Global fitting of a two-state model to a series of DEER traces

This example shows how to fit a two-state model to a series DEER traces. Each of the two states, A and B, has a one-Gauss distance distribution, and each DEER trace comes from a sample with different fractional populations of the two states. This could be the consequence of a chemical or conformational equilibrium. The model contains global parameters needed for all samples traces (the distribution parameters) and local parameters needed for individual samples traces (the fractional populations).

/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)
/home/runner/work/DeerLab/DeerLab/examples/advanced/ex_global_twostates_parametric.py:59: DeprecationWarning: `trapz` is deprecated. Use `trapezoid` instead, or one of the numerical integration functions in `scipy.integrate`.
  P /= np.trapz(P)

import numpy as np
import matplotlib.pyplot as plt
import deerlab as dl

green = "#3cb4c6"
red = "#f84862"
violet = "#4550e6"

# File location
path = "../data/"
files = [
    "example_twostate_data_1.DTA",
    "example_twostate_data_2.DTA",
    "example_twostate_data_3.DTA",
]

# Experimental parameters
tau1 = 0.4  # First inter-pulse delay, μs
tau2 = 4.5  # Second inter-pulse delay, μs
tmin = 0.2  # Start time, μs

Vmodels, ts, Vexps = [], [], []
for file in files:

    # Load the experimental data
    t, Vexp = dl.deerload(path + file)

    # Pre-processing
    Vexp = dl.correctphase(Vexp)    # Phase correction
    Vexp = Vexp / np.max(Vexp)      # Rescaling (aesthetic)
    t = t - t[0]                    # Account for zerotime
    t = t + tmin

    # Put the datasets into lists
    ts.append(t)
    Vexps.append(Vexp)

# Define the distance vector
r = np.linspace(2, 7, 200)

# Define a custom distance distribution model function
def Ptwostates(meanA, meanB, stdA, stdB, fracA):
    PA = fracA * dl.dd_gauss(r, meanA, stdA)
    PB = (1 - fracA) * dl.dd_gauss(r, meanB, stdB)
    P = PA + PB
    P /= np.trapz(P)
    return P


# 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.stdA.set(lb=0.05, ub=0.8, par0=0.1)
Pmodel.stdB.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 = [[] for _ in range(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"],
    stdA=["stdA_1", "stdA_2", "stdA_3"],
    stdB=["stdB_1", "stdB_2", "stdB_3"],
)

# Fit the datasets to the model globally
fit = dl.fit(globalmodel, Vexps)

# Extract the fitted fractions
fracAfit = [fit.fracA_1, fit.fracA_2, fit.fracA_3]
fracBfit = [1 - fit.fracA_1, 1 - fit.fracA_2, 1 - fit.fracA_3]

plt.figure(figsize=(10, 8))
for i in range(Nsignals):

    # Get the fitted signals and confidence bands
    Vfit = fit.model[i]

    # Get the fitted distributions of the two states
    PAfit = fracAfit[i] * dl.dd_gauss(r, fit.meanA, fit.stdA)
    PBfit = fracBfit[i] * dl.dd_gauss(r, fit.meanB, fit.stdB)

    # Plot
    plt.subplot(Nsignals, 2, 2 * i + 1)
    plt.plot(ts[i], Vexps[i], ".", color="grey")
    plt.plot(ts[i], Vfit, color=violet)
    plt.xlabel("Time t (µs)")
    plt.ylabel(f"V$_{i+1}$(t) (arb.u)")
    plt.legend(["Data", "Fit"], loc="best", frameon=False)

    plt.subplot(Nsignals, 2, 2 * i + 2)
    plt.fill(r, PAfit, alpha=0.6, color=green)
    plt.fill(r, PBfit, alpha=0.6, color=red)
    plt.xlabel("Distance r (nm)")
    plt.ylabel("P(r) (nm$^{-1}$)")
    plt.legend(["State A", "State B"], loc="best", frameon=False)
    plt.autoscale(enable=True, axis="x", tight=True)

plt.tight_layout()
plt.show()