Neutron scattering studies on dynamics of lipid membranes

Lipid molecules spontaneously form bilayers in water that are the basic building block of cell membranes. The bilayers define boundaries between cells and compartmentalize the cell into specialized organelles to accommodate various biological functions. These bilayers are, therefore, stable enough to maintain their structure yet soft and fluid enough such that embedded molecules move freely within the membranes. This unique balance of properties allows lipid bilayers to act as dynamic platforms, and the motions span a broad range of length and time scales. At long length and time scales, membranes deform, fuse, and undulate. Such membrane motions are collective movements of hundreds of self-assembled lipid molecules. By contrast, at short length and time scales, individual lipid molecules diffuse, rotate, and protrude within the membrane. This rich variety in lipid motions has direct implications for biological processes, and the individual and collective membrane fluctuations are controlled by the membrane properties.

Figure 1 summarizes lipid motions spanning a broad dynamic range together with different experimental techniques.¹ Optical techniques cover length scales longer than the wavelength of light (several hundred nm) and the time scales longer than ms. However, it is important to note that recent developments in super-resolution optical techniques extend both the length and timescale resolutions of microscopy methods.² Spectroscopic techniques, such as dielectric and nuclear magnetic resonance (NMR) spectroscopies, cover a broad range of time scales, but the timescale information is not readily associated with the length scale of the motions. Scattering techniques using light, x-ray, and neutron, on the other hand, access both length and time scales simultaneously, and the spatiotemporal range of the different techniques depends on the probe. Light scattering covers relatively long length scales while x-ray covers atomic to molecular length scales. Typically, the energy resolution (or observation time scales) is related to the incident energy of the probe, which is very high for x-rays (∼keV) and higher than the thermal energy of light (∼eV). On the other hand, thermal or cold neutrons have wavelengths close to the atomic to molecular scales and probe energies close to thermal energy (∼meV). Therefore, neutrons are good probes of the thermal fluctuations of atoms, molecules, and molecular assemblies. Given the power of neutron scattering tools for the study of lipid bilayers and the rapidly growing number of publications, there are several prior review papers that also discuss neutron scattering and lipid bilayers as well as introduce the properties of neutrons well.^3–8 

Among dynamic neutron scattering techniques, triple-axis and time-of-flight (TOF) spectrometers cover energy ranges typically in meV scales (sub ps in time scales), while backscattering (BS) accesses down to 1 μeV scales (ns time scales) and neutron spin echo (NSE) techniques accesses tens of neV scales (μs time scales). In lipid membrane dynamics studies, mostly BS and NSE techniques are used to access individual and collective lipid motions, such as rotation, translation, acyl tail motions, and collective membrane fluctuations. Some review papers focused on the dynamics of lipid molecules^5,7,9,10 and collective membrane fluctuations^1,7,9–11 have been published. Here, in this review, we mainly focus on the collective membrane fluctuations and how these experimental data are analyzed based on membrane dynamics theories. Section II introduces the theory of dynamic neutron scattering. Various examples that use NSE to study different types of bilayers composed of different types of lipids, various additives, or internal membrane organizations are given in Sec. III. Self-motions of individual lipid molecules as well as the hydration water dynamics are briefly reviewed in Sec. IV. Recent advances to measure collective acyl tail motions are given in Sec. V, and the paper closes with a summary and outlook for the field. Abbreviations used in this paper are listed at the end.

Measuring the DSF, $S ( Q , ω )$⁠, requires keeping track of the energy exchanged between the neutrons and the sample (⁠ $ℏ ω$⁠) that are scattered at a defined angle (θ_s or corresponding Q). This type of measurement is called inelastic or quasi-elastic neutron scattering (INS or QENS). INS typically refers to scattering originating from oscillatory motions with a specific timescale and energy transfer and therefore reflects excitation processes in a sample. The $S ( Q , ω )$ shows a characteristic peak at a finite energy transfer ω_p, which follows a dispersion relationship in the $( Q , ω )$ plane. Meanwhile, QENS originates from motions that have a range of relaxation times and associated energy transfers and therefore reflects relaxation processes in a sample. In this case, the $S ( Q , ω )$ is characterized as a broadening of the elastic peak around $ω ≈ 0$⁠, where the degree of the broadening depends on Q. Most spectrometers determine the energy exchanged by analyzing the initial and final neutron energies. Neutron BS and TOF instruments are capable of resolving 1–100 μeV changes in neutron energy, providing dynamics information on picosecond to nanosecond time scales.^15,16 These techniques mostly measure the incoherent or “self” dynamics—the correlations between the relative positions of a given atom at different times—by selecting appropriate Q values and are very useful for determining the diffusion of hydration water, lipids, and even other small molecules embedded in lipid membranes.

As collective membrane fluctuations are much slower than the individual molecular motions, an improved energy resolution spectroscopy is necessary. The NSE technique, which is the highest energy resolution neutron spectroscopy technique,¹⁷ has been developed to measure relaxation times up to 1 μs.¹⁸ It is noted that NSE is mostly applied to measuring coherent dynamics—dynamics that originate from correlations between relative positions of different atoms at different times—or the collective dynamics in lipid membranes. Though the number of examples is limited, NSE has been used to measure self-motions of lipid molecules.¹⁹ This technique also directly measures the ISF, S(Q, t), instead of $S ( Q , ω )$⁠. Because NSE works in the time domain, it is best suited to measuring relaxation processes.

For example, H₂O and D₂O scattering length densities vary by an order of magnitude and in sign, $− 0.56 × 10 − 6$ and $6.36 × 10 − 6$ Å⁻², respectively. When a protiated particle is dissolved in H₂O, the scattering length density of the particle is close to that of H₂O, and therefore, the coherent scattering intensity is not strong. However, if the same particle is dissolved into D₂O, the difference in the scattering length density, i.e., the scattering contrast, is much larger, and we observe strong scattering signals originating from the particle. As such, we choose different deuteration schemes depending on what we want to observe in a neutron scattering experiment.

In the case of lipid bilayers, we may use the following schemes to observe different contributions from different components within the system. In a BS experiment, when protiated lipids are dissolved into D₂O [see Fig. 2(a)], hydrogen motions in the lipids are the target of the observation, while water motions can be focused by employing a sample with perdeuterated lipids in H₂O as shown in Fig. 2(b). In an NSE experiment, when protiated lipids are in D₂O as shown in Fig. 2(c), the neutron scattering contrast provides the structure and dynamics of the whole bilayers. On the other hand, when tail-deuterated lipids are dissolved in D₂O [Fig. 2(d)], internal membrane structure and dynamics are detailed as the scattering contrast is given to distinguish the head groups of the lipids.

For the case of NSE measurements, it is known that the estimated bending modulus from the ZG framework gives larger values than expected. In early studies, researchers used an effective solvent viscosity η_eff, 3–4 times larger than solvent viscosity instead of η to extract reasonable values of κ. The hypothesis for this correction was because the length and time scales covered by NSE are sensitive to the internal dissipation mechanisms, an additional source of friction from the solvent at a short length and time scales may affect the dynamics, as was first proposed for surfactant monolayer dynamics studies.^30,31 It is noted that the artificial factor 3 is known to be avoided when complete expression of ZG formalism is calculated by integrating S(Q, t).^32–34 

The first application of the modification to the ZG framework was performed by Lee and co-workers,⁴⁰ where they estimated the contribution of the second term in the $κ ̃$ was about $10 κ$⁠, or the effective bending modulus measured by NSE was about an order of magnitude larger than κ. Some following studies also suggested that the second term in the expression for $κ ̃$ was about an order of magnitude larger,^41,42 which confirmed that NSE data are quite sensitive to the internal dissipation. This is a unique feature of the application of the NSE technique to measure membrane dynamics as this type of internal membrane dissipation is not readily accessible to other techniques.

