def fitFunction(x,param):
#unpack position vector
x1 = x[0:size1]
x2 = x[size1:size2end]
x3 = x[size2end:size3end]
#create rate vectors
y1 = np.zeros(size1)
y2 = np.zeros(size2)
y3 = np.zeros(size3)
#get rates
for index,item in enumerate(x1):
y1[index] = SDMMrates(0,int(item),N,dGBP,dGp,dGBM,dGassoc,dGMM,param,c,mode)
for index,item in enumerate(x2):
y2[index] = SDMMrates(2,int(item),N,dGBP,dGp,dGBM,dGassoc,dGMM,param,c,mode)
for index,item in enumerate(x3):
y3[index] = SDMMrates(11,int(item),N,dGBP,dGp,dGBM,dGassoc,dGMM,param,c,mode)
#recombine rate vector
out = np.concatenate((y1,y2,y3))
return out
def fitFunction(x, param1, param2, param3, param4):
#unpack position vector
x1 = x[0:size1]
x2 = x[size1:size2end]
x3 = x[size2end:size3end]
x4 = x[size3end:size4end]
x5 = x[size4end:size5end]
x6 = x[size5end:size6end]
#create rate vectors
y1 = np.zeros(size1)
y2 = np.zeros(size2)
y3 = np.zeros(size3)
y4 = np.zeros(size4)
y5 = np.zeros(size5)
y6 = np.zeros(size6)
#get rates
for index, item in enumerate(x1):
y1[index] = SDMMrates(int(item), 10, N, dGBP, param1, param2, param3,
param4, kbm, c, mode)
for index, item in enumerate(x2):
y2[index] = SDMMrates(int(item), 9, N, dGBP, param1, param2, param3,
param4, kbm, c, mode)
for index, item in enumerate(x3):
y3[index] = SDMMrates(int(item), 8, N, dGBP, param1, param2, param3,
param4, kbm, c, mode)
for index, item in enumerate(x4):
y4[index] = SDMMrates(int(item), 7, N, dGBP, param1, param2, param3,
param4, kbm, c, mode)
for index, item in enumerate(x5):
y5[index] = SDMMrates(int(item), 6, N, dGBP, param1, param2, param3,
param4, kbm, c, mode)
for index, item in enumerate(x6):
y6[index] = SDMMrates(int(item), 5, N, dGBP, param1, param2, param3,
param4, kbm, c, mode)
#calculate relative rates
y1 = y1 / y1[0]
y2 = y2 / y2[0]
y3 = y3 / y3[0]
y4 = y4 / y4[0]
y5 = y5 / y5[0]
y6 = y6 / y6[0]
#recombine rate vector
out = np.concatenate((y1, y2, y3, y4, y5, y6))
return out
print('kbm ={:.1e}, error: {:.0e}'.format(popt[0],pErr[0]))
##############################################################################
###create mismatch position dependence (Figure 3B)############################
SDratesP = np.zeros(size1)
SDratesMM2 = np.zeros(size2)
SDratesMM11 = np.zeros(size3)
for index,item in enumerate(xdataP):
SDratesP[index] = SDMMrates(0,int(item),N,dGBP,dGp,dGBM,dGassoc,dGMM,*popt,c,mode)
for index,item in enumerate(xdataMM2):
SDratesMM2[index] = SDMMrates(2,int(item),N,dGBP,dGp,dGBM,dGassoc,dGMM,*popt,c,mode)
for index,item in enumerate(xdataMM11):
SDratesMM11[index] = SDMMrates(11,int(item),N,dGBP,dGp,dGBM,dGassoc,dGMM,*popt,c,mode)
plt.semilogy(xdataP,SDratesP)
plt.semilogy(xdataMM2,SDratesMM2)
plt.semilogy(xdataMM11,SDratesMM11)
##############################################################################
###plot measurements (Figure 3B)############################
dGBP = 2.52 #base pairing energy
dGp = 3.5 #branch migration initiation energy
dGBM = 7.4 #branch migration penalty
dGassoc = 2.5 #association energy
dGMM = 9.5 #mismatch penalty
#define time constant
kbm = 36E3 #branch migration rate constant
##############################################################################
