Chemistry and Physics of Lipids Long-range excitations in phospholipid membranes

We investigated the existence of long-range excitations and correlated structures in phospholipid membranes by means of grazing-incidence neutron spin echo spectroscopy, grazing-incidence small-angle neutron scattering, and corresponding theoretical calculations inspired by smectic-membrane theory. All these methods con ﬁ rmed the existence of thermal excitations in the plane of the surface of the phospholipid membranes or the corresponding structures, respectively. Also, these measurements revealed a temperature dependence of these ex- citations. These excitations are associated with 100nm in-plane correlations around physiological temperatures and of 75nm at 16°C. A single excitation has an energy around the μ eV-regime. A temperature series revealed a high abundance at physiological temperatures and pronounced long-range in-plane structures, which are strongly suppressed at temperatures below 20°C. From the length-scales and energy transfers involved we surmise that these excitations may play a role in several functions of the cell membranes such as stability and energy dissipation along the membrane. From a fundamental point of view, the observed behavior of those excitations is congruent with that of a quasi-particle (surface mode phonon, smomon ) that exists in the plane of phospholipid membranes.


Introduction
Investigating and understanding the dynamics of phospholipid membranes is of vital importance for the understanding of mechanisms in nature that are based on such membranes. That includes phenomena such as the transition of material through a cellular membrane by diffusion, endocytosis, exocytosis or transcytosis (Wolkers et al., 2003). This presents potential in the areas of drug delivery (Cevc, 1997;Touitou et al., 2000;Jaksch et al., 2016) and interplay between cellular behavior and phospholipid membranes (Tanaka, 2013). Additionally, also the behavior of the membranes themselves without additional constituents may be of interest, when for example considering membrane stability, or stability against outside stimuli. For example, this can play a role in phospholipid membranes lubricating mammalian joints (Mirea et al., 2013). Any of those fields is both of basic interest in fields such as biology, pharmacology and medical sciences and has a direct applicability in those fields.
In addition to those fields, also the in-plane diffusion in the membrane (Armstrong et al., 2014(Armstrong et al., , 2013 may be affected by the long-range excitations that are reported here. While that takes place on a different time-and length-scale it is conceivable that long-and short range excitations in a membrane are not completely decoupled. An overview on neutron (Fragneto and Rheinstädter, 2007) and Xray (Salditt, 2005) techniques applied to biological membranes was delivered by Fragneto and Rheinstädter or Salditt, respectively. The dynamic behavior of phospholipid membranes is of special interest in that context, as it governs the mechanisms of movement associated with the membranes. In our previous publication (Jaksch et al., 2017) we were able to show the existence of an hitherto unobserved eigenmode of such membranes. Those modes here we associate with an in-plane structure as identified by Bragg peaks at Q ∥ ≈ 0.01 Å −1 . This mode was found using grazing-incidence neutron spin-echo spectroscopy (GINSES) (Jaksch et al., 2017). There we were able to extract information about the rheological behavior of the membranes on a nanoscale, that could be shown to coincide with predictions of a model by Romanov and Ul'yanov (2002). While that method allowed to access the dynamics of phospholipid membranes in an hitherto unfeasible manner it was severely limited in terms of use of instrument time, as each single spectrum required approximately three days of beam time.
Here we make use of the associated length scale and investigate the characteristic structures for those excitations.
In order to scan for the existence of such modes in a more efficient manner, we adapted the approach of (Constantin et al., 2006) (Caille, 1972), or indeed focusing on the structure dependent Bragg Peaks at all, we were looking for evidence of a structure associated with the previously observed excitations, that was earlier identified by our GINSES measurements. As GISANS measurements are an established method, there are neutron scattering instruments which are excellently suited for that kind of experiment, whereas for our GINSES measurements the main focus of the instrument construction was in transmission mode. That experimental advantage promised a more speedy experiment than performed otherwise.
This also opened a possibility to further explore the previously assumed temperature behavior of the modes, about which we only hyposized before. By varying the temperature below the liquid disordered phase transition of the membranes (Mortensen et al., 1988;Bultmann et al., 1991) a significant change in the behavior of the mode was expected. Indeed, the correlating structures change, both in abundance as well as in size, with temperature.
The data presented here thus addresses two aspects simultaneously: First, an additional, different method indeed confirms the modes are not an instrumental artefact as GISANS and GINSES are both based on different measurement principles, aiming at structure and dynamics respectively. Second, using the increased speed of measurement a larger temperature interval could be covered, proving the temperature dependent behavior of the modes, which also prove they couple well to the phase behavior of the membrane system, as expected.
That being said, the information that can be retrieved from GISANS measurements about the surface modes of the membranes is limited and only reveals the possible existence of said mode indirectly via the characteristic length scale. There are only very few directly accessible parameters, using only GISANS. Despite that, we still deem the method presented here to be a valuable tool, as it makes scanning a wide range of parameters, such as temperature or concentration, feasible. Finally, also the theoretical aspect of those coherent excitations can be further elucidated by the theoretical calculations based on smectic membrane theory and synthetic created data.