Independent of the development of WB,³⁵ Arriaga and colleagues experimentally observed a crossover of the relaxation rate Γ from $Γ ∝ Q 3$ to $Γ ∝ Q 2$ depending on Q. The Q² dynamics was attributed to the intermonolayer slipping mode proposed in the SL model.⁴³ The slipping modes, or hybrid curvature-compression modes as Monroy et al. called them,^43–45 relate to the crucial coupling between bending and lateral compression of the membrane, first pointed out by Yeung and Evans,⁴⁶ and the theoretical dispersion relation was derived in the SL model.^37,38 The hybrid mode is also referred to as a friction mode since it involves the frictional coupling between the two leaflets of the bilayer sliding past with each other. The friction modes relax as $Γ hyb ∼ Q 2$ which was exactly the observed dynamics at relatively higher Q in the NSE experiment on unilamellar vesicles (ULVs) of POPC bilayers.⁴³ They estimated the intermonolayer friction coefficient b, which determines the relaxation time of the friction mode, to be on the order of 10⁹ Pa s/m for the POPC bilayers. While the friction coefficient is one of challenging parameters to experimentally observe (see recent microfluidic experiment results by Anthony and colleagues⁴⁷) NSE has been suggested as another tool to access the mode relating to the interleaflet coupling.

Mell and colleagues studied the friction mode further by comparing the dynamics of DMPC, POPC, and SMPC bilayers.⁴⁴ They measured the NSE signal at room temperature where DMPC and POPC were in the fluid phase. While the friction mode was observed in the case of POPC bilayers, this mode was not certain in the DMPC bilayers. They speculated that molecular disorder favors acyl tail interdigitation in unsaturated POPC compared to the fully saturated DMPC that promotes free-sliding between the bilayers in the case of DMPC bilayers. Consequently, the relaxation is expected to be slower in POPC membranes, which may be the reason why the friction modes appeared in the NSE range for POPC. Furthermore, in the case of SMPC that the bilayers were in the gel phase, and the high coupling expected in the gel phase prevented the detection of the friction mode in the solid-like bilayers. Mell and colleagues discuss more details of NSE data analysis based on the hybrid curvature-compression modes in their papers.⁴⁵ 

As it appears in Sec. III C in more detail, Farago^31,48 and Nagao⁴⁹ independently observed surfactant membrane thickness fluctuations, and later the same mode was confirmed in lipid bilayers.⁴¹ These studies stimulated a theoretical development to consider dynamics of thick membranes. Bingham, Smye, and Olmsted (BSO) proposed an asymmetric membrane theory that considers temporal variations of the bilayer thickness and three contributions in the lipid bilayer dynamics were found; the standard undulation mode, the intermembrane mode which is similar to the sliding mode of SL theory, and the peristaltic mode that corresponds to the thickness fluctuations.⁵⁰ They concluded that thickness fluctuations are driven by the compressibility of the membrane and are damped due to solvent and membrane viscosities. They estimated the predicted thickness fluctuations relaxation time using membrane parameters in the literature, and the predicted relaxation time of $≈ 100$ ns was consistent with the experimental observations by Woodka et al.⁴¹ 

At short time scales accessible to NSE, Gupta and colleagues observed a crossover from short time dynamics to the single membrane fluctuations at about 3 ns in the time dependent mean squared displacement.^9,53,54 By combining computer simulations with their NSE data, they proposed that the short time dynamics reflected the lateral motions of lipids that were restricted to about the size of the molecule.⁵³ Granek, on the other hand, proposed the experimentally observed short time dynamics were possibly due to thickness deformations of wavelengths shorter than the membrane half-thickness.⁵⁵ He pointed out that his interpretation assumes Gaussian statistics, while Gupta's observation included non-Gaussian behavior. Later, Gupta and colleagues used additional data to show their original idea of the lipid motion is a valid explanation for the short time dynamics.⁵⁶ 

More recently, Hoffmann raised a caution for both the short timescale dynamics as well as thickness fluctuations as these data might have been affected by the data quality.³⁴ Also, the estimates of the dynamics parameters could be varied depending on the method of the analysis used,⁵⁷ and there are ongoing active developments in the field to better understanding lipid membrane dynamics. It is also noted here that lipid molecules are known to have tilt degrees of freedom, which creates another dissipation mechanism that is characterized by tilt modulus.^58–62 Although the tilt modulus has not been integrated into the NSE analysis framework, Nagle has shown that the tilt modulus affects the fluctuation amplitude and the value of κ measured by x-ray diffuse scattering (XDS).^63,64 Given the similar length scales of the XDS and NSE experiments, the tilt modulus may also affect the membrane dynamics measured at short times with NSE, and future works should explore these potential effects. In Secs. III B–III I, we review some experimental observations of lipid membrane dynamics and the extracted membrane properties using the analysis frameworks developed to date.

In early NSE studies, the membrane dynamics were measured for hydrated bilayer stacks on a substrate. In the first NSE study of lipid bilayer dynamics, Pfeiffer and colleagues³⁹ prepared highly ordered stacks of DPPC bilayers at a high hydration level. The advantage of using stacked supported bilayers is the ability to specify the scattering vector so that undulations parallel to the membrane surface are selectively measured. The measured ISFs were explained by a single exponential function with the relaxation rate $Γ ∝ Q 2.5$⁠. The exponent was in between a free membrane (⁠ $Γ ∝ Q 3$⁠) and membrane stack as a two-component smectic-A liquid crystal (⁠ $Γ ∝ Q 2$⁠)²³ models. The authors suggested that the measured dynamics were explained better considering the coupling of the local density fluctuations in the top and bottom leaflets to the bending mode, which corresponds to the second mode of the SL theory.³⁷ From their NSE data, they estimated a friction coefficient b of the order of 10⁸ Pa s/m.³⁹ 

In 2006, Rheinstädter, Häuβler, and Salditt performed an NSE experiment on highly ordered stacked DMPC bilayers with a significantly improved energy resolution compared to the first studies by Pfeiffer.⁶⁵ They observed two relaxation processes: a faster mode with relaxation time scales between 1 to 10 ns that originated from mixed undulation dynamics and baroclinic modes, and the other slower mode with a relaxation time of about 100 ns originating from the surface relaxation mode.⁶⁶ They estimated the bending modulus $κ ≈ 14 k B T$ that reasonably agrees with the values measured with other techniques, and the bilayer surface viscosity was estimated to be 16 times larger than that of water. They also observed softening of the membrane undulations right above the main transition temperature. The anomalous swelling behavior that is known as the inter-bilayer distance is anomalously increased right above the melting transition temperature,⁶⁷ and bilayer softening has been observed at the anomalous swelling regions.⁶⁸ Interestingly, Rheinstädter et al. observed membrane softening at a specific length scales of about 420 Å. This length scale is larger than the ripple periodicity, but the authors concluded that the soft mode was linked to the formation of the rippled structure in the lower temperature phase.

Seto and colleagues used non-oriented multilamellar vesicles (MLVs) to observe undulation fluctuations for DMPC bilayers. They applied the ZG model to analyze the NSE data while avoiding the length scale corresponding to the distance between bilayers, where the strong elastic scattering peak hindered the quasi-elastic scattering signal. They observed stiffening of the membranes in the anomalous swelling regimes.⁶⁹ On the other hand, in the work by Kuklin and colleagues,⁷⁰ ULVs were used to measure the relaxation dynamics. In this case, the average relaxation time was faster in the anomalous swelling regions, indicating softening of the bilayers. They concluded that anomalous swelling is induced by the increased short-range repulsive interactions between membranes, and the change in the undulation fluctuations does not affect significantly in the inter-bilayer force balance.

