def dropletmodel(t):
#----------------------------------------------------------------------------------
# Dispersed-state component model
Vdis_model = dl.dipolarmodel(t,
r,
Pmodel=dl.dd_gauss,
Bmodel=dl.bg_exp,
npathways=2)
# Liquid-droplet-state component model
Vld_model = dl.dipolarmodel(t,
r,
Pmodel=dl.dd_gauss,
Bmodel=dl.bg_strexp,
npathways=2)
# Create a dipolar signal model that is a linear combination of both components
Vmodel = dl.lincombine(Vdis_model, Vld_model, addweights=True)
Vmodel = dl.link(Vmodel,
reftime1=['reftime1_1', 'reftime1_2'],
reftime2=['reftime2_1', 'reftime2_2'],
lam1=['lam1_1', 'lam1_2'],
lam2=['lam2_1', 'lam2_2'])
# Make the second weight dependent on the first one
Vmodel = dl.relate(Vmodel, weight_2=lambda weight_1: 1 - weight_1)
return Vmodel, Vdis_model, Vld_model
# Construct the distance axis
r = np.linspace(2.5, 4.5, 200)
# Pre-allocate the empty lists of models
Pmodels = [[]] * Nmax
Vmodels = [[]] * Nmax
# The basic model for the components (can be e.g. dl.dd_rice)
basisModel = dl.dd_gauss
# Model construction
for n in range(Nmax):
# Construct the n-Gaussian model
Pmodels[n] = dl.lincombine(*[basisModel] * (n + 1))
# Construct the corresponding dipolar signal model
Vmodels[n] = dl.dipolarmodel(t, r, Pmodel=Pmodels[n])
# Fit the models to the data
fits = [[]] * Nmax
for n in range(Nmax):
fits[n] = dl.fit(Vmodels[n], Vexp, reg=False)
#%%
# Extract the values of the Akaike information criterion for each fit
aic = np.array([fit.stats['aic'] for fit in fits])
# Compute the relative difference in AIC
aic -= aic.min()
# Plotting
fig = plt.figure(figsize=[6, 6])
𝜏2 = 4.4 # μs
𝜏1 = 0.4 # μs
# Load the experimental data
t, Vexp = np.load('../data/example_data_#3.npy')
# Construct the distance vector
r = np.linspace(2, 6, 100)
# 4-pulse DEER can have up to four different dipolar pathways
Nmax = 4
# Create the 4-pulse DEER signal models with increasing number of pathways
experiment = dl.ex_4pdeer(𝜏1, 𝜏2)
Vmodels = [
dl.dipolarmodel(t, r, npathways=n + 1, experiment=experiment)
for n in range(Nmax)
]
# Fit the individual models to the data
fits = [[]] * Nmax
for n, Vmodel in enumerate(Vmodels):
fits[n] = dl.fit(Vmodel, Vexp)
#%%
# Extract the values of the Akaike information criterion for each fit
aic = np.array([fit.stats['aic'] for fit in fits])
# Compute the relative difference in AIC
aic = aic - aic.min() + 1 # ...add plus one for log-scale
# Load the experimental data
t1,Vexp1 = np.load('../data/example_4pdeer_#3.npy')
t2,Vexp2 = np.load('../data/example_4pdeer_#4.npy')
# Put the datasets into lists
ts = [t1,t2]
Vs = [Vexp1,Vexp2]
# Normalize the datasets
Vs = [V/np.max(V) for V in Vs]
# Distance vector
r = np.linspace(2,5,150) # nm
# Construct the dipolar models for the individual signals
V1model = dl.dipolarmodel(ts[0],r)
V2model = dl.dipolarmodel(ts[1],r)
# Make the global model by joining the individual models
globalmodel = dl.merge(V1model,V2model)
# Link the distance distribution into a global parameter
globalmodel = dl.link(globalmodel,P=['P_1','P_2'])
# Fit the model to the data
fit = dl.fit(globalmodel,Vs)
# %%
plt.figure(figsize=[10,7])
violet = '#4550e6'
import deerlab as dl
# %%
# Load the experimental data
t, Vexp = np.load('../data/example_data_#1.npy')
# Pre-process
Vexp = dl.correctphase(Vexp)
Vexp = Vexp / np.max(Vexp)
# Distance vector
r = np.linspace(2, 5.5, 80)
# Construct the 4-pulse DEER dipolar model
Vmodel = dl.dipolarmodel(t, r)
Vmodel.reftime.set(par0=0.5, lb=0.0, ub=1.0)
# Fit the model to the data using covariane-based uncertainty
fit_cm = dl.fit(Vmodel, Vexp)
# Fit the model to the data using bootstrapped uncertainty
fit_bs = dl.fit(Vmodel, Vexp, bootstrap=10)
# Compute the covariance-based uncertainty bands of the distance distribution
Pci50_cm = fit_cm.PUncert.ci(50)
Pci95_cm = fit_cm.PUncert.ci(95)
# Compute the bootstrapped uncertainty bands of the distance distribution
Pci50_bs = fit_bs.PUncert.ci(50)
Pci95_bs = fit_bs.PUncert.ci(95)
Vs = [V1, V2, V3, V4, V5]
# Total ligand concentrations used in experiments
L = [0.3, 3, 10, 30, 300] # µM