Materials and methods
The experimental results in this manuscript have been obtained by GISANS. The data evaluation as well as the computational results are based on software written by the authors (Monkenbusch et al., 2019). The sample preparation followed the protocol as outlined in Jaksch et al. (2015Jaksch et al. ( , 2017.

GISANS
The sample was prepared on a solid silicon block 5 × 10 × 20 cm in size. The Si-block was polished (better than 0.2 nm local roughness) and subsequently treated with RCA cleaning (Kern and Puotinen, 1970) to achieve a hydrophilic surface. In order to achieve a well-ordered, selfassembled layer structure the SoyPC (L-α-phosphatidylcholine, Avanti Polar Lipids) was dissolved in isopropanol p.A. and gently shaken (∼1-2 s −1 ) until a completely homogeneous solution was obtained (approximately 10 min). Shaking was subsequently continued for another 10 min. The Si-block meanwhile was placed in a frame to prevent the solution from flowing-off of the surface. Subsequently the solution was deposited on the Si-block, which was placed in a vacuum oven and aligned to be horizontal. In order to achieve slow and even drying the oven was left at room temperature, while the inside pressure was regulated to 25 kPa under reflux conditions. This is above the vapor pressure for the solution, thus no bubbling occurred.
After 12 h the maximum vacuum (below 25 kPa) was used to finally dry the sample. Olfactory inspection did not reveal any traces of remaining isopropanol. The Si-block with the deposited sample was then placed into a water tight frame, which was fully filled with D 2 O to achieve maximum hydration of the sample. Being placed at the instrument KWS-1 (Feoktystov et al., 2015) the sample was temperature controlled by a water thermostat.

GISANS
The GISANS experiments were performed at the KWS-1 (Feoktystov et al., 2015) instrument at the Heinz Mainer-Leibnitz Centre (MLZ), Garching, Germany. As previous attempts were limited by a weak signal to noise ratio and needed to be improved in terms of optimized instrument resolution, pixel size and background (Jaksch et al., 2018) a pinhole setup was chosen, where the size of the sample aperture is ideally mapped to the size of a pixel on the detector. This was achieved by using a 7 × 7 mm, a collimation length of 20 m and a sample-detector distance of 14 m. As the pixel size is 8 mm in both directions, this leads to a near optimal mapping on the detector and very low background.
The incident angle in all cases was 0.2°.

Data evaluation
The data was normalized using the qtiKWS software as provided  (Pipich, 2012). The resulting images were analyzed using python code written by the authors. All computational data was created with a Fortran script described in our publication about the software (Monkenbusch et al., 2019). A representative detector image can be seen in Fig. 1. The primary beam had to be shadowed to achieve a good signal to noise ratio, hence the low signal area in the center of the image. The final in plane cut is the averaging over both sides (top and bottom) of the in-plane cut shown. There was no averaging in Q ∥ -direction. Since the sample aperture was ideally matched to the pixel size, a sharp peak would also present as a single pixel with higher intensity than its surroundings.

