Compartmental model of cytoskeletal polarization during chemotaxis

- 30 mins

This blog post summarizes the class project that I did with @boribong this semester. We created a phenomenological model of neutrophil polarization during chemotaxis, a straightforward attempt where we compartmentalized a cell radially to to simulate the heterogeneous cytoskeletal reorganization. Check out this cool animation that I made! F-actin polymerization in red, myosin contraction activity in Blog post coming soon!

Cytoskeletal Polarization

This is my first attempt at creating a blog post directly from my jupyter notebook. Here goes! :)

Incorporating network structure into coupled cytoskeletal network

Headers and functions

%matplotlib inline
import matplotlib.pyplot as plt
import PyDSTool as dst
import numpy as np
import numpy.random as random
import seaborn as sns
import matplotlib.cm as cm
from matplotlib.pyplot import figure, show, rc
import networkx as nx
import pandas as pd
from tqdm import tqdm
import pickle
plt.rcParams['figure.figsize']=10,5
def makeheatmap(string,pointset):
    pts=pointset
    col=[]
    mat=[]
    for j in range(0,len(pts[string+'0'])):
        for i in range(0, COMPARTMENTS):
            col.append(pts[string+str(i)][j])
        mat.append(col)
        col=[]
    mat.reverse()
    #mat.transpose()
    fig,ax=plt.subplots()
    ax=sns.heatmap(mat,cmap="YlGnBu")
    
def initialLdist(COMPARTMENTS,maxL,s):
    x=np.linspace(0,2.0,COMPARTMENTS+1)
    L=[]
    for i in range(0,len(x)):
        L.append(maxL*np.exp(-((x[i]-1.0)/s)**2))
    return L

def actindefinition(edgelist):
    A=edgelist
    vardict={}
    for n in A.keys():
        ASSIGNMENT="gamma_actin*(shs(S,kactin*RacGTP"+n+"-k_actin_degr*"
        numNeigh=len(A[n])
        ASSIGNMENT=ASSIGNMENT+"("+str(numNeigh)+"*Actin"+n
        for nei in A[n]:
            ASSIGNMENT=ASSIGNMENT+"-Actin"+nei
        ASSIGNMENT=ASSIGNMENT+"+w_actin))-Actin"+n+")"
        vardict['Actin'+n]=ASSIGNMENT
    return vardict

def myosindefinition(edgelist):
    A=edgelist
    vardict={}
    for n in A.keys():
        ASSIGNMENT="shs(S,kmyosin*RhoA"+n+"-k_degr_myosin*"
        numNeigh=len(A[n])
        ASSIGNMENT=ASSIGNMENT+"("+str(numNeigh)+"*Myosin"+n
        for nei in A[n]:
            ASSIGNMENT=ASSIGNMENT+"-Myosin"+nei
        ASSIGNMENT=ASSIGNMENT+"))-Myosin"+n
        vardict['Myosin'+n]=ASSIGNMENT
    return vardict

Watts-Strogatz randomization

# Generating random graphs 
N=360
K=4


n=N #int(raw_input('Please enter number of nodes in graph: ') or "10")
if n<=0:
    sys.exit('n has to be positive!')

nodelist=np.arange(0,n)
k=K #int(raw_input('Please enter average degree of each node.\nFor n=%i, enter an even integer between 1 and n: ' % n) or '2')
if k%2 !=0:
    sys.exit('k is not even!')
if k >n:
    sys.exit('k is too large!')

degreecount=np.arange(-k/2,(k+2)/2)
G=nx.Graph()

for i in range(0,len(nodelist)):
    for j in range(0,len(degreecount)):
        if i+degreecount[j]>n-1:
            G.add_edge(str(nodelist[i]),str(nodelist[i+degreecount[j]-n-1]))
            #print i,"\t",j,"\t",nodelist[i],nodelist[i+degreecount[j]-n-1]
        else:
            if nodelist[i+degreecount[j]]!=nodelist[i]:
                G.add_edge(str(nodelist[i]),str(nodelist[i+degreecount[j]]))