Takeda and colleagues studied free standing lipid bilayers by adding CaCl₂ to the aqueous solvent to enhance inter-membrane charge interactions, which significantly increases the inter-bilayer distance compared to multi-lamellar stacks.^29,71 These free standing membranes are an ideal system for the application of the ZG theory in the dynamic range accessed by NSE.^29,71 Hirai and colleagues measured a mixture of glycosphingolipid, cholesterol (chol), and phospholipid (majority was PC lipid) by means of NSE.⁷² They prepared ULVs by sonicating the lipid aqueous solutions and applied the ZG theory to calculate the bending modulus.

Large unilamellar vesicles (LUVs), which are the current standard membrane geometry for NSE studies of free standing membranes, were first measured with NSE in 2009 by two independent groups.^73,74 Both groups suggested that the NSE data were reasonably well fit with the ZG model. Arriaga and colleagues examined an application of the theory to the NSE data and concluded it gave a reasonable bending modulus for POPC.⁷⁴ On the other hand, Yi, Nagao, and Bossev measured various saturated and unsaturated PC lipid bilayers and observed an increase in the bending modulus with the bilayer thickness while lipid unsaturation softened the membranes.⁷³ These works laid the foundation for the study of undulation dynamics in free standing lipid bilayers using NSE.

In addition, membranes near an air or substrate interface have been studied using grazing incidence neutron spin echo (GINSE). A grazing incident beam can penetrate different depths of the membrane depending on the incident angle, making GINSE a powerful technique to study membrane dynamics as a function of the distance from the interface. The membrane dynamics at interfaces have been studied with GINSE for different lipids and with different additives.^75–79 

Another class of collective membrane fluctuations that can be measured by NSE is thickness fluctuations. The initial studies of thickness fluctuations were done on soap films, where such fluctuations play an important role during film rupture.⁸⁰ In the 1980s, thickness fluctuations in a solvent free lipid bilayer were reported under equilibrium conditions based on laser light reflection results.^81–83 Subsequent work by Haskell et al. studied thickness fluctuations in thin lipid films using reflectance fluctuation spectroscopy.⁸⁴ Huang estimated the thickness fluctuation amplitude to be several tenths of nanometers for glyceryl monooleate-squalene membranes based on a membrane deformation free energy model.⁸⁵ In MD simulations on the scale of several nanoseconds, spectral decomposition of both undulatory and thickness fluctuations in lipid bilayers was observed.⁸⁶ 

In nanometer scale surfactant membranes in solution, Farago first realized there were enhanced fluctuations around the length scale of surfactant membrane thicknesses.^31,48 In an SDS-pentanol–water–dodecane lyotropic phase, he and his colleagues prepared oriented lamellar sheets to measure these dynamics by means of NSE. They found two well-separated relaxation processes: the faster mode was assigned to undulation fluctuations, while the slower relaxations originated from thickness fluctuations, whose relaxation time was estimated to be roughly 3 ns.

The observed relaxation times for thickness fluctuations in the oil-swollen nonionic surfactant bilayers increased from 5 up to 1000 ns as the bilayer thickness increased.⁸⁸ These experiments were performed using deuterated oil and water, so that the coherent scattering was dominated by the surfactant–surfactant correlations. Nagao further studied the effects of the scattering contrast by replacing deuterated oil with protiated oil and concluded that the thickness fluctuations could be measured in both scattering contrasts, but the use of deuterated oil was best for more detailed measurements of the thickness fluctuations.⁸⁹ 

Woodka and colleagues were the first to measure thickness fluctuations in lipid LUVs using NSE.⁴¹ Keeping the same headgroup chemistry, the effects of lipid tail length on the thickness fluctuations signals were studied by employing acyl tail-deuterated DMPC-d54, DPPC-d62, or DSPC-d70 ULVs in D₂O. The ISF measured by NSE followed the ZG prediction; however, a clear enhancement in the dynamics was observed around the length scale of the bilayer thickness. The relaxation time of the fluctuations was estimated to be on the order of 100 ns, which was much slower than the oil-swollen surfactant bilayers with a similar bilayer thickness,⁴⁹ and the fluctuation amplitude was approximately 10%–20% of the bilayer thickness in the fluid phase. In the gel phase, no such enhancement was observed due to much slower dynamics, which was consistent with the computer simulation result by West and Schmidt.⁹⁰ 

In order to know the effects of hydrocarbon tail length on the membrane dynamics, an equimolar mixture of DMPC and DSPC was measured with NSE, in which Ashkar et al. showed that both undulation and thickness fluctuations were enhanced compared to a pure DMPC or DSPC bilayer.⁹⁵ Kelley et al. further studied these mixtures by systematically changing the molar ratio between DMPC and DSPC.⁹⁶ The mixed bilayers were thinner than the composition-weighted average expected based on the single component membranes, while the lipid volumes followed predictions assuming ideal mixing. This suggested that the lipid packing within the bilayer was disrupted and A_L increased in the mixtures. Because of such disruption of the molecular arrangements, the membrane became more dynamic. Interestingly, these changes in the dynamic parameters were well explained by the variation in A_L. Each dynamic parameter, κ, K_A, and η_m, followed their respective scaling functions with A_L that were predicted in some theories for membrane dynamics. The result emphasized the synergy between structure and dynamics of the lipid bilayers.⁹⁶ 

Brüning and colleagues studied undulation fluctuations of DMPC upon addition of lipids with unsaturated acyl tails or charged head groups.⁹⁷ For this study, DMPC was replaced with either DOPC (monounsaturation in both acyl tails) or DOTAP (monounsaturation in both acyl tails and cationic head group) up to a mole fraction of 50% (50 mol. %). The bending modulus κ decreased as the amount of DOPC was increased. A similar reduction of κ was observed for the mixtures of DMPC and DOTAP, and the authors concluded that the charge effects were much less significant than the effects of the unsaturated acyl tails.

Cholesterol (chol) is an essential lipid species in eukaryotic cells, and as such, the effects of chol on the membrane structure and dynamics are still actively studied. In a study by Hirai and colleagues,⁷² a decrease in κ was seen when glycosphingolipid was mixed to DOPC or POPC at a molar fraction of 10%, while addition of chol made the membrane more rigid in the fluid phase. The authors pointed out that the ternary mixture of glycosphingolipid, PC, and chol had a low value κ, suggesting the formation of raft domains softened the membrane and made it more fluid. Arriaga and colleagues measured effects of chol on POPC bilayers.⁹⁸ Considering the contribution from translational diffusion of the vesicles in the analysis, they observed about twofold increase in the bending modulus as the chol increased up to 50 mol. %. They concluded that the observed stiffening effect of chol on POPC bilayers was consistent with the structural condensation caused by hydrogen-bonding between the phospholipids and cholesterol. On the other hand, when Brüning and colleagues measured fluctuation dynamics of DMPC with chol bilayers, they observed a much larger increase in the DMPC membrane bending rigidity. The sixfold increase in the bending modulus of DMPC membranes containing 40 mol. % chol suggested that the POPC molecules partially diminished the condensing effect of chol due to mono-unsaturation in a single acyl tail.⁹⁹ 