# Distance vector
r = np.linspace(1.5, 6, 90)
# Construct a non-parametric distance distribution that is a
# linear combination of two non-parametric distributions
PAmodel = dl.freedist(r)
PBmodel = dl.freedist(r)
Pmodel = dl.lincombine(PAmodel, PBmodel, addweights=True)
# Construct the dipolar models of the individual signals
Vmodels = [dl.dipolarmodel(t, r, Pmodel) for t in ts]
# Create the global model
titrmodel = dl.merge(*Vmodels)
# Make the two components of the distance distriution global
titrmodel = dl.link(titrmodel,
PA=['P_1_1', 'P_1_2', 'P_1_3', 'P_1_4', 'P_1_5'],
PB=['P_2_1', 'P_2_2', 'P_2_3', 'P_2_4', 'P_2_5'])
# Functionalize the chemical equilibrium model
titrmodel.addnonlinear('Kdis',
lb=3,
ub=7,
par0=5,
description='Dissociation constant')
# %%
# Import required packages
import numpy as np
import matplotlib.pyplot as plt
import deerlab as dl
# %%
# Load the experimental data
t, Vexp = np.load('../data/example_5pdeer_#1.npy')
# Distance vector
r = np.linspace(2, 5, 200) # nm
# Construct dipolar model with two dipolar pathways
Vmodel = dl.dipolarmodel(t, r, npathways=2)
# The refocusing time of the second pathway can be well estimated by visual inspection
Vmodel.reftime2.set(lb=3, ub=4, par0=3.5)
# Fit the model to the data
fit = dl.fit(Vmodel, Vexp)
# %%
# Extract fitted dipolar signal
Vfit = fit.model
Vci = fit.modelUncert.ci(95)
# Extract fitted distance distribution
Pfit = fit.P
#%%
# Load the experimental 4-pulse and 5-pulse DEER datasets
t4p, V4p = np.load('../data/example_4pdeer_#2.npy')
t5p, V5p = np.load('../data/example_5pdeer_#2.npy')
# Since they have different scales, normalize both datasets
V4p = V4p / np.max(V4p)
V5p = V5p / np.max(V5p)
# Run fit
r = np.linspace(2, 4.5, 100)
# Construct the individual dipolar signal models
V4pmodel = dl.dipolarmodel(t4p, r, npathways=1)
V5pmodel = dl.dipolarmodel(t5p, r, npathways=2)
V5pmodel.reftime2.set(lb=3, ub=3.5, par0=3.2)
# Make the joint model with the distribution as a global parameters
globalmodel = dl.merge(V4pmodel, V5pmodel)
globalmodel = dl.link(globalmodel, P=['P_1', 'P_2'])
# Fit the model to the data (with fixed regularization parameter)
fit = dl.fit(globalmodel, [V4p, V5p], regparam=0.5)
# %%
plt.figure(figsize=[10, 7])
violet = '#4550e6'
Vexp = dl.correctphase(Vexp)
Vexp /= max(Vexp)
# Construct the energy and distance distribution models
forcefield_energymodel = dl.Model(forcefield_energy)
forcefield_Pmodel = dl.Model(forcefield_P)
# Set boundaries and initial conditions
forcefield_Pmodel.c1.set(lb=-1, ub=1, par0=0)
forcefield_Pmodel.c2.set(lb=-1, ub=1, par0=0)
forcefield_Pmodel.c3.set(lb=-1, ub=1, par0=0)
forcefield_Pmodel.c0.set(lb=-1, ub=1, par0=0)
# Construct the dipolar signal model
Vmodel = dl.dipolarmodel(t,
r,
Pmodel=forcefield_Pmodel,
Bmodel=dl.bg_homfractal)
# Fit the model to the data
fit = dl.fit(Vmodel, Vexp)
fit.plot(axis=t)
plt.ylabel('V(t)')
plt.xlabel('Time $t$ (μs)')
plt.show()
#%%
# Evaluate the models at the fitted parameters
Pfit = forcefield_Pmodel(fit.c0, fit.c1, fit.c2, fit.c3)
energy = forcefield_energymodel(fit.c0, fit.c1, fit.c2, fit.c3)
# Construct the model object
Pmodel = dl.Model(Ptwostates)
# Set the parameter boundaries and start values
Pmodel.meanA.set(lb=2, ub=7, par0=5)
Pmodel.meanB.set(lb=2, ub=7, par0=3)
Pmodel.widthA.set(lb=0.05, ub=0.8, par0=0.1)
Pmodel.widthB.set(lb=0.05, ub=0.8, par0=0.1)
Pmodel.fracA.set(lb=0, ub=1, par0=0.5)
# Generate the individual dipolar signal models
Nsignals = len(Vexps)
Vmodels = [[]] * Nsignals
for n in range(Nsignals):
Vmodels[n] = dl.dipolarmodel(ts[n], r, Pmodel)
Vmodels[n].reftime.set(lb=0, ub=0.5, par0=0.2)
# Combine the individual signal models into a single global models
globalmodel = dl.merge(*Vmodels)
# Link the global parameters toghether
globalmodel = dl.link(globalmodel,
meanA=['meanA_1', 'meanA_2', 'meanA_3'],
meanB=['meanB_1', 'meanB_2', 'meanB_3'],
widthA=['widthA_1', 'widthA_2', 'widthA_3'],
widthB=['widthB_1', 'widthB_2', 'widthB_3'])
# Fit the datasets to the model globally
fit = dl.fit(globalmodel, Vexps)
# Extract the fitted fractions