#f.close()
for node in G.nodes():
    if node in G.neighbors(node):
        G.remove_edge(node,node)
        print "removed an edge"
def rewire(H,p): 
#Function takes in a graph and a probability p, and returns average shortest path length and average clustering coefficient of the rewired graph    
    nodeset=set(H.nodes())

    for node in H.nodes(): #rewiring
        neighborset=set(H.neighbors(node))
        targetlist=list(nodeset-neighborset)
        for tailnode in H.neighbors(node):
            r=random.random()
            if r<p:
                node_selection=random.randint(0,len(targetlist)-1)
                H.remove_edge(node,tailnode)
                H.add_edge(node,targetlist[node_selection])
    #asp=[]
    return H
def generate_adlist(G):
    node=G.nodes()
    neighbors={}
    for e in G.edges():
        for n in node:
            neighbors[n]=G.neighbors(n)
    return neighbors
removed an edge

Generate and store adjacency lists for rewired graphs

beta=list(np.logspace(-3.0,-1.56,5)) # Specify probabilities of rewiring
#P=[0.01]
beta.insert(0,0.0)
Adict=[]
for b in beta:
    A={}
    graph=rewire(G.copy(),b)
#     graph=graph.to_undirected()
#   graph=rewire(G,0.15)
    A=generate_adlist(graph)
    Adict.append(A)
#B=generate_adlist(G)

Model definition

COMPARTMENTS=N-1

RevisedCompArgs=dst.args(name='small-world-cyto',
        varspecs={
        # input set to constant initial value by default
        'L[i]':'for(i,0,'+str(COMPARTMENTS)+',0)',#kp-klr*L[i]*R[i]-kd)',
        'PIP[i]':'for(i,0,'+str(COMPARTMENTS)+',gamma_pip*(shs(S,wlr*L[i]*R[i]-wpip)-PIP[i]))',
        # Regulators
        'RacGTP[i]':"for(i,0,"+str(COMPARTMENTS)+",shs(S,-w_rac_rac*RacGTP[i]+w_rac_pip*PIP[i])-RacGTP[i])",
        'RhoA[i]':"for(i,0,"+str(COMPARTMENTS)+",(shs(S,wlr_rho*L[i]*R[i]-w_actin_rho*Actin[i])-RhoA[i]))",                   
    },
        pars={
# PIP Parameters
        'wpip':0.45,     
        'gamma_pip':0.5,
        'wlr':1.0,       
# RacGTP activation
        'w_rac_pip':3.0, 
# Rac
        'w_rac_rac':1.5,
# Rho
        'w_actin_rho':6.0,
        'wlr_rho':1.0,               
        'S':10,
        'kactin':1.0,#0.1,
        'w_actin':0.77,
        'k_actin_degr':1.0,
        'gamma_actin':10.0,
        'kmyosin':1.0,
        'k_degr_myosin':10
    },
                       ics={
    },
                       fnspecs={
        'shs':(['sig','summ'],'1.0/(1.0+exp(-sig*summ))'),
        'actinweight':(['n','denom'],'n/denom')
                               },
                       tdata=[0,20]
                       )
SimData=[]
for A in tqdm(Adict):
    act=[]
    RevisedCompArgs.varspecs.update(actindefinition(A))
    RevisedCompArgs.varspecs.update(myosindefinition(A))
    # RevisedCompArgs.varspecs.update(actindefinition(B))
    # RevisedCompArgs.varspecs.update(myosindefinition(B))
    #s=[0.1,0.3,0.5,0.7,0.9,1.1,1.3,1.5]
    s=[0.5]
    AMRatio=[]
    #for v in s:
    L=initialLdist(COMPARTMENTS,1.5,s)
    Rinitial=1.0
    PIPinitial=0.0
    Racinitial=0.0
    Actininital=0.0
    Rhoinitial=0.0
    Myosininitial=0.0
    for i in range(0,COMPARTMENTS+1):
        R=str('R'+str(i))
        RevisedCompArgs.pars[R]=Rinitial
        PIP=str('PIP'+str(i))
        RevisedCompArgs.ics[PIP]=PIPinitial
        Rac=str('RacGTP'+str(i))
        RevisedCompArgs.ics[Rac]=Racinitial
        Actin=str('Actin'+str(i))
        RevisedCompArgs.ics[Actin]=Actininital
        Rho=str('RhoA'+str(i))
        RevisedCompArgs.ics[Rho]=Rhoinitial
        Myosin=str('Myosin'+str(i))
        RevisedCompArgs.ics[Myosin]=Myosininitial
        Lval=str('L'+str(i))
        RevisedCompArgs.ics[Lval]=L[i]
    RevisedCompDS=dst.Vode_ODEsystem(RevisedCompArgs)
    pts=RevisedCompDS.compute('test').sample(dt=0.5)
    SimData.append(pts)
len(SimData)
6
# Example of makeheatmap() usage
makeheatmap('Myosin',SimData[0])

png

def minmaxglobal(Llist):
    maxglob=[]
    minglob=[]
    for L in Llist:
        maxglob.append(max(L))
        minglob.append(min(L))
    mini=min(minglob)
    maxi=max(maxglob)
    normllist=[]
    normlist=[]
    for i in range(0,len(Llist)):
        normlist=[]
        for j in range(0,len(Llist[i])):
            normlist.append((Llist[i][j]-mini)/(maxi-mini))
        normllist.append(normlist)
    return normllist

