#cell connections</span>
-            <span class="k">if</span> <span class="n">b</span><span class="o">.</span><span class="n">partner</span> <span class="ow">is</span> <span class="ow">not</span> <span class="bp">None</span><span class="p">:</span>
-                <span class="n">cell_vertex</span> <span class="o">=</span> <span class="n">b</span><span class="o">.</span><span class="n">partner</span><span class="o">.</span><span class="n">parent</span><span class="o">.</span><span class="n">vertex</span>
-                <span class="k">if</span> <span class="n">g</span><span class="o">.</span><span class="n">edge</span><span class="p">(</span><span class="n">p</span><span class="o">.</span><span class="n">vertex</span><span class="p">,</span><span class="n">cell_vertex</span><span class="p">)</span> <span class="ow">is</span> <span class="bp">None</span><span class="p">:</span> <span class="c1">#only one connection per pair</span>
-                    <span class="n">g</span><span class="o">.</span><span class="n">add_edge</span><span class="p">(</span><span class="n">p</span><span class="o">.</span><span class="n">vertex</span><span class="p">,</span><span class="n">cell_vertex</span><span class="p">)</span>
-    <span class="n">pos</span><span class="o">=</span><span class="n">fruchterman_reingold_layout</span><span class="p">(</span><span class="n">g</span><span class="p">)</span>
-    <span class="c1">#graph_draw(g, vertex_text=g.vertex_index, vertex_font_size=18, output=&quot;/tmp/graph.png&quot;,</span>
-    <span class="c1">#            output_size=(2000, 2000))</span>
-    <span class="k">if</span> <span class="n">draw</span><span class="p">:</span>
-        <span class="n">graph_draw</span><span class="p">(</span><span class="n">g</span><span class="p">,</span> <span class="n">edge_pen_width</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">vertex_text</span><span class="o">=</span><span class="n">g</span><span class="o">.</span><span class="n">vertex_index</span><span class="p">,</span> <span class="n">vertex_size</span><span class="o">=</span><span class="n">v_size</span><span class="p">,</span> <span class="n">vertex_font_size</span><span class="o">=</span><span class="mi">15</span><span class="p">,</span> <span class="n">output_size</span><span class="o">=</span><span class="p">(</span><span class="mi">2000</span><span class="p">,</span> <span class="mi">2000</span><span class="p">))</span>
-    <span class="k">return</span> <span class="n">g</span>
-</pre></div>
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-</div>
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 <div class="cell border-box-sizing code_cell rendered">
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-<div class="prompt input_prompt">In&nbsp;[18]:</div>
+<div class="prompt input_prompt">In&nbsp;[144]:</div>
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-<div class=" highlight hl-ipython2"><pre><span></span><span class="n">g</span><span class="o">.</span><span class="n">vertex_index</span><span class="p">[</span><span class="n">vertices</span><span class="p">[</span><span class="mi">1</span><span class="p">]]</span>
+<div class=" highlight hl-ipython2"><pre><span></span><span class="k">def</span> <span class="nf">random_graph</span><span class="p">(</span><span class="n">graph_method</span><span class="p">,</span> <span class="n">n_cells</span><span class="p">,</span> <span class="n">n_proteins</span><span class="p">,</span> <span class="n">n_cell_binding</span> <span class="o">=</span> <span class="mi">30</span><span class="p">,</span> <span class="n">n_protein_binding</span> <span class="o">=</span> <span class="mi">4</span><span class="p">,</span><span class="n">concentration</span><span class="o">=</span><span class="mf">0.02</span><span class="p">,</span><span class="n">reactivity</span><span class="o">=</span><span class="mf">0.01</span><span class="p">,</span><span class="n">mobility</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span><span class="n">max_time</span><span class="o">=</span><span class="mf">2.</span><span class="p">):</span>
+<span class="c1">#    cells,proteins=init_monomers(n_cells, n_proteins, n_cell_binding, n_protein_binding)</span>
+<span class="c1">#    polymerize(cells,proteins)</span>
