I knocked up some crude wrappers so I could simulate expected RD behaviour
under a variety of conditions (see attached file). Use as follows:
'''prototype script for relaxation dispersion sims'''
from os import sys
sys.path.append('DIRECTORY_WHERE_YOU_SAVED_RDfunctions.py')
from RDfunctions import *
# binding parameters. P for macromolecule, A for ligand.
kon = 1e3
concP = 1e-3
concA = 1e-3
Kd = 160e-6
# shift change parameters 60 Hz = 1 ppm at 15N freq on 600 MHz
dw = 60
# intrinsic R2 value
R20=10.0
#one curve
simulateRDCurve(kon, concP, concA, Kd, dw, R20)
#specifying cpmg_fields
simulateRDCurve(kon, concP, concA, Kd, dw, R20, cpmg_fields=range(50,1001,50))
# loop to plot curves at different Kds
for Kd in range(3,12):
simulateRDCurve(kon, concP, concA, 10**(-Kd), dw, R20)
#focus on a subplot and fix the axes
plt.subplot(2,1,1) # focus on R2eff plot
plt.axis([None,None,0,12]) # leave x axis alone and set y to 0 to 12
plt.subplot(2,1,2) # focus on I/I0 plot
plt.axis([None,None,0,0.5]) # leave x axis alone and set y to 0 to 12
Dr. Brian O. Smith --------------------------- Brian Smith at glasgow ac uk
Institute of Molecular, Cell and Systems Biology & School of Life Sciences,
College of Medical, Veterinary & Life Sciences,
Joseph Black Building, University of Glasgow, Glasgow G12 8QQ, UK.
Tel: 0141 330 5167/6459/3089 Fax: 0141 330 4600
----------------------------------------------------------------------
The University of Glasgow, charity number SC004401
from os import sys
from math import sqrt
from pylab import *
sys.path.append('/usr/share/nessy')
from math_fns.models import model_1, model_2, model_3, model_4, model_5
def generateR2effs(model, cpmg_fields, parameters):
y_values=[]
for y in range(0, len(cpmg_fields)):
if (cpmg_fields[y] == 0):
y_values.append(parameters[0])
elif (model == 'model_2'):
R2eff = model_2(float(cpmg_fields[y]), parameters)
y_values.append(R2eff)
elif (model == 'model_3'):
R2eff = model_3(float(cpmg_fields[y]), parameters)
y_values.append(R2eff)
return [cpmg_fields, y_values]
def generateIs(model, cpmg_fields, cpmg_delay, parameters):
y_values=[]
for y in range(0, len(cpmg_fields)):
if (cpmg_fields[y] == 0):
y_values.append(1.0)
elif(model == 'model_2'):
R2eff = model_2(float(cpmg_fields[y]), parameters)
y_value = 1.0 / exp(R2eff*cpmg_delay)
y_values.append(y_value)
elif (model == 'model_3'):
R2eff = model_3(float(cpmg_fields[y]), parameters)
y_value = 1.0 / exp(R2eff*cpmg_delay)
y_values.append(y_value)
return [cpmg_fields, y_values]
def complexConc(Ptot, Atot, Kd):
'''Class to calculate concentration of a complex given total
concentrations of
the components and the dissociation constant
[PA] = (1/2)(([Ptot] + [Atot] + Kd) +- (([Ptot] + [Atot] + Kd)^2 -
4[Ptot][Atot])^(1/2))
'''
# Parameters
b = (Ptot + Atot + Kd)
PA = 0.5 * (b - sqrt(b**2 - 4*Ptot*Atot))
return PA
def boundFraction(Ptot, Atot, Kd):
'''Class to calculate fractional saturation of a macromolecule given
total concentrations of
the components and the dissociation constant
[PA]/([PA]+[P])
'''
PA = complexConc(Ptot, Atot, Kd)
bF = PA / Ptot
return bF
def plotRDCurve(kex, dw, pa, R20, cpmg_delay=0.08,
cpmg_fields=range(0,2001,10)):
#relaxation parameters
R20 = 10
# paramters in relaxation dispersion terminology
# pa for bound state
pb = (1 - pa)
# fast 2 site exchange
phi = pa * pb * dw**2
# slow 2 site exchange - nessy model 3 calculates these for itslf
#psi = kex**2 - dw**2
#eta = -2*dw*(pa*kex - pb*kex)
pfast = [R20,phi,kex]
pslow = [R20,kex,dw,pb]
if (kex >= 10*dw):
print 'fast'
model = 'model_2'
R2plot = generateR2effs(model, cpmg_fields, pfast)
ax1 = plt.subplot(2,1,1)
plt.xlabel('vCPMG')
plt.ylabel('R2eff')
plot(R2plot[0][1:],R2plot[1][1:])
ax2 = plt.subplot(2,1,2, sharex=ax1)
plt.xlabel('vCPMG')
plt.ylabel('I/I0')
I2plot = generateIs(model, cpmg_fields, cpmg_delay, pfast)
plot(I2plot[0][1:],I2plot[1][1:])
show()
elif (kex <= 0.1*dw):
print 'slow'
model = 'model_3'
R2plot = generateR2effs(model, cpmg_fields, pslow)
ax1 = plt.subplot(2,1,1)
plt.xlabel('vCPMG')
plt.ylabel('R2eff')
plot(R2plot[0][1:],R2plot[1][1:])
ax2 = plt.subplot(2,1,2, sharex=ax1)
plt.xlabel('vCPMG')
plt.ylabel('$I/I_{0}$')
I2plot = generateIs(model, cpmg_fields, cpmg_delay, pslow)
plot(I2plot[0][1:],I2plot[1][1:])
show()
else:
print 'intermediate'
def simulateRDCurve(kon, concP, concA, Kd, dw, R20, cpmg_delay=0.08,
cpmg_fields=range(0,2001,10)):
koff = Kd * kon
pa = boundFraction(concP, concA, Kd)
# rates in relaxation dispersion terminology
kab = kon
kba = koff
kex = kab + kba
plotRDCurve(kex, dw, pa, R20, cpmg_delay, cpmg_fields)
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