    

f=figure(figsize=(8,8))
ax=f.add_axes([0.1, 0.1, 0.8, 0.8],polar=True)
theta = np.linspace(0.0, 2.0*np.pi, 359)
C=['yellow','orange','red','purple','blue']
NormActin=minmaxglobal(Actinvalues)
for i in range(0,5):
    radii =  NormActin[i] #10*np.random.rand(N)
#print(len(radii))
    width = np.pi/359.0 #np.pi/4*np.random.rand(N)
    bars = ax.bar(theta, radii, width=width, bottom=0.0)

    for r,bar in zip(radii, bars):
        bar.set_facecolor(C[i])
        bar.set_alpha(1.0)

png

actinFinal=[]
myosinFinal=[]
D=SimData[4]
for i in range(0,COMPARTMENTS):
    actinFinal.append(D['Actin'+str(i)][-1]) 
    myosinFinal.append(D['Myosin'+str(i)][-1])
VALS=[]
VALS.append(myosinFinal)
VALS.append(actinFinal)

f=figure(figsize=(8,8))
ax=f.add_axes([0.1, 0.1, 0.8, 0.8],polar=True)
theta = np.linspace(0.0, 2.0*np.pi, 359)
C=['red','blue']
for i in range(0,len(VALS)):
    radii =  VALS[i]
    width = np.pi/359.0 
    bars = ax.bar(theta, radii, width=width, bottom=0.0)

    for r,bar in zip(radii, bars):
        bar.set_facecolor(C[i])
        bar.set_alpha(1.0)

png

import pickle
f=open('./simulationdata.dat','w')
pickle.dump(SimData,f)

Plot final network configurations for different $\beta$ values

f, ax = plt.subplots(1,5, subplot_kw=dict(projection='polar'),figsize=(20,5))
for fig in range(0,5):
    actinFinal=[]
    myosinFinal=[]
    D=SimData[fig]
    for i in range(0,COMPARTMENTS):
        actinFinal.append(D['Actin'+str(i)][-1]) 
        myosinFinal.append(D['Myosin'+str(i)][-1])
    VALS=[]
    VALS.append(actinFinal)
    VALS.append(myosinFinal)

    theta = np.linspace(0.0, 2.0*np.pi, 359)
    C=['red','blue']
    for i in range(0,len(VALS)):
        radii =  VALS[i]
        width = np.pi/359.0 
        bars = ax[fig].bar(theta, radii, width=width, bottom=0.0)

        for r,bar in zip(radii, bars):
            bar.set_facecolor(C[i])
            bar.set_alpha(1.0)
    ax[fig].set_title('$\\beta$= %0.3f'%beta[fig])
plt.savefig('./cytoskeletal-network-rewiring.png')

png

Generate animations

COMPARTMENTS=359
data=[]
data.append(SimData[0])
data.append(SimData[5])
B=['0.000','0.012']
for t in tqdm(range(0,20)):
    f, ax = plt.subplots(1,2, subplot_kw=dict(projection='polar'),figsize=(10,5))
    for fig in range(0,2):
        actinFinal=[]
        myosinFinal=[]
        for i in range(0,COMPARTMENTS):
            actinFinal.append(data[fig]['Actin'+str(i)][t]) 
            myosinFinal.append(data[fig]['Myosin'+str(i)][t])
        VALS=[]
        VALS.append(actinFinal)
        VALS.append(myosinFinal)
        theta = np.linspace(0.0, 2.0*np.pi, 359)
        C=['red','blue']
        for i in range(0,len(VALS)):
            radii =  VALS[i]
            width = np.pi/359.0 
            bars = ax[fig].bar(theta, radii, width=width, bottom=0.0)

            for r,bar in zip(radii, bars):
                bar.set_facecolor(C[i])
                bar.set_alpha(1.0)
        ax[fig].set_title('$\\beta$='+B[fig])
    plt.savefig('./polarization-timecourse-t='+str(t)+'.png')