Arriaga and colleagues further analyzed the dynamics in POPC/chol mixed bilayers considering the hybrid compression-curvature modes and found that the intermonolayer friction coefficient, b, increased with increasing chol concentration,⁴³ which was consistent with a fluorescent spectroscopy study.¹⁰⁰ The results suggested chol increases the coupling between POPC leaflets and that chol can act as a coupling agent between leaflets. Furthermore, they suggested that chol makes lipid membranes stiffer but also more fluid as it increases the friction between the leaflets.¹⁰¹ These results, the increase in κ for DMPC and POPC bilayers observed by NSE, are consistent with the previous observations with other techniques.^102,103

Chakraborty and colleagues used NSE, solid state deuterium NMR, and MD simulation and observed an increase in the bending modulus with increasing chol concentration in DOPC bilayers.^104,105 They concluded that chol locally increases the bending rigidity of DOPC membranes due to an increase in the packing order. However, previous studies of the same lipid mixtures using micropipette aspiration,¹⁰⁶ XDS,¹⁰³ shape fluctuation spectroscopy, and electrodeformation measurements¹⁰⁷ suggested that chol had almost no effect on the bending modulus of mixed DOPC and chol membranes. These controversial results led to several discussions in the field.^108,109 An interesting point raised by Nagle et al.¹⁰⁸ is that the techniques used in Chakraborty et al. measured the bending dynamics in the time domain and were therefore sensitive to various internal membrane dissipation mechanisms, while other more commonly used static techniques or long length scale measurements are insensitive to these effects.¹¹⁰ This point is still an ongoing discussion but suggests NSE can provide new insight into the role of cholesterol on the dynamics at short length and time scales because NSE is sensitive to the internal dissipation in the membrane.

Mixtures of different lipid molecules are also biologically relevant. For example, myelin membranes are composed of a variety of different molecules, and the myelin sheath is a multilamellar membrane wrapped around axons of neurons to insulate. Multiple sclerosis is a neurodegenerative disease leading to demyelination and axon damage in the human central nervous system. Model mimics of the native and diseased membrane compositions are well-characterized, and Krugmann and colleagues studied structure and dynamics of such mimic myelin membranes. They prepared ULVs with native and diseased membrane mimics and observed an approximate 25% reduction of the lipid membrane bending modulus of the diseased mimic. Although the diseased mimic membranes contained more cholesterol, the amount of sphingomyelin also decreased, and the decrease in κ was attributed to the decrease in sphingomyelin content in the membrane.¹¹¹ 

In order to establish how the elastic properties of soft membranes are affected by protein–membrane interactions, a variety of NSE studies have been performed on lipid bilayers containing various peptides or proteins. Lee and colleagues started this line of studies by incorporating a pore-forming antimicrobial peptides, melittin, into DOPC bilayers.⁴⁰ At low melittin concentrations, below which the ULVs were not all perforated, the bending modulus of the DOPC bilayers decreased with added peptide as the melittin perturbed the acyl tail packing. As the melittin concentration, and the corresponding density of membrane spanning pores increased, the value of κ also increased. This increase was likely due to the high modulus of the pores and inter-pore interactions which had a stiffening effects on the DOPC bilayers.

The effects of similar pore-forming antimicrobial peptides, gramicidin and alamethicin, on saturated DMPC bilayers were studied by Kelley and colleagues.¹¹² At low concentrations where the added peptides had no effect on the overall membrane structure, the effective rigidity of the membranes changed by up to a factor of 2, with gramicidin stiffening the membrane and alamethicin softening the membrane. They also observed enhanced thickness fluctuations at low gramicidin concentrations, while the thickness fluctuations were dampened all studied alamethicin concentrations as well as at higher concentrations of gramicidin. They suggested that the incorporation of gramicidin at low concentrations accelerated the membrane dynamics by decreasing the membrane viscosity, and these enhanced fluctuations that may help increase the probability of gramicidin dimerization needed to form transmembrane pores as was theoretically predicted in work by Helfrich and Jakobsson.¹¹³ Their results suggested that adding peptides may simultaneously increase the bending modulus while decreasing the membrane viscosity, which may indicate that the elasticity and viscosity of membranes can be tuned independently. Moreover, these studies highlight that the general term of “fluidity” does not always correspond to changes in membrane elasticity.

In a slightly more complicated bilayer mixtures, effects of amyloid-β proteins on the structure and dynamics were studied by Hirai and colleagues.¹¹⁴ They prepared LUVs composed of a glycosphingolipid (G_M1), chol, and DOPC or DPPC. Complementary SAXS studies showed that the G_M1-chol domains were preferentially located on the outer leaflets. In turn, amyloid-β proteins are assumed to be bound to the negatively charged G_M1-chol rich domains. The NSE studies showed that the fluid lipid membranes were significantly stiffened due to the amyloid-β binding to the G_M1/chol/DOPC membranes, while only a slight increase in the bending modulus was measured for the gel phase membranes (G_M1/chol/DPPC). Based on these findings, the authors concluded that such a change in membrane dynamics could be involved in the onset of some amyloid disorders diseases. Moreover, Heller and Zolnierczuk showed that the conformational change of a bound HIV-1 fusion peptide derivative increased the bending modulus of DMPC/DMPG (a molar ratio of 7/3) LUVs.¹¹⁵ Circular dichroism spectroscopy indicated that peptide had an α-helical conformation at a low concentrations (peptide to lipid ratio, $P / L ≈ 1 / 200$⁠) but adopted a β-sheet conformation at a high peptide concentration (⁠ $P / L ≈ 1 / 50$⁠). The bilayers were also thickened and stiffened by addition of these high peptide concentrations. As the β-sheet conformation is related to fusion in the native fusion protein sequence, the observed increase in bending modulus could have implications for the function of the fusion peptide.

Compiling the results of these studies suggests that the addition of peptides that form β-sheet tend to stiffen lipid bilayers, while the effects of α-helical peptides appear to be more complicated. To better understand the effects of α-helical peptides on the membrane structure and dynamics, Qiang and Zolnierczuk studied the effects of aurein 1.2 peptide, one of the shortest α-helical antimicrobial peptide found in nature, on a model lipid membrane composed of DMPC and DMPG using a combination of SANS and NSE.¹¹⁶ Upon addition of the peptide, the membrane became softer at $P / L = 1 / 100$⁠, while at a higher peptide concentration of $P / L = 1 / 30$⁠, the membrane became stiffer. The authors suggested that the changes in the membrane properties caused by the peptides are due to a delicate balance of several competing factors. A detailed understanding of these different factors is imperative to precisely control or modulate the interactions when improving the performance of antimicrobial peptides. For example, recent studies of the effects of SARS-CoV-2 fusion peptide on the properties of biomembranes showed incorporation of the peptides made the membrane more rigid.¹¹⁷ 

Instead of encapsulating peptides or proteins into membranes, Gilbert and colleagues encapsulated two different proteins, β-galactosidase or aspartic protease, into the water channels in lipid sponge phase nanoparticles.¹¹⁸ These enzymes are used in various processes in the food industry. Combined studies of the protein and membrane properties showed that enzymes retained their activity in the water channels and also stiffened the host membrane composed of diglycerol monooleate, glycerol monooleate, and polysorbate that encapsulated the water channels. The stiffening effects seen in the case of aspartic protease were most likely caused by hydrogen bonding between amino acids in the protein and carbonyl groups in the lipid head groups, which replaced the water–carbonyl hydrogen bonds, as shown by the MD simulations.