Results
In order to illuminate both the experimental data as well as the theory used for the interpretation of that data, this section is separated into GISANS results and computational results, where calculations based on the paper by Romanov and Ul'yanov (2002) for supported smectic membranes are presented.

GISANS
Beginning at 37°C the sample was cooled down in several steps to 16°C and then reheated to inital conditions. The sample was equilibrated for 15 min before each measurement. Where appropriate, earlier results of GINSES measurements are correlated with the GISANS results. An overview over the results is given in Fig. 2. The clear position of the first dynamic peak shows the characteristic length of the detected mode. There are several areas in the temperature map that shall be discussed here. The first and most striking feature is that the position of one main peak at values slightly below Q ∥ = 0.01 Å −1 and one or two higher order peaks can be distinguished at any temperature, except for the coexistence area of the L α and L β phase. Even though the statistical significance in the case of a single scattering curve is low, since the maximum is only one point due to the detector resolution, considering all curves together as done in Fig. 2(a) shows the presence of those peaks. The coexistence area then is also the area where a hysteresis of the extracted correlation length parameter = ∥ λ π Q 2 / phase max (see Fig. 4), can be observed. This hysteresis is true for most of the parameters discussed here. Another striking feature is that seemingly the peak position is extremely stable against temperature variation within one phase. Looking at the extracted characteristic length λ phase in Fig. 4(a) this is however revealed to be not strictly true in all cases and to be a visual misconception in some cases, when the peaks are extremely broad or ill defined by being simply a single point. For a better understanding of this one should consider the sample history. The cooling ramp is the initial phase and leads to an additional annealing of the sample. This annealing makes the peaks better defined and also shifts them to slightly higher Q-values and consequently a lower λ phase . While this annealing process makes the peak position more stable, also a higher data point density in this region is available. So, while in the lower Q-region the errorbar is vanishingly small, it is larger in the heating ramp. This is a simple effect of this point density, where the fitting algorithm finds a higher χ 2 when more points are available, but does not reflect a real uncertainty. Apart from the correlation length the overall intensity of the excitations is of interest. Here the amplitude of the Gaussian fits shown in Fig. 2(b) is directly proportional to the abundance of excitations per unit area in the membrane. The corresponding data is shown in Fig. 4. The amplitude of the first peak consistently drops from 27 to 10 cooling down to 31°C, interestingly without an apparent phase transition and again drops below the L-β phase transition down to 5. Upon reheating nearly the full amplitude is recovered and the amplitude is developing with increasing temperature in a comparable manner as when being cooled down. The consistent drop is interrupted by the data point at T = 31°C. The fitting for that specific point however was very unstable and we therefore do not include this deviation in our analysis.
From these data we can conclude that the density of excitations is higher above T = 25°C and decreases by a factor of five between 37 and 16°C. So, apart from the phase transition around 22°C the consistently highest density of excitations occurs around physiological temperatures. This density of excitations can generally be associated with the energy density in the membrane, while the width of the peak is a measure of the different contributing wavelengths to that specific excitation, i.e. the wavelength distribution. While the steep increase towards body temperature is only signified by a single point, the value is also nearly regained after heating.

