hydration¶

This module from DNPLab implements the process of calculating parameters that describe hydration dynamics using ODNP data as described in various studies from Songi Han and John Franck. The calculations follow:

J.M. Franck et al.; Progress in Nuclear Magnetic Resonance Spectroscopy 74 (2013) 33–56 http://dx.doi.org/10.1016/j.pnmrs.2013.06.001

J.M. Franck, S. Han; Methods in Enzymology, Chapter 5, Volume 615, (2019) 131-175 https://doi.org/10.1016/bs.mie.2018.09.024

To use the dnpHydration module first create a dictionary with the necessary inputs and add it to a workspace as 'hydration_inputs'. For example, start by defining the inputs dictionary,

import dnplab
import numpy as np

Enhancements = # list of signal enhancements
Enhancement_powers = # list of powers in Watts corresponding to Enhancements
T1s = # list of T1 values in seconds
T1_powers = # list of powers in Watts corresponding to T1s

inputs = {
          'E_array' : np.array(Enhancements),
          'E_powers' : np.array(Enhancement_powers),
          'T1_array' : np.array(T1s),
          'T1_powers' : np.array(T1_powers),
          'T10': 2.0, # T1 measured with power=0
          'T100': 2.5, # T1 measured with SL=0 and power=0
          'spin_C': 100, # spin concentration in micromolar
          'field': 350, # magnetic field in mT
          'smax_model': 'tethered', # choice of smax model
          'interpolate_method': 'second_order' # choice of interpolation method
          }

Now you can either create a workspace and add the dictionary under the key 'hydration_inputs',

workspace = dnplab.create_workspace('hydration_inputs', inputs)

Or add to an existing workspace,

workspace.add('hydration_inputs', inputs)

In rare cases the bulk water or second order T1 interpolation constants may need to be altered. This is not necessary for the dnpHydration module to operate, but if needed this can be done by adding the dictionary 'hydration_constants' to the workspace. For example,

constants = {
             'ksigma_bulk': 95.4, # bulk ksigma value
             'krho_bulk': 353.4, # bulk krho value
             'klow_bulk': 366, # bulk klow value
             'tcorr_bulk': 54, # bulk tcorr value
             'D_H2O': 2.3e-9, # bulk water diffusivity
             'D_SL': 4.1e-10, # diffusivity of spin probe in bulk water
             'delta_T1_water': 1 # change in water proton T1 due to microwaves
             'T1_water': 2.5, # T1 of bulk water protons
             'macro_C': 100, # concentration of macromolecule in uM
             }

workspace.add('hydration_constants', constants)

Next, pass the workspace to dnpHydration to perform calculations using,

hydration_results = dnplab.dnpHydration.hydration(workspace)

Or for in-place operation simply use,

dnplab.dnpHydration.hydration(workspace)

If returned, hydration_results is a dictionary that has the elements listed in the table below. If only in-place operation, the workspace will now contain a 'hydration_results' dictionary. Note: even if the dictionary is returned, the 'hydration_results' dictionary is still added to the workspace

key	type	description
uncorrected_Ep	numpy array	fit to Equation 12 by varying coupling factor and p_1/2
uncorrected_xi	float	coupling factor from uncorrected_Ep fit (unitless)
interpolated_T1	numpy array	interpolation of T1 measurements
ksigma_array	numpy array	left side of Equation 42
ksigma_fit	numpy array	fit to Equation 42 by varying κ_σ and p_1/2
ksigma	float	cross-relaxivity, κ_σ, (s^-1 M^-1)
ksigma_stdd	float	standard deviation in κ_σ (s^-1 M^-1)
ksigma_bulk_ratio	float	ratio of κ_σ to bulk value (κ_σ,bulk = 95.4 s^-1 M^-1).
krho	float	self-relaxivity, κ_ρ, (s^-1 M^-1)
krho_bulk_ratio	float	ratio of κ_ρ to bulk value (κ_ρ,bulk = 353.4 s^-1 M^-1)
klow	float	[(5/3)κ_ρ - (7/3)κ_σ] (s^-1 M^-1)
klow_bulk_ratio	float	ratio of κ_low to bulk value (κ_low,bulk = 366 s^-1 M^-1)
coupling_factor	float	κ_σ / κ_ρ (unitless)
tcorr	float	translational correlation time, τ_corr (ps), see Equations. 21-23
tcorr_bulk_ratio	float	ratio of τ_corr to bulk value (τ_corr,bulk = 54 ps)
Dlocal	float	local diffusivity, D_local, (m²/s), see Equations 18-20

If needed, access the results individually as follows,

interpolated_t1 = hydration_results['interpolated_T1']
ksigma_array = hydration_results['ksigma_array']
ksigma = hydration_results['ksigma']
coupling_factor = hydration_results['coupling_factor']
etc.

Or,

interpolated_t1 = workspace['hydration_results']['interpolated_T1']
ksigma_array = workspace['hydration_results']['ksigma_array']
ksigma = workspace['hydration_results']['ksigma']
coupling_factor = workspace['hydration_results']['coupling_factor']
etc.

For explanation of 'smax_model' see https://doi.org/10.1039/c0cp02126a. For explanations of 'interpolate_method' options or any of the equations used to calculate the hydration parameters refer to http://dx.doi.org/10.1016/j.pnmrs.2013.06.001 and https://doi.org/10.1016/bs.mie.2018.09.024.