Nonsteroidal anti-inflammatory drugs (NSAIDs) are the most widely used drugs for their antipyretic, analgesic, and anti-inflammatory actions. The effects of the NSAIDs on the membrane dynamics have been studied using NSE by several groups. Boggara and colleagues studied effects of pH and ibuprofen on the dynamics of DMPC bilayers.¹¹⁹ The membrane rigidity was almost constant between pH = 5 and 7, but lower at low pH. Upon addition of ibuprofen, the bilayers became softer, and the rigidity did not change significantly with changing pH. By combining SANS and MD simulations, they explained the results considering the lipid head group hydration and ibuprofen partitioning into the membrane. Contrary to this result, Jaksch and colleagues observed a stiffening effect in GINSE studies of SoyPC bilayers containing ibuprofen.⁷⁶ They suggested this stiffening might be related to long-term toxic effects of some NSAIDs. Sharma and colleagues studied general effects of NSAIDs, including ibuprofen, aspirin, and indomethacin, on the dynamics of DMPC bilayers.¹²⁰ Their NSE results showed a softening of the bilayers upon addition of the three NSAIDs. They concluded that incorporation of NSAIDs modulates the mechanical properties of the membrane, which may in turn affect physiological processes. The effects of acetaminophen on the DOPC bilayers were studied by De Mel and colleagues.¹²¹ Although acetaminophen is not considered an NSAIDs because it does not have significant anti-inflammatory activity, like NSAIDs, acetaminophen is a small aromatic molecule used to treat pain. De Mel et al. observed softening of the membrane upon addition of acetaminophen using NSE, but SANS suggested the bilayer structure was unchanged. They further suggested that the short time lipid motions were enhanced by the addition of acetaminophen because the drug molecule increased the space between lipid molecules.

The effects of a local anesthesia, lidocaine, on membrane dynamics have also been studied with NSE. Yi and colleagues demonstrated that lidocaine modified the bilayer structure by increasing the A_L and decreasing the thickness of DMPC bilayers containing with 5% of DMPG.¹²² The NSE measurements showed an increase in the bending modulus in the fluid phase upon lidocaine addition, while the temperature dependent change of the bending modulus was less steep across the main transition temperature. Similar effects were observed when a saponin, aescin, was incorporated into DMPC bilayers.¹²³ Aescin had anti-inflammatory and anti-edematous properties and is used to treat chronic venous insufficiency. They observed softening of the membrane below the main transition temperature of DMPC, while the membrane becomes more rigid at high temperatures with aescin addition. They concluded that the large triterpenic backbone stiffened the bilayers at high temperatures, while hydrogen bond formation between the hydroxyl groups of aescins sugar moieties with the carbonyl and negatively charged phosphate groups of DMPC seems to have an important effect on the bending modulus at low temperatures.

The effects of vitamin E acetate, which is a potential instigator of electronic-cigarette/vaping-associated lung injury (EVALI), on the dynamics of a model pulmonary surfactant without proteins have also been studied with NSE.¹²⁴ DiPasquale and colleagues constructed pulmonary surfactant mimics composed of DPPC, POPC, POPG, and chol and investigated the effects of varying amounts of vitamin E acetate on the membrane rigidity. Interestingly, the pulmonary mimic was more rigid than the pure DPPC bilayers; however, the addition of vitamin E acetate softened both the pulmonary surfactant mimic and pure DPPC bilayers. The authors stated that although it remains to be seen if vitamin E acetate is the sole culprit of EVALI, the data suggest vitamin E acetate is capable of reducing the elastic properties of the pulmonary surfactant that plays a vital role in respiration.

Cardiolipin (CL) lipids are a class of anionic phospholipids that are found predominantly in the inner mitochondrial membrane of eukaryotic cells and in the plasma membranes of certain bacteria. This class of lipids is composed of two phosphate moieties, and the linkage between the two phosphates restricts their mobility and reduces the headgroup volume compared to other classes of phospholipids. This smaller headgroup volume is what allows CL lipids to form non-lamellar structures. Pan and colleagues studied the structure and dynamics of tetraoleoyl CL bilayers using densitometry, SANS, SAXS, and NSE together with MD simulations.¹²⁵ They measured the molecular volume, area per lipid, and the bilayer thickness together with the bilayer bending modulus. Notably, the results showed that CL bilayers had a much larger κ than DMPC or DOPC bilayers despite also having a significantly larger A_L. Castillo and colleagues mixed a model CL with other lipids to create a more complex mimic of mitochondrial membranes and studied the effects pancratistatin, a natural anti-cancer agent, on the dynamics of the inner mitochondrial membrane.¹²⁶ They observed an increase in the bending modulus upon addition of pancratistatin, and the changes in membrane properties could result in the relocation and release of cytochrome c to initiate the apoptosis cascade in cells.

There are a number of other organic and inorganic compounds found in nature that interact with biological membranes. Inspired by compounds that are known to contaminate the food chain, Brüning and Farago studied the effects of perfluorooctanoic acid on the mechanical properties of DMPC bilayers.¹²⁷ Perfluorinated compounds are widely used to prepare fire-extinguishing foams, anticorrosion agents, and lubricants and are known to persist in the environment.¹²⁸ As such, Brüning and Farago measured the NSE signal from the DMPC ULVs with and without a mole fraction of 5% or 10% perfluorooctanoic acid, and the membrane relaxation dynamics were observed to slow down. This slowdown was associated with an increase in the bending modulus of the DMPC bilayers upon addition of perfluorooctanoic acid.

Usuda and colleagues studied effects of alkanes on the dynamics of DPPC bilayers.¹²⁹ They kept the mole fraction of alkane constant 40% and increased the chain length i from octane (C8) to tetradecane (C14). The longer alkanes were observed to condense in the bilayer center. Although the bilayer thickness did not increase significantly, κ decreased while the K_A values extracted from measurements of the thickness fluctuations increased with increasing the number of carbons in the alkanes. The opposite trends in κ and K_A were explained as a change in β, and the authors suggested that intermonolayer coupling decreased when the oil molecules condensed at the center of the bilayers. Misuraca and colleagues studied the effects of linear and branched alkanes on the membrane dynamics in model protocell membrane vesicles.¹³⁰ The effects of the studied alkanes depended on the temperature, where softer membranes were formed at low temperatures, while slightly more rigid bilayers were formed at high temperatures. As the membrane stability increased at high temperatures upon addition of the alkanes, the authors concluded that the alkanes helped maintain the lamellar structure of the protocell membranes at high temperatures, as these lipid compositions would prefer to form micelles at these temperatures if the alkanes were not incorporated. As such, the inclusion of alkanes into protocell membranes might have been one way early cells survived at high temperature conditions.

Instead of specifically incorporating hydrocarbon chains in the hydrophobic region of the lipid bilayers, Kumari and colleagues incorporated an imidazolium ionic liquid to DMPC bilayers.¹³¹ The ionic liquids were dispersed at the bilayer–water interface, and the NSE results indicated the bending modulus increased when the hydrophobic cation was incorporated into the bilayer. Hoffmann and colleagues studied the influence of the adsorption of small silica nanoparticles to the outer vesicle surface.¹³² While the silica nanoparticles did not significantly affect the vesicle structure, they did make the membrane softer. Meanwhile, Chakraborty and colleagues studied the effects of encapsulating hydrophobically modified gold nanoparticles into the hydrophobic region of the bilayers on the membrane dynamics.¹³³ They observed a softening of DPPC bilayers upon incorporation of the gold nanoparticles.