###single value output########################################################
toeholdLength = 10
mismatchPosition = 2
mismatchPosition2 = 20
SDrate = SDMMrates(mismatchPosition2, toeholdLength, N, dGBP, dGp, dGBM,
dGassoc, dGMM, kbm, c, mode, mismatchPosition)
print(
'mean reaction time: {:.1f} s (toehold length: {:.0f} mismatch positions: {:.0f} and {:.0f})'
.format(1 / SDrate, toeholdLength, mismatchPosition, mismatchPosition2))
##############################################################################
###create mismatch position dependence #######################################
position = np.arange(1, N, 1)
SDrates = np.zeros(N)
for mismatchPosition2 in range(N):
SDrates[mismatchPosition2] = SDMMrates(mismatchPosition2, toeholdLength, N,
dGBP, dGp, dGBM, dGassoc, dGMM, kbm,
c, mode, mismatchPosition)
I1OT = 0.0
I2OT = 0.0
O = 0.0
I1T = 0.0
I2T = 0.0
I2I1T = 0.0
I1I2T = 0.0
c = 1.0E-9 #can be arbitrary, since k1 and k2 are concentration independent
k11p, k11m, k12 = SDMMrates(18,
4,
20,
dGBP,
dGp,
dGBM,
dGassoc,
dGMM,
kbm,
c,
"singleIncumbent",
output=3)
k21p, k21m, k22 = SDMMrates(3,
4,
20,
dGBP,
dGp,
dGBM,
dGassoc,
dGMM,
kbm,
c,
#initiate samples
toe3Samples = np.zeros((sampleSize, N))
toe4Samples = np.zeros((sampleSize, N))
toe5Samples = np.zeros((sampleSize, N))
#initiate produce parameter samples
parameterSamples = np.random.multivariate_normal(popt, pcov, sampleSize)
#calculate MM position dependence for each set of parameters
i = 0
for pi in parameterSamples:
for mismatchPosition in range(1, N):
toe3Samples[i, mismatchPosition] = SDMMrates(mismatchPosition, 3, N,
dGBP, *pi, kbm, c, mode)
toe4Samples[i, mismatchPosition] = SDMMrates(mismatchPosition, 4, N,
dGBP, *pi, kbm, c, mode)
toe5Samples[i, mismatchPosition] = SDMMrates(mismatchPosition, 5, N,
dGBP, *pi, kbm, c, mode)
#calculate relative rate
toe3Samples[i, :] = toe3Samples[i, :] / SDMMrates(0, 3, N, dGBP, *pi, kbm,
c, mode)
toe4Samples[i, :] = toe4Samples[i, :] / SDMMrates(0, 4, N, dGBP, *pi, kbm,
c, mode)
toe5Samples[i, :] = toe5Samples[i, :] / SDMMrates(0, 5, N, dGBP, *pi, kbm,
c, mode)
i = i + 1
print('dGp ={:.1f}, error: {:.1f}'.format(popt[0], pErr[0]))
print('dGBM ={:.1f}, error: {:.1f}'.format(popt[1], pErr[1]))
print('dGassoc ={:.1f}, error: {:.1f}'.format(popt[2], pErr[2]))
print('dGMM ={:.1f}, error: {:.1f}'.format(popt[3], pErr[3]))
##############################################################################
###create mismatch position dependence (Figure 3A)############################
position = np.arange(1, N, 1)
for toeholdLength in range(5, 11):
SDrates = np.zeros(N)
for mismatchPosition in range(N):
SDrates[mismatchPosition] = SDMMrates(mismatchPosition, toeholdLength,
N, dGBP, *popt, kbm, c, mode)
plt.semilogy(position, SDrates[1:N] / SDrates[0])
##############################################################################
###plot measurements (Figure 3A)############################
#restart color cycle
plt.gca().set_prop_cycle(None)
#plot data
plt.errorbar(xdataT05[1:], ydataT05[1:], yerr=ydataT05[1:] * error, fmt='v')
plt.errorbar(xdataT06[1:], ydataT06[1:], yerr=ydataT06[1:] * error, fmt='D')