Generates Ligand distribution plots

S=[0.1,0.5,1.1]
M=[0.5,1.0,1.5]
S.reverse()
M.reverse()
f, ax = plt.subplots(1,2, subplot_kw=dict(projection='polar'),figsize=(10,5))
theta = np.linspace(0.0, 2.0*np.pi, 359)
width = np.pi/359.0 
C=['#c0c0c0','#989898','#383838']
#C=['#DAECF3','#022D41','#1AA687']
#C=['#616536','#A4E666','#31B96E']
#C=['red','purple','blue']
i=0
for s in S:
    radii=initialLdist(358,1.5,s)
    bars = ax[0].bar(theta, radii, width=width, bottom=0.5,edgecolor=C[i])

    for r,bar in zip(radii, bars):
        bar.set_facecolor(C[i])
        bar.set_alpha(1.0)

    i=i+1
i=0
for m in M:
    radii=initialLdist(358,m,0.75)
    bars = ax[1].bar(theta, radii, width=width, bottom=0.5,edgecolor=C[i])

    for r,bar in zip(radii, bars):
        bar.set_facecolor(C[i])
        bar.set_alpha(1.0)
    i=i+1
    
ax[0].get_xaxis().set_visible(False)
ax[0].get_yaxis().set_visible(False)
ax[0].set_title('Depth of Gradient')
ax[1].get_xaxis().set_visible(False)
ax[1].get_yaxis().set_visible(False)
ax[1].set_title('Perceived Ligand gradient')
#plt.savefig('./ligand-distribution.png',dpi=500)

png

Generates consolidate heatmap collection of all variables with no rewiring

f=open('simulationdata.dat')
SimDat=pickle.load(f)
PTS=SimDat[0]
def makeheatmap(pointset):
    COMPARTMENTS=358
    pts=pointset
    col=[]
    mat=[]
    HEATMAPS=[]
    mat=[]
    LVALS=[]
    for i in range(0,len(pts['t'])):
        LVALS.append(initialLdist(358,1.5,0.75))
    HEATMAPS.append(LVALS)
    VARIABLES=['Actin','Myosin','PIP','RacGTP','RhoA']
    for string in VARIABLES:
        mat=[]
        col=[]
        for j in range(0,len(pts[string+'0'])):
            for i in range(0, COMPARTMENTS):
                col.append(pts[string+str(i)][j])
            mat.append(col)
            col=[]
        mat.reverse()
        HEATMAPS.append(mat)
    
    fig,ax=plt.subplots(2,3,figsize=[15,8],sharex=True, sharey=True)
    k=0
    print(len(HEATMAPS))
    NAMES=['Ligand(input)','Actin','Myosin','PIP','RacGTP','RhoA']

    fig.text(0.5, 0.05, 'Compartments', ha='center', va='center')
    fig.text(0.1, 0.5, 'Time', ha='center', va='center', rotation='vertical')
    for i in range(0,len(ax)):
        for j in range(0,len(ax[i])):
            ax[i][j].get_yaxis().set_visible(False)
            ax[i][j].get_xaxis().set_visible(False)
           
            ax[i][j].set_title(NAMES[k])
            sns.heatmap(HEATMAPS[k],ax=ax[i][j],cmap="YlGnBu")
            k=k+1
        
makeheatmap(PTS)
plt.savefig('./representative-results-compilation.png',dpi=500)
6

png

Comparing strengths of ligand distribution

beta=[0.0]
A={}
graph=rewire(G.copy(),beta)
A=generate_adlist(graph)