Another class of additives that interacts with lipid bilayers is polymers. Polymers are sometimes used as to coat liposomes for drug delivery applications to introduce “stealth” properties¹³⁴ or used to protect cell membranes from various dysfunctions. To understand how adding polymers affect the membrane structure and dynamics, De Mel and colleagues mixed poly(ethylene oxide)-mono-n-octadecyl ether with DOPC bilayers.¹³⁵ The hydrophobic octadecyl group attached to the polymer resided in the lipophilic hydrocarbon core of the bilayer and disrupted the lipid packing, and thereby lead to a reduction in the membrane bending modulus. Contrary to this result, Wang et al.¹³⁶ and Yu et al.¹³⁷ showed that incorporation of triblock copolymers stiffened bilayers. Wang and colleagues prepared poly(methacryloyloxyethyl phosphorylcholine)-poly(propylene oxide)-poly(methacryloyloxyethyl phosphorylcholine) triblock copolymers that effectively function as membrane-targeting cellular rescue agents.¹³⁶ The bending modulus of DMPC bilayers increased upon addition of the block copolymer both in the fluid and gel phases. Likewise, Yu and colleagues studied the effects of an end-phosphorylated polyethylene glycol triblock copolymer with a hydrophobic bisphenol A center on the membrane properties.¹³⁷ This class of polymer is used as the virulence-directed agent for treating diseases and disorders involving microbial pathogens. Although the polymer did not change the membrane structure significantly, an increase in the membrane bending modulus was observed. These studies highlight the importance of the end functional groups in determining the effects polymers have on lipid vesicles. Studies on the effects of polymers on membrane dynamics should be extended to understand the effects of extracellular macromolecules found in nature in the future.

Here, we see how internal membrane structures affect the membrane dynamics. The first example is the bending modulus measured in phase separated DMPC and DSPC mixed bilayers with coexisting fluid and gel domains.¹³⁸ As DMPC and DSPC differ in acyl tail length by four carbons, the melting transition temperature differs about 30 K. Depending on the mixing ratio between DMPC and DSPC, the membrane segregates into gel and fluid phases in-between the melting transition temperatures and forms global domains. Kelley, Butler, and Nagao measured the bending fluctuations in this gel–fluid coexistence region and showed that the effective bending modulus followed the area fraction of the gel domains. Furthermore, the experimental data were well explained using a theoretical model for the effective rigidity of a membrane containing an inhomogeneous distribution of a rigid phase.¹³⁹ On the other hand, studies by Hirai and colleagues focused the dynamics of membranes containing small domains, specifically, model raft-domains, to study the overall membrane properties.^72,114

A completely different approach was taken by Nickels and colleagues, in which they focused on the dynamics of small raft domains by employing the neutron contrast matching technique.¹⁴⁰ They isolated the $≈ 13$ nm diameter nanodomains residing in $≈ 60$ nm ULVs by employing appropriate deuteration schemes. The observed bending modulus of the nanometer sized domains appeared to be different from the modulus of the surrounding continuous phase. The results suggested that mismatches in bending modulus between domains and the matrix should be accounted for when explaining the emergence of lateral heterogeneities in lipid systems. On the other hand, lateral diffusion of nanometer sized domains on lipid vesicles was studied by Sakuma and colleagues using NSE.¹⁴¹ The obtained diffusion coefficient was explained in terms of the hydrodynamic model of Brownian objects in a fluid membrane.¹⁴² These examples lay the foundation for the studies of the dynamics of domains in lipid bilayers, which we expect will further be explored using neutron scattering techniques in future.

In contrast to the effects of lateral heterogeneity in membrane caused by the presence of domains, Rickeard and colleagues considered the effects of transverse heterogeneity in membrane properties by studying the dynamics of asymmetric bilayers.¹⁴³ The asymmetric vesicles were composed of an outer leaflet enriched in egg sphingomyelin (ESM) and an inner leaflet enriched in POPE and prepared using a cyclodextrin-mediated exchange protocol. Notably, the bending fluctuations of the asymmetric bilayers measured by NSE showed trends not predicted by their symmetric counterparts. The asymmetric bilayers show suppressed bending fluctuations compared to the symmetric bilayers, and the authors concluded that the compositional asymmetry and leaflet coupling influence the internal dissipation within the bilayer and result in membrane properties that cannot be directly predicted from corresponding symmetric bilayers.¹⁴³ 

Since biomembranes are much more complicated than synthetic model membranes, the bottom up approach taken in the examples shown in this subsection help develop a fundamental understanding of the properties of membranes that will be useful in future studies of more biologically relevant systems.

In this subsection, we overview NSE studies more complex biologically and relevant systems, cell-derived membranes, and even cells themselves. Nickels and colleagues studied the fluctuation dynamics of Bacillus subtilis lipid extract, which contained PE, PG, CL, and lysyl-PG lipids in addition to neutral lipids (mostly diacylglycerol).¹⁴⁴ The extract also contained a distribution of saturated branched and unbranched fatty acids. They then measured the bending modulus of the lipid vesicles prepared from the lipid extract and compared the results with molecular dynamics simulations. More recently, Himbert and colleagues measured human red blood cell membrane dynamics using a combination of XDS, NSE, and computer simulations.¹⁴⁵ All these techniques showed that the red blood cell membranes without cytoskeletal networks are softer than synthetic model biological membranes. The authors suggested that nature has designed the red blood cell to be soft for reasons including in the permeability of gas molecules and to accommodate possible local area changes.

In situ studies of photosynthetic machinery in cyanobacterial cells were performed by Stingaciu and colleagues.^146,147 The flattened membrane structure in cyanobacterial cells, called thylakoids, responds to variations in environmental conditions, and there are corresponding changes in the membrane properties. In particular, the thylakoid membrane undulatory motions in vivo were measured with and without light exposure, and the authors observed that the membranes were softer in the dark conditions than in high light conditions. They concluded that electron transfer between photosynthetic reaction centers and the associated electrochemical proton gradient across the thylakoid membrane result in a significant driving force for excess membrane dynamics.¹⁴⁶ They further studied the effects of disrupting the photosynthetic electron transfer by treating the thylakoid membrane with a chemical: 3-(3,4-dichlorophenyl)-1,1-dimethylurea. They found that the disruption pathway rigidified the native membranes in the dark cycle yet softened the membrane in light conditions. A slowdown of the membrane fluctuations under the dark condition was also observed for thickness fluctuations. The disrupted electron transfer chain and the decreased proton motive force within the lumenal space partially explain the observed changes in the mechanical properties of the membranes and support the hypothesis that the photosynthetic process is tied to thylakoid rigidity in the cyanobacterial cell.¹⁴⁷ 

The collective membrane fluctuations discussed in Sec. III are limited to length scales of the long and short wavelength cutoffs. The long wavelength cutoff is usually taken as the particle or membrane patch sizes, while the short wavelength cutoffs corresponds to approximately the membrane thickness. The dynamics of lipid and surrounding molecules at even shorter length scales and close to the molecular scales have also been investigated by means of incoherent QENS.^5,6,10,148