Computational
At first, it should be noted that we do not present simulated data here, in the sense that some kind of Monte Carlo simulation is presented, but rather an execution of the equations by Romanov and Ul'yanov (2002) with appropriate values and boundary conditions, the computations were performed with the parameters given in Table 1. The corresponding code is discussed in our publication about the used software (Monkenbusch et al., 2019).
In order to extract the dynamic contribution from code that essentially only produces the intermediate scattering function as in NSE the intermediate scattering functions were fitted with the expression S(Q, τ)/S(Q, τ = 0) = (1 − A) exp((G 1 τ) β ) + A exp(− G 2 τ) · cos(ωτ) + const. Here A is the amplitude of the oscillation, G 1 and G 2 are the decay Fig. 2. (a) Temperature vs. intensity map for all recorded scattering data during the cooling phase. There are several regions that can clearly be identified, such as the peak regions and the coexistence region for the L-α and L-β phase. (b) Representative intensity vs. scattering vector Q ∥ plots as were used to create (a). The curves are shifted by factors of 10 1 to 10 4 (bottom to top) for better visibility. The fits (black lines) show both the resulting curves as well as the fitting interval that was used to create them. constants for the purely elastic and the coherent excitation contribution, respectively, β is the stretching parameter and ω the frequency of the oscillation. A constant for the plateau at long Fourier times is added.
Here the amplitude A can be associated with the presence of a dynamic contribution, without it a simple exponential decay is observed.
Representative corresponding fits are shown in Fig. 5(a). The resulting amplitude for a range of Q-values is then used to gauge the contribution of the coherent excitation, which results in a plot that reproduces the location of the peaks in the cuts of the measured GISANS images very well. Here it is important to note, that the data in Fig. 5(b) is not connected to the intensity distribution as observed in GISANS, but merely shows the abundance of the previously mentioned modes on the length scale associated with the respective Q ∥values.
When compared with the previously published measured GINSES data, the correct location of the minima and maxima of the intermediate scattering function cannot be replicated. However, the qualitative behavior and the Q-dependency are identical. Indeed, the extracted structural features from GISANS coincide with the maxima calculated for the amplitudes in the intermediate scattering function. Also, the maxima and minima of the calculated in-plane cut show shifted maxima in intensity when compared to the measured GISANS data. We attribute this to the fact that the theory is expecting infinitely thin layers, while the real bilayers have a physical thickness.
We also used the algorithms to create a GISANS image directly only from the deduced data. The resulting image is shown in Fig. 3(a). The structures as investigated in the GISANS data above can also be seen here in the areas of lower intensity between the out-of-plane peaks of the lamellar structure. This also explains, that the simple assumption of having flexible membranes with undulations can lead to the observed data. This is further illustrated by an in-plane cut shown in Fig. 3(b). The structures, albeit at slightly shifted Q ∥ -values are visible, and as there is no incoherent background in the simulation, also more higher order peaks can be seen.

Discussion and conclusions
Combining the results shown above with our previous results on the dynamics of phospholipid membranes (Jaksch et al., 2017) a new image emerges. We now can clearly separate the out-of-plane structure of the membranes on a length scale of ≈6 nm and an in-plane correlation which we can link to the dynamics observed in GINSES of ≈100 nm. The measurements presented here also allow to observe a temperature  Table 1. The out-of-plane cut clearly shows the lamellar spacing of the phospholipid membranes, while the in-plane structure is only visible in the low intensity regions between the out-of-plane peaks. (b) In-plane cut at Q ⊥ = 0.18 Å −1 similar to the data obtained in Fig. 2(b).

Table 1
Input parameters for calculated scattering curves as shown in Fig. 5. Other parameters were kept constant at 10 total layers, d = 6 nm repeat distance and ρ = 1000 kg m −3 density.