plt.errorbar(xdataT07[1:], ydataT07[1:], yerr=ydataT07[1:] * error, fmt='>')
plt.errorbar(xdataT08[1:], ydataT08[1:], yerr=ydataT08[1:] * error, fmt='o')
plt.errorbar(xdataT09[1:], ydataT09[1:], yerr=ydataT09[1:] * error, fmt='^')
#define energy parameters
dGBP = 2.52 #base pairing energy
dGp = 3.5 #branch migration initiation energy
dGBM = 7.4 #branch migration penalty
dGassoc = 2.5 #association energy
dGMM = 9.5 #mismatch penalty
#define time constant
kbm = 36E3 #branch migration rate constant
##############################################################################
###single value output########################################################
toeholdLength = 4
mismatchPosition = 5 #position 0 results in no mismatch
meanSDrate = SDMMrates(mismatchPosition, toeholdLength, N, dGBP, dGp, dGBM,
dGassoc, dGMM, kbm, c, mode)
print(
'mean reaction time: {:.1f} s (toehold length: {:.0f} mismatch position: {:.0f})'
.format(1 / meanSDrate, toeholdLength, mismatchPosition))
##############################################################################
###create mismatch position dependence #######################################
position = np.arange(1, N, 1)
SDrates = np.zeros(N)
for mismatchPosition in range(N):
SDrates[mismatchPosition] = SDMMrates(mismatchPosition, toeholdLength, N,
dGBP, dGp, dGBM, dGassoc, dGMM, kbm,
c, mode)
kbm = 36E3 #branch migration rate constant
##############################################################################
###single value output########################################################
N = 17 #number of displacement positions
toeholdLength = 4
mismatchPosition = 5 #position 0 results in no mismatch
#initiate data vector
dataPoints = 100
keff = np.zeros(dataPoints)
kfirst = np.zeros(dataPoints)
ksecond = np.zeros(dataPoints)
c = np.logspace(-6,-1,dataPoints)
for i in range(dataPoints):
keff[i] , ksecond[i] , kfirst[i] , cThresh = SDMMrates(mismatchPosition,toeholdLength,N,dGBP,dGp,dGBM,dGassoc,dGMM,kbm,c[i],mode,output=2)
plt.loglog(c,keff)
plt.loglog(c,kfirst,'k--')
plt.loglog(c,ksecond*c,'k--')
plt.axvline(x=cThresh,color='grey',linestyle='dotted')
plt.ylim(np.min(keff)*0.9,np.max(keff)*2)
plt.xlabel("Concentration (M)")
plt.ylabel("Displacement rate (1/s)")
sampleSize = 1000
#initiate samples
singleMMSamples = np.zeros((sampleSize,N))
doubleMMSamples = np.zeros((sampleSize,N))
#initiate produce parameter samples
parameterSamples = np.random.multivariate_normal(popt, pcov,sampleSize)
#calculate MM position dependence for each set of parameters
i=0
for pi in parameterSamples:
for mismatchPosition in range(1,N):
singleMMSamples[i,mismatchPosition] = SDMMrates(mismatchPosition,toeholdLength,N,dGBP,*pi,kbm,c,mode,0)
doubleMMSamples[i,mismatchPosition] = SDMMrates(mismatchPosition,toeholdLength,N,dGBP,*pi,kbm,c,mode,2)
#calculate relative rate
singleMMSamples[i,:] = singleMMSamples[i,:] / SDMMrates(0,toeholdLength,N,dGBP,*pi,kbm,c,mode,0)
doubleMMSamples[i,:] = doubleMMSamples[i,:] / SDMMrates(0,toeholdLength,N,dGBP,*pi,kbm,c,mode,0)
i = i + 1
#form array of samples
singleMMArray = np.asarray(singleMMSamples)
doubleMMArray = np.asarray(doubleMMSamples)
#calculate upper and lower percentiles