A comprehensive series of experiments on lipid molecular motions were performed by Sackmann and co-workers starting in 1988. Pioneering work using an ultracold neutron gravity spectrometer was performed by Pfeiffer et al., and they determined that the lateral diffusion constant of a lipid molecule was $D = 2.6 × 10 − 7 cm 2 / s$ which was slightly larger than the value obtained by the photobleaching technique.¹⁴⁹ They then extended their study to verify the details of dynamical behavior of lipid molecules by incoherent QENS. They showed the differences in the dynamics of individual lipid molecules in the gel and fluid phases and interpreted their properties applying the concept of the packing density.^150,151 They also investigated the dynamics of hydration water using perdeuterated DPPC (DPPC-d75) deposited on a substrate and solvated with either H₂O or D₂O. They observed no anisotropy of the water dynamics normal and parallel to the lipid membrane depending on the orientation. Moreover, only rotational motions of water molecules were observed at low hydration levels, and jump diffusive motions similar to bulk water were seen in highly hydrated membranes.¹⁵² In the final paper by these authors, they investigated the hydration dependence of the local diffusion as well as the acyl tail motions of DPPC molecules. The results showed that the QENS spectra from the fluid phase were not explained by acyl tail dynamics alone, and the diffusion of the molecule within its solvation cage must also be considered to fit the data.¹⁵³ 

In 2005, Rheinstädter et al. published their first paper on the dynamics of lipid molecules and the hydration water.¹⁵⁴ They measured the dynamics of a mixture of DMPC-d54 and D₂O with a BS spectrometer and observed coherent scattering from the acyl tails and interstitial water. Based on these results, they discussed the freezing of the acyl tails and reported a second freezing transition that they attributed to the hydration water. In the following papers, they identified two types of motions; a fast relaxation process associated with the translational diffusion of the lipid and water molecules, and the slow collective motion in lipid membranes occurs over several lipid distances.^19,155,156 Following these works, Busch et al. investigated the mechanism of long-range diffusion in DMPC lipid membranes using a TOF spectrometer.¹⁵⁷ They concluded that the lipid dynamics were not confined in the fluid phase, and individual lipid molecules flow with their neighbors as a dynamically assembling patch across the membrane.¹⁵⁷ Meanwhile, Wanderlingh et al. measured QENS spectra for POPC and DOPC and showed the presence of three types of motions: slow diffusion of the entire phospholipid molecules in a confined cylindrical region, conformational motions of the acyl tails, and fast uniaxial rotations of the hydrogen atoms around their carbon atoms.¹⁵⁸ The most recent developments on the local dynamics of lipids were made by Peters and co-workers. They built a theoretical framework and derived the corresponding analytical expressions for the ISFs measured with QENS. The model is named “dynamical Matryoshka model” and describes the dynamics of lipid molecules as a nested hierarchical convolution of three motional processes. This model was then used to fit the QENS signals from DMPC and DMPG membranes and successfully described the dynamics in supported bilayers as well as MLVs.^159–161 

The effect of additives on the lipid molecular motions have also attracted the attention of several research groups. Rheinstädter and co-workers studied the effect of chol on the nanosecond lipid dynamics using triple-axis, BS, and NSE spectrometers. They found that adding chol resulted in a pronounced stiffening of the membranes on the nanometer length scale both in the gel and fluid phases, and at the same time, the collective nanoscale diffusion was significantly slower.^162–164 Sharma et al. investigated the effect of antimicrobial peptides on the dynamics of DMPC membrane and showed that the peptides caused an enhancement in the lateral motions of lipid molecules in the gel phase but had a stiffening effect in the lipid fluid phase. Additionally, they showed the effects of the peptides on the lipid dynamics disappeared in the membranes containing 20 mol. % chol.^165,166 Sharma et al. also investigated the effects of an amyloid β peptide as well as aspirin on the membrane dynamics and discussed the potential relationships between the effects of these added molecules and their biological functions.^120,167 They further extended their studies to reveal the dynamics of a membranes made from liver lipid extracts in the presence of an ionic liquid.¹⁶⁸ A recent contribution by Santamaria et al. focused on how the SARS-CoV-2 fusion peptide affected the membrane properties and the influence of Ca ions and chol in the fusion process. From a set of NR, SANS, and QENS experiments, they proposed a molecular mechanism for SARS-CoV-2 cell entry.¹¹⁷ 

Following the pioneering work by König et al. in 1994, the hydration water dynamic in the vicinity of lipid membranes was revisited by Swenson et al. in 2008.¹⁶⁹ They prepared three samples: fully protiated DMPC with heavy water (DMPC/D₂O), acyl tail deuterated DMPC with heavy water (DMPC-d54/D₂O), and acyl tail deuterated DMPC with light water (DMPC-d54/H₂O). The dynamical behavior of the water molecules was obtained by subtracting the QENS data measured for the DMPC-d54/D₂O sample from that of DMPC-d54/H₂O. From the Q dependence of the relaxation time, they concluded that the water relaxation process is that of jump diffusion, and the diffusion constant was lower than that of bulk water by only a factor of two.

In 2015, further QENS experiments on the dynamics of hydration water molecules in orientated membranes were performed by Rheinstädter and colleagues.^170,171 They analyzed the QENS data using the Kohlrausch–Williams–Watts function and concluded that the hydration water dynamics were anisotropic and sub-diffusive in nature at nanometer-length scales. In order to compare the dynamics of water and lipid molecules, Yamada et al. prepared two samples: perdeuterated DMPC (DMPC-d67) with H₂O and protiated DMPC with D₂O.¹⁷² They categorized the hydration water into three types: free water with dynamics slightly different from that of bulk water, loosely bound water with dynamics one-order of magnitude slower that of free water, and tightly bound water with comparable dynamics to that of DMPC molecules. The slow dynamics of the loosely and tightly bound water compared to bulk water were also reported in a MD simulation, where the tightly bound water that form strong hydrogen bonds with DMPC had a translational diffusion coefficient 20 times smaller than that of bulk water.¹⁷³ These QENS and MD simulation results also were quantitatively consistent with those measured by DSC¹⁷⁴ and terahertz spectroscopy.¹⁷⁵ Further studies have been done to investigate the effects of metal cations bound at phospholipid headgroups on the hydration water dynamics.¹⁷⁶ The results suggested that the number of loosely bound water molecules is determined by the nature of the phospholipid membrane.

So far, we have seen studies of collective membrane dynamics in which NSE was used to measure the undulation and thickness fluctuations on length scales similar to or greater than the bilayer thickness. At the molecular level, measuring the incoherent scattering originating from hydrogen atoms in lipid or water molecules using BS or TOF instruments, molecular motions such as diffusion of the individual lipid and water molecules as well as acyl tail motions were studied. In addition to these studies, collective motions of the acyl tail structural correlations have been measured to further understand the origins of membrane properties. The acyl tail correlation peak seen in scattering data at $Q ≈ 1.5$ Å⁻¹ originates from the lipid molecular packing and has traditionally measured in x-ray diffraction to determine the structure of the lipid molecular packing and to estimate the distances between the acyl tails and/or A_L.^177–180 These correlation peaks are also observable in neutron scattering measurements when the hydrogens in acyl tails are replaced with deuterium.

Chen and colleagues were the first to measure the collective acyl tail correlation dynamics in DLPC membranes using inelastic x-ray scattering.¹⁸¹ They observed three eigen modes, two of which appeared at the energy scales of $≈ ± 7$ meV (corresponding to sub ps time scales) and the other appeared around an energy exchange $ω ≈ 0$⁠. They concluded that the two of the three eigen modes originated from the sound mode, and the other mode was related to the thermal diffusivity of the lipids. Rheinstädter and colleagues built upon this study and measured INS from employing DMPC-d54 membranes.¹⁸² They also observed the three eigen modes, and in addition, they observed an additional mode at $ω ≈ 0$ which they attributed to additional intramolecular degrees of freedom and contributions from incoherent scattering.