+    <span class="n">cells</span><span class="p">,</span><span class="n">proteins</span><span class="o">=</span><span class="n">init_monomers</span><span class="p">(</span><span class="n">n_cells</span><span class="p">,</span> <span class="n">n_proteins</span><span class="p">,</span> <span class="n">n_cell_binding</span> <span class="o">=</span> <span class="n">n_cell_binding</span><span class="p">,</span> <span class="n">n_protein_binding</span> <span class="o">=</span> <span class="n">n_protein_binding</span><span class="p">)</span>
+    <span class="n">polymerize_spacial</span><span class="p">(</span><span class="n">cells</span><span class="p">,</span> <span class="n">proteins</span><span class="p">,</span> <span class="n">n_protein_binding</span><span class="o">=</span><span class="n">n_protein_binding</span><span class="p">,</span> <span class="n">concentration</span><span class="o">=</span><span class="n">concentration</span><span class="p">,</span> <span class="n">reactivity</span><span class="o">=</span><span class="n">reactivity</span><span class="p">,</span> <span class="n">mobility</span><span class="o">=</span><span class="n">mobility</span><span class="p">,</span> <span class="n">max_time</span><span class="o">=</span><span class="n">max_time</span><span class="p">)</span>
+    <span class="k">return</span> <span class="n">graph_method</span><span class="p">(</span><span class="n">cells</span><span class="p">,</span><span class="n">proteins</span><span class="p">,</span><span class="n">draw</span><span class="p">),</span><span class="n">cells</span><span class="p">,</span><span class="n">proteins</span>
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@@ Line 911: / Line 19,957: @@
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-<div class="output_wrapper">
-<div class="output">
-<div class="output_area"><div class="prompt output_prompt">Out[18]:</div>
-<div class="output_text output_subarea output_execute_result">
-<pre>1</pre>
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+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
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+<div class="inner_cell">
+<div class="text_cell_render border-box-sizing rendered_html">
+<p>As long as we want to see a rendered result we just switch the draw variable to True</p>
 </div>
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 </div>
 <div class="cell border-box-sizing code_cell rendered">
 <div class="input">
-<div class="prompt input_prompt">In&nbsp;[29]:</div>
+<div class="prompt input_prompt">In&nbsp;[145]:</div>
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      <div class="input_area">
-<div class=" highlight hl-ipython2"><pre><span></span><span class="n">cells</span><span class="p">[</span><span class="mi">23</span><span class="p">]</span><span class="o">.</span><span class="n">bindings</span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="o">.</span><span class="n">partner</span><span class="o">.</span><span class="n">parent</span><span class="o">.</span><span class="n">bindings</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">partner</span><span class="o">.</span><span class="n">parent</span>
+<div class=" highlight hl-ipython2"><pre><span></span><span class="n">draw</span> <span class="o">=</span> <span class="bp">True</span>
 </pre></div>
@@ Line 940: / Line 19,980: @@
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-<div class="output_wrapper">
-<div class="output">
-<div class="output_area"><div class="prompt output_prompt">Out[29]:</div>
-<div class="output_text output_subarea output_execute_result">
-<pre>&lt;__main__.Cell instance at 0x7f05b3f2a7e8&gt;</pre>
 </div>
+<div class="cell border-box-sizing text_cell rendered">
+<div class="prompt input_prompt">
 </div>
-</div>
-</div>
-</div>
-<div class="cell border-box-sizing code_cell rendered">
-<div class="input">
-<div class="prompt input_prompt">In&nbsp;[&nbsp;]:</div>
 <div class="inner_cell">
-    <div class="input_area">
+<div class="text_cell_render border-box-sizing rendered_html">
-<div class=" highlight hl-ipython2"><pre><span></span>
+<p>Now we can build a random graph by plugging in some numbers and runnign a single line of code. (The "_=" just suppresses text output)</p>
-</pre></div>
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-</div>
-    </div>
-  </div>
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