# Diffusion experiments

## Contents

### Implementations

NMR spectroscopy allows measurement of the coefficient of self-diffusion (Ds) which is defined[1] as the translational diffusion coefficient at zero gradient of the chemical potential. Most frequently that condition simply implies zero concentration gradient.

Ds is related to the hydrodynamic properties and size of the molecule indicative of its aggregation state. Unlike ultracentrifugation or dynamic light scattering, both also measuring Ds, NMR methods work at mM concentration, i.e. in the conditions used for structural work by NMR.

## LED

LED stands for longitudinal encode-decode or "longitudinal eddy current delay" experiment. The LED experiment is an evolutionary improvement of the PFGSTE (stimulated echo: 90oPFG-90o-T-90oPFG-acquire) experiment proposed by Tanner in 1970[2]. In LED experiments[3] magnetization is stored along the z-axis during most of the pulse sequence, so T1 relaxation is predominant. Since in macromolecules the T1 relaxation is slower than the T2 relaxation, the LED experiment is better suited to the measurement of Ds of slower diffusing molecules where longer "diffusion delay" is required to detect attenuation of the signal.

The water-sLED experiment[4] is a modification of the LED experiment[3] with added water suppression (Water flip-back and RAW). water-sLED allows determination of Ds for molecules with molecular weights of up to ~40 kDa.

The amplitude of the echo in these experiments follows the equation below:

$A(2\tau) = A(0) e^{-(\gamma \delta G)^2(\Delta-\frac{\delta}{3})D_s}$

Where:

• γ - gyromagnetic ratio of the nucleus
• δ - duration of the PFG
• Ds - constant of self-diffusion
• Δ time between beginnings of the two gradient pulses

## BPP-SED

The BPP-SED experiment [5] combines the BPP-LED and SED (selective echo dephasing) water suppression schemes; it is designed to measure self-diffusion constants of biomolecules in up to 95% H2O. This experiment requires a tri-axial PFG probe as gradients along the x,y,z axes are used.