Solution NMR to Quantify Mobility in Membranes: Diffusion, Protrusion, and Drug Transport Processes

Abstract

Lipid bilayer membranes are soft, fluid, and dynamic architecture where molecules are constantly moving and thermally fluctuating under physiological conditions. In this review, a strategy to quantify molecular dynamics in membranes is introduced by utilizing solution-state NMR spectroscopy as a versatile, noninvasive technique. The dynamics involves lateral diffusion and protrusion motion, in parallel and vertical direction to the membrane surface. Dynamical behavior of small-sized drugs, chemicals, and peptides is also reviewed in relation to the lipid movements in membranes, on the basis of recent multinuclear NMR in combination with the pulsed field gradient technique. Finally, in-cell NMR method is introduced as a promising technique to capture drug transport processes in real time, to shed light on mechanisms of deliveries to living cells without perturbation of the system.

Microscopic theory of spin–spin and spin–lattice relaxation of bound protons in cellular and myelin membranes—A lateral diffusion model (LDM)

“…, describing the transverse relaxation of lipid-bound protons in bilayers is not linear in time t: Γ(t) = R 2 (t) ⋅ t. As the quantity R 2 (t) depends on time t, it cannot be referred to as a "relaxation rate constant", instead we call it a relaxation rate function. Importantly, the main contribution to the transverse relaxation rate function R 2 (t) ∼ ln t, Equation (31), with the proportionality coefficient strongly orientation dependent, nulling at the magic angle orientation. This logarithmic R 2 (t) behavior is intermediate between the case of unrestricted diffusion, 33,34 where R 2 is a constant (does not depend on time), and the case of fully restricted diffusion proposed by Furman et al, 47 where the relaxation was described by a Gaussian-type function, that is, Γ(t) ∼ t 2 .…”

“…For example, Schoch et al 24 reported $$$ D\sim 0.8\cdot {10}^{-4}-4\cdot {10}^{-3}\kern0.2em {\upmu \mathrm{m}}^2/\mathrm{msec} $$$ for supported lipid bilayers and $$$ D\sim 13\cdot {10}^{-3}-20\cdot {10}^{-3}\kern0.2em {\upmu \mathrm{m}}^2/\mathrm{msec} $$$ for free‐floating bilayers. Quite a few other studies also reported D for model bilayer systems in the range of $$$ {10}^{-4}-{10}^{-2}\kern0.2em {\upmu \mathrm{m}}^2/\mathrm{msec} $$$ (e.g., 25–31 ). Hence, the motion of lipid‐bound protons can be considered as a lateral 2D diffusion, which is accompanied by lipid molecule rotation (Figure 1).…”

“…For example, Schoch et al 24 reported D ∼ 0.8 ⋅ 10 −4 − 4 ⋅ 10 −3 𝜇𝑚 2 ∕msec for supported lipid bilayers and D ∼ 13 ⋅ 10 −3 − 20 ⋅ 10 −3 𝜇𝑚 2 ∕msec for free-floating bilayers. Quite a few other studies also reported D for model bilayer systems in the range of 10 −4 − 10 −2 𝜇𝑚 2 ∕msec (e.g., [25][26][27][28][29][30][31] ). Hence, the motion of lipid-bound protons can be considered as a lateral 2D diffusion, which is accompanied by lipid molecule rotation (Figure 1).…”

“…where R 2 (t, 𝛼) is defined by a general Equation ( 27) with a long-time asymptotic in Equation (31). For a special case of the magic angle 𝛼 m , the relaxation rate function, R 2 (t, 𝛼 = 𝛼 m ) = 4𝜅 2 𝜆∕9, does not depend on time t, and L (Δ𝜔, 𝛼 m ) reduces to a standard Lorentzian form:…”