Further neutron spectroscopy studies by Rheinstädter and colleagues using a higher energy resolution BS spectrometer allowed them to probe energy ranges from $∼ 1$ to $∼ 10 μ$ eV.¹⁵⁶ They measured the dynamics of DMPC in D₂O, which were predominantly the incoherent dynamics from the hydrogen atoms in the DMPC molecules. They also measured the dynamics of DMPC-d54 in D₂O, which were predominantly the coherent dynamics of the acyl tail correlations. Comparing the spectra from the two samples showed that contrary to the incoherent dynamics, where the relaxation time decreased with increasing Q, coherent signal showed a maximum relaxation time of about 50 ps in the fluid phase at Q values corresponding to the acyl tail correlation peak.

Nagao and colleagues extended the energy resolution further by employing NSE and Mössbauer time domain interferometry (MTDI)¹⁸³ and study the acyl tail correlation dynamics over a combined dynamic range from a few ps up to 300 ns.¹⁸⁴ In the fluid phase of DMPC bilayers, they observed two relaxation modes with relaxation times of $≈ 30$ and $≈ 500$ ps, and the relaxation times did not change significantly with temperature. The relaxation time of the faster mode measured in these studies was consistent with the previous observation by Rheinstädter et al.,¹⁵⁶ while the slower mode measured with NSE was outside of the energy resolution of the BS spectrometer and not seen in the previous studies. Nagao et al. explained these two modes as the density modes of the acyl tails (faster mode) and of the lipid molecules (slower mode). Interestingly, the density mode of the acyl tails was about an order of magnitude slower than the structural correlation dynamics of an analogous linear alkane (tetradecane) that has the structural relaxation times of about 3 ps in a bulk solution.¹⁸⁵ On the other hand, the slower mode was attributed to rearrangements of the lipid molecules within the membranes, and the measured relaxation time agreed well with a previous NMR study of lipid diffusion.¹⁸⁶ In the gel phase, the structural correlations were heterogeneous, and the measured relaxation time changed with varying temperatures from 10 to 100 ns.

Employing a relationship for the structural relaxation time scales and the macroscopic liquid viscosity in three dimensional molecular liquids,^187,188 Nagao and colleagues estimated the membrane viscosity of two-dimensional lipid bilayers. The calculated membrane viscosity using the relaxation time attributed to the lipid molecular rearrangements (slower mode in the fluid phase) fell in the middle of the broadly distributed values for membrane viscosity reported in the literature, and the authors concluded that the lipid molecular rearrangements within the membrane were the origin of the membrane viscosity.¹⁸⁴ This study opened up a new strategy to identify the molecular origins of the membrane viscosity.

Here, we reviewed measurements of the individual and collective lipid dynamics measured with neutron scattering techniques. The studied dynamics include lipid molecular rotational and translational diffusion within the membrane, acyl tail dynamics, as well as the collective undulation and thickness fluctuations of the membranes. These motions occur at different length and time scales from sub Å to tens of nm in length and sub ps to sub μs in time scales that are accessible with neutron scattering techniques. The effects of different lipid compositions and various additives on the membrane dynamics have been studied by various groups, and the number and complexity of such membrane studies continue to grow. As the cell membrane is complicated, more detailed understanding of the molecular mechanisms of bilayer formation, stability, and functionality is demanded. The current efforts toward understanding the dynamics in model lipid membranes are essential as studies move to more and more complex systems, specifically, the work reviewed here lays the foundation for understanding future studies of lipid–protein interactions. These studies may also help connect lipid molecular movements to the elastic and viscous properties of lipid bilayers in the future.

Although the spatiotemporal capabilities of neutron scattering instruments well suited for the study lipid membrane dynamics, the number of neutron spectrometers is limited. Increasing the amount of beam time by increasing the number of instruments or increasing the neutron flux will help accelerate to understanding molecular mechanisms of membrane dynamics. Moreover, recent developments in neutron spectroscopy techniques further enhance the accessible dynamic ranges. For QENS studies, the development of the high resolution BS spectrometer IN16B enhances the highest energy resolutions compared to those of conventional BS instruments.¹⁸⁹ Recent advances of NSE technology is also enhancing the time resolution of the technique, and it is now possible to extend the measurement times up to 1 μs on state of the art NSE instruments.^18,190 While the ns time range is sufficient to observe thermal fluctuations in model systems, many biological processes occur at time scales beyond thermal fluctuations, and extending the time resolution of the NSE technique to even longer time scales will allow access to such processes in the future. Another interesting development in the QENS field is the efforts to separate the coherent and incoherent scattering contributions by employing polarization analysis.^191–194 Polarization analysis enables precise separation of the collective and self-motions^195,196 and will be highly beneficial for lipid membrane studies. Most importantly, the neutron spectroscopy techniques reviewed here are accessible to general users through a proposal program at each facility worldwide. We encourage interested readers to contact instrument scientists at your facility of preference and develop ideas for new theories and experiments.

The authors are grateful to Dr. E. G. Kelley for the critical reading of the manuscript. M.N. acknowledges the support from the Center for High Resolution Neutron Scattering (CHRNS), jointly funded by the National Institute of Standards and Technology Center for Neutron Research and the National Science Foundation under Agreement No. DMR-2010792. H.S. was supported by JSPS KAKENHI, Grant-in-Aid for Scientific Research on Innovative Areas No. JP19H05717.

The authors have no conflicts to disclose.

Michihiro Nagao: Conceptualization (equal); Writing – original draft (lead). Hideki Seto: Conceptualization (equal); Writing – original draft (supporting).

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

Instrumentation

BS

backscattering

DLS

dynamic light scattering

DSC

differential scanning calorimetry

DSF

dynamic structure factor

EISF

elastic incoherent structure factor

GINSE

grazing incidence neutron spin echo

INS

inelastic neutron scattering

ISF

intermediate scattering function

MD

molecular dynamics

MTDI

Mössbauer time domain interferometry

NMR

nuclear magnetic resonance

NR

neutron reflectometry

NSE

neutron spin echo

QENS

quasielastic neutron scattering

SANS

small-angle neutron scattering

SAXS

small-angle x-ray scattering

TOF

time-of-flight

XDS

x-ray diffuse scattering

Membrane theories

BSO

Bingham, Smye and Olmsted

SL

Seifert and Langer

WB

Watson and Brown

ZG

Zilman and Granek

Chemicals

chol

cholesterol

CL

cardiolipin

C₁₂E₅

pentaethylene glycol monododecyl ether

DLPC

dilauroyl-phosphocholine

DMPC

dimyristoyl-phosphocholine

DMPG

dimyristoyl-phosphoglycerol

DOPC

dioleoyl-phosphocholine

DOPG

dioleoyl-phosphoglycerol

DOTAP

dioleoyl-trimethylammonium-propane

DPPC

dipalmitoyl-phosphocholine

DSPC

distearoyl-phosphocholine

ESM

egg sphingomyelin

G_M1

ganglioside GM1

PAzPC

palmitoyl-azelaoyl-phosphocholine

PC

phosphocholine

PE

phosphoethanolamine

PG

phosphoglycerol

POPC

palmitoyl-oleoyl-phosphocholine

POPE

palmitoyl-oleoyl-phosphoethanolamine

POPG

palmitoyl-oleoyl-phosphoglycerol

SDS

sodium dodecylsulphate

SMPC

stearoyl-myristoyl-phosphocholine

SoyPC

L-α-phosphocholine

General

EVALI

electronic-cigarette/vaping-associated lung injury

HIV

human immunodeficiency virus

LUV

large unilamellar vesicle

MLV

multilamellar vesicle

NSAID

nonsteroidal anti-inflammatory drug

SARS-CoV

severe acute respiratory syndrome-associated coronavirus

ULV

unilamellar vesicle