35°C
Compression modulus B/Pa 3.0 × 10 6 Surface tension γ/N m 0.03 Intra-membrane viscosity η 3 /Pa s 7.5 × 10 −3 Bending modulus κ/k B T 19 S. Jaksch, et al. Chemistry and Physics of Lipids 225 (2019) 104788 dependence of the in-plane structures. This leads to the conclusion that the features we are describing here are indeed associated with the membrane modes as shown above and therefore of a dynamic nature. The variables and parameters used for computation in this section are described in Table 1. They are based on the data presented in this manuscript and our previous manuscript (Jaksch et al., 2017). One question that is left open is the exact nature of the excitations in real space. There are a range of possible modes for a collective motion of a membrane stack, such as undulations, peristaltic modes, baroclinic modes and second sound modes (Gelbart et al., 2012). Here it is worth mentioning that those modes who are originally considered to be present in single bilayer systems are on the length-scale of the thickness of that bilayer, while here longer distances are probed. A few considerations can however be made. Since the observations are strictly in plane, and no out-of-plane contribution is visible, we can assume a strict inplane density correlation. Also, the lower modes as described by the Romanov calculations (Romanov and Ul'yanov, 2002) would necessarily move the complete layer stack, which seems unlikely. The last consideration concerns the peristaltic mode. In this case, as it would be between the bilayers, a transport of water is to be expected, which introduces additional friction and energy constraints to that mode, which at least seem unlikely. So, in the absence of experimental evidence one way or the other, undulations or density fluctuations as in an acoustic wave seem to be the most likely options.
Taken altogether, the measurements show the following picture: (1) There are excitations in phospholipid membranes, (2) these excitations are associated to sufficiently regular structures to be observed in a time and spatially averaging method such as GISANS and (3) the involved energies are below the threshold to be thermally excited (on the order of hν ≈ 1 μeV for a single excitation from GISANS and GINSES).
Considering the length scales and energies involved in those systems we can speculate on the effects by the excitations discussed above. The modes as such have energy, lifetime and speed. Taking those properties together they can be considered fundamental for properties such as energy transport along a membrane, and also for dissipation of that energy over a certain area. Energies that are thermally available in such systems usually amount to ∼k B T, which is consistent with the activation energies found in GINSES. Larger energies then can be dissipated or transported in membrane patches, which can contain multiple excitations at a time. Also, the width of the peaks in GISANS hints to the fact that a range of single excitations with subtly different frequencies contribute to the overall undulation, otherwise sharper peaks would be expected. Each of the single excitations however has an energy low enough to be easily excited at room temperature. This could help to dissipate local high energy densities to prevent membrane damage. Also, as they are an in-plane correlation this modes could play a role in the transport of larger objects, such as membrane proteins that otherwise might be sterically or enthalpically suppressed, analogous to flotsam being transported by a wave.
A comparison with biologic systems the energies and length scales associated with E. Coli bacteria can be considered (Swiecicki et al., 2013). The overall length of a bacterium is on the order of 2-4 μm and the cross section diameter is ∼1.5 μm. Diffusion speeds along the membrane are on the order of a few μm s −1 . Thus we know that an excitation as reported here can travel along the bacterium as the propagation range is virtually identical to the dimensions of the bacterium (calculated from a 2 ns frequency and lifetime of the same order from GINSES and the speed of sound of 1500 m s −1 in water). Additionally, considering the speed and dimensions, the kinetic energy during diffusion of a bacterium is on the order of ∼5 μeV, which coincides with the energy of a single mode of the coherent excitations with ℏω = ℏ 2π / 2ns ≈ 5 μeV. Another striking fact is, that the abundance of excitations seems to have a maximum at physiological temperatures, which at least suggests a biological relevance.
Thus, energy from external stimuli or temperature which can be expected to occur in such a system can be transported with ease along the membrane. This transport and dissipation of energy can potentially help prevent a rupturing of the membrane and contribute to its biological function.
From a fundamental physics point of view, these excitations exhibit all properties expected from quasi-particles such as phonons. Since they however depend on a lamellar structure of the system they are distinct from them, which makes them surface mode phonons or smomons. While the frequency remains constant the amplitude of the coherent contribution is strongly Q-dependant. The inset shows the measured GINSES data from our previous publication (Jaksch et al., 2017). While we were not able to reproduce completely identical figures by computation, the qualitative similarity is striking. (b) Amplitudes of the fits shown in (a).