COMPARTMENTS=N-1

RevisedCompArgs=dst.args(name='small-world-cyto',
        varspecs={
        # input set to constant initial value by default
        'L[i]':'for(i,0,'+str(COMPARTMENTS)+',0)',#kp-klr*L[i]*R[i]-kd)',
        'PIP[i]':'for(i,0,'+str(COMPARTMENTS)+',gamma_pip*(shs(S,wlr*L[i]*R[i]-wpip)-PIP[i]))',
        # Regulators
        'RacGTP[i]':"for(i,0,"+str(COMPARTMENTS)+",shs(S,-w_rac_rac*RacGTP[i]+w_rac_pip*PIP[i])-RacGTP[i])",
        'RhoA[i]':"for(i,0,"+str(COMPARTMENTS)+",(shs(S,wlr_rho*L[i]*R[i]-w_actin_rho*Actin[i])-RhoA[i]))",                   
    },
        pars={
# PIP Parameters
        'wpip':0.45,     
        'gamma_pip':0.5,
        'wlr':1.0,       
# RacGTP activation
        'w_rac_pip':3.0, 
# Rac
        'w_rac_rac':1.5,
# Rho
        'w_actin_rho':6.0,
        'wlr_rho':1.0,               
        'S':10,
        'kactin':1.0,#0.1,
        'w_actin':0.77,
        'k_actin_degr':1.0,
        'gamma_actin':10.0,
        'kmyosin':1.0,
        'k_degr_myosin':10
    },
                       ics={
    },
                       fnspecs={
        'shs':(['sig','summ'],'1.0/(1.0+exp(-sig*summ))'),
        'actinweight':(['n','denom'],'n/denom')
                               },
                       tdata=[0,20]
                       )
SimData=[]
act=[]
RevisedCompArgs.varspecs.update(actindefinition(A))
RevisedCompArgs.varspecs.update(myosindefinition(A))
# RevisedCompArgs.varspecs.update(actindefinition(B))
# RevisedCompArgs.varspecs.update(myosindefinition(B))
S=[0.01,0.1,0.2,0.3,0.4,0.5,0.55,0.6,0.7,0.8,0.9,1.0]
#s=[0.5]
AMRatio=[]
#for v in s:
for s in tqdm(S):
    L=initialLdist(COMPARTMENTS,1.5,s)
    Rinitial=1.0
    PIPinitial=0.0
    Racinitial=0.0
    Actininital=0.0
    Rhoinitial=0.0
    Myosininitial=0.0
    for i in range(0,COMPARTMENTS+1):
        R=str('R'+str(i))
        RevisedCompArgs.pars[R]=Rinitial
        PIP=str('PIP'+str(i))
        RevisedCompArgs.ics[PIP]=PIPinitial
        Rac=str('RacGTP'+str(i))
        RevisedCompArgs.ics[Rac]=Racinitial
        Actin=str('Actin'+str(i))
        RevisedCompArgs.ics[Actin]=Actininital
        Rho=str('RhoA'+str(i))
        RevisedCompArgs.ics[Rho]=Rhoinitial
        Myosin=str('Myosin'+str(i))
        RevisedCompArgs.ics[Myosin]=Myosininitial
        Lval=str('L'+str(i))
        RevisedCompArgs.ics[Lval]=L[i]
    RevisedCompDS=dst.Vode_ODEsystem(RevisedCompArgs)
    pts=RevisedCompDS.compute('test').sample(dt=0.5)
    ratioVals=[]
    for j in range(0,COMPARTMENTS+1):
        ratioVals.append(pts['Actin'+str(j)][-1]/pts['Myosin'+str(j)][-1])
    AMRatio.append(ratioVals)
            
def minmaxnorm(A):
    MI=min(A)
    MA=max(A)
    B=[]
    for a in A:
        B.append((a-MI)/(MA-MI))
    return B
mag=[]
for i in range(0,len(AMRatio)):
    re=0
    im=0
    for j in range(0,len(AMRatio[0])):
        re=re+AMRatio[i][j]*np.cos(np.pi/180.0*j)
        im=im+AMRatio[i][j]*np.sin(np.pi/180.0*j)
    mag.append(np.sqrt(re**2+im**2))
plt.plot(S,minmaxnorm(mag))
plt.xlabel('Standard Deviation | Steepness of Gradient')
plt.ylabel('Actin:Myosin Ratio | Polarization')
plt.savefig('chemotaxis-phenotype-ligand-input.png',dpi=500)
# mag1=[]
# for s in S:
#     L=initialLdist(COMPARTMENTS,1.5,s)
#     for i in range(0,len(L)):
#         re=re+L[i]*np.cos(np.pi/180.0*i)
#         im=im+L[i]*np.sin(np.pi/180.0*i)
#     mag1.append(np.sqrt(re**2+im**2))
# plt.plot(S,minmaxnorm(mag1),'r')

png

Effect of network randomization

beta=[0.0,0.012]
Adict=[]
for b in beta:
    A={}
    graph=rewire(G.copy(),beta)
    A=generate_adlist(graph)
    Adict.append(A)

COMPARTMENTS=N-1

RevisedCompArgs=dst.args(name='small-world-cyto',
        varspecs={
        # input set to constant initial value by default
        'L[i]':'for(i,0,'+str(COMPARTMENTS)+',0)',#kp-klr*L[i]*R[i]-kd)',
        'PIP[i]':'for(i,0,'+str(COMPARTMENTS)+',gamma_pip*(shs(S,wlr*L[i]*R[i]-wpip)-PIP[i]))',
        # Regulators
        'RacGTP[i]':"for(i,0,"+str(COMPARTMENTS)+",shs(S,-w_rac_rac*RacGTP[i]+w_rac_pip*PIP[i])-RacGTP[i])",
        'RhoA[i]':"for(i,0,"+str(COMPARTMENTS)+",(shs(S,wlr_rho*L[i]*R[i]-w_actin_rho*Actin[i])-RhoA[i]))",                   
    },
        pars={
# PIP Parameters
        'wpip':0.45,     
        'gamma_pip':0.5,
        'wlr':1.0,       
# RacGTP activation
        'w_rac_pip':3.0, 
# Rac
        'w_rac_rac':1.5,
# Rho
        'w_actin_rho':6.0,
        'wlr_rho':1.0,               
        'S':10,
        'kactin':1.0,#0.1,
        'w_actin':0.77,
        'k_actin_degr':1.0,
        'gamma_actin':10.0,
        'kmyosin':1.0,
        'k_degr_myosin':10
    },
                       ics={
    },
                       fnspecs={
        'shs':(['sig','summ'],'1.0/(1.0+exp(-sig*summ))'),
        'actinweight':(['n','denom'],'n/denom')
                               },
                       tdata=[0,20]
                       )
SimData=[]
act=[]

# RevisedCompArgs.varspecs.update(actindefinition(B))
# RevisedCompArgs.varspecs.update(myosindefinition(B))
S=[0.01,0.1,0.2,0.3,0.4,0.5,0.55,0.6,0.7,0.8,0.9,1.0]
#s=[0.5]
ValueList=[]
for A in Adict:
    AMRatio=[]
    RevisedCompArgs.varspecs.update(actindefinition(A))
    RevisedCompArgs.varspecs.update(myosindefinition(A))
    #for v in s:
    for s in tqdm(S):
        L=initialLdist(COMPARTMENTS,1.5,s)
        Rinitial=1.0
        PIPinitial=0.0
        Racinitial=0.0
        Actininital=0.0
        Rhoinitial=0.0
        Myosininitial=0.0
        for i in range(0,COMPARTMENTS+1):
            R=str('R'+str(i))
            RevisedCompArgs.pars[R]=Rinitial
            PIP=str('PIP'+str(i))
            RevisedCompArgs.ics[PIP]=PIPinitial
            Rac=str('RacGTP'+str(i))
            RevisedCompArgs.ics[Rac]=Racinitial
            Actin=str('Actin'+str(i))
            RevisedCompArgs.ics[Actin]=Actininital
            Rho=str('RhoA'+str(i))
            RevisedCompArgs.ics[Rho]=Rhoinitial
            Myosin=str('Myosin'+str(i))
            RevisedCompArgs.ics[Myosin]=Myosininitial
            Lval=str('L'+str(i))
            RevisedCompArgs.ics[Lval]=L[i]
        RevisedCompDS=dst.Vode_ODEsystem(RevisedCompArgs)
        pts=RevisedCompDS.compute('test').sample(dt=0.5)
        ratioVals=[]
        for j in range(0,COMPARTMENTS+1):
            ratioVals.append(pts['Actin'+str(j)][-1]/pts['Myosin'+str(j)][-1])
        AMRatio.append(ratioVals)
    ValueList.append(AMRatio)
k=0
lab=['Wt','Noc']
for AMRatio in ValueList:
    mag=[]
    for i in range(0,len(AMRatio)):
        re=0
        im=0
        for j in range(0,len(AMRatio[0])):
            re=re+AMRatio[i][j]*np.cos(np.pi/180.0*j)
            im=im+AMRatio[i][j]*np.sin(np.pi/180.0*j)
        mag.append(np.sqrt(re**2+im**2))
    plt.plot(S,minmaxnorm(mag),label=lab[k])
    k=k+1
plt.legend()
plt.xlabel('Standard Deviation | Steepness of Gradient')
plt.ylabel('Actin:Myosin Ratio | Polarization')
plt.savefig('rewiring-comparison.png',dpi=500)

png

No statistical difference observable. This will be more meaningful with more random networks maybe?


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