(C) PLOS One
This story was originally published by PLOS One and is unaltered.
 . . . . . . . . . .



The bending rigidity of the red blood cell cytoplasmic membrane [1]

['Sebastian Himbert', 'Department Of Physics', 'Astronomy', 'Mcmaster University', 'Hamilton', 'On', 'Origins Institute', 'Angelo D Alessandro', 'Department Of Pathology', 'Cell Biology']

Date: 2022-12 

An important mechanical property of cells is the membrane bending modulus, κ. In the case of red blood cells (RBCs) there is a composite membrane consisting of a cytoplasmic membrane and an underlying spectrin network. Literature values of κ are puzzling, as they are reported over a wide range, from 5 k B T to 230 k B T. To disentangle the contribution of the cytoplasmic membrane from the spectrin network, we investigated the bending of red blood cell cytoplasmic membranes (RBC cm ) in the absence of spectrin and adenosine triphosphate (ATP). We used a combination of X-ray diffuse scattering (XDS), neutron spin-echo (NSE) spectrometry and Molecular Dynamics (MD) simulations. Our results indicate values of κ of order 4 k B T to 6 k B T, relatively small compared to literature values for most single component lipid bilayers. We suggest two ways this relative softness might confer biological advantage.

Funding: This research was funded by the Natural Sciences and Engineering Research Council of Canada (NSERC), the Canada Foundation for Innovation (CFI) and the Ontario Ministry of Economic Development and Innovation. S.H. is the recipient of the H.G. Thode Postdoctoral Fellowship at McMaster University. M.C.R. is the recipient of an Early Researcher Award of the Province of Ontario and a University Scholar of McMaster University. S.M.Q. was the recipient of a Postdoctoral Fellowship from Canadian Blood Services. We acknowledge the support of the National Institute of Standards and Technology, U.S. Department of Commerce, in providing the neutron research facilities used in this work. Access to NGA-NSE and the NGB30-SANS was provided by the Center for High Resolution Neutron Scattering, a partnership between the National Institute of Standards and Technology and the National Science Foundation under Agreement No. DMR-2010792. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

This is an open access article, free of all copyright, and may be freely reproduced, distributed, transmitted, modified, built upon, or otherwise used by anyone for any lawful purpose. The work is made available under the Creative Commons CC0 public domain dedication.

Here we measure the bending rigidity of the RBC’s cytoplasmic membrane to clearly separate the elastic contribution of the membrane from that of the spectrin network. We will call these RBC cm . Our samples also have no ATP (adenosine triphosphate), which has sometimes been reported to affect membrane fluctuations [ 12 , 19 ], but sometimes not [ 11 ]. Solid-supported multi-lamellar RBC cm stacks were prepared for measurements of X-ray diffuse scattering (XDS), and unilamellar RBC liposomes were prepared for neutron spin-echo (NSE) spectroscopy. We also performed coarse grained Molecular Dynamics (MD) simulations of multi-component membranes that essentially matched the lipid composition of the RBC cm in the experiments. Table 1 shows our values of κ to facilitate comparison with literature values.

Supposing that the bending modulus of the cytoplasmic membrane is only about 5 k B T, it is noteworthy that this κ is significantly smaller than bending rigidities reported for single component lipid bilayers of similar thickness that have values of κ typically between 15 k B T and 50 k B T [ 15 – 28 ]. It is further intriguing that the cytoplasmic membrane contains considerable cholesterol which is conventionally thought to stiffen lipid membranes, although that depends on the lipid [ 19 ].

A particularly appropriate measure of elasticity is the bending modulus κ, which gives the energy required to bend away from the resting state. Table 1 shows values for the bending modulus κ of RBCs that have been reported over the years, ranging from 5 k B T to 230 k B T [ 4 , 6 – 9 , 11 , 12 ]. A reasonable hypothesis for this disparity is that the bending modulus depends on the length scale of the measurements. On length scales smaller than the mesh size of the spectrin network of ≈80 nm, the average bending modulus could be due mostly to the cytoplasmic membrane, while the spectrin network would add a contribution at longer length scales [ 13 ]. When measuring RBC elasticity on small length scales, values for κ of 5 k B T [ 7 ] and 7 k B T [ 9 ] have been reported in contrast to the much larger values for length scales of the entire RBC [ 4 , 8 , 11 , 12 ]. According to the above hypothesis, this would imply a substantial bending modulus for the spectrin network. It may be noted, however, this is inconsistent with a report that the bending modulus of the spectrin network is very small [ 14 ].

A suite of techniques has been used to study cell elasticity. Mechanical properties on cellular length scales were measured by micropipette aspiration [ 4 ], while atomic force microscopy (AFM) [ 5 ] probes elastic behavior on the nanoscale. Cell stiffness is also studied indirectly by spectral analysis of flickering of cells under a microscope [ 6 – 8 ], as well as optical interferometric techniques [ 9 , 10 ].

Cellular functions, such as mobility, division and vesicle trafficking, are intrinsically related to a cell’s ability to comply to deformation [ 1 – 3 ]. In the case of red blood cells (RBCs) that have no internal structure, this ability depends upon their two-dimensional “shell”, which consists of a spectrin network tethered to a cytoplasmic membrane.

Materials & methods

This research was approved by the Hamilton Integrated Research Ethics Board (HIREB) under approval number 1354-T. Informed consent was obtained from all blood donors by signing a written consent form. The authors confirm that all methods were performed in accordance with the relevant guidelines and regulations. Certain trade names and company products are identified in order to specify adequately the experimental procedure. In no case does such identification imply recommendation or endorsement by the National Institute of Standards and Technology (NIST), nor does it imply that the products are necessarily the best for the purpose.

Preparation of RBC liposomes 10 ml of blood samples were collected from volunteers in heparanized blood collection tubes. RBC liposomes were then prepared from all samples following a previously published protocol [32, 33]. Briefly: The blood was washed twice and the RBCs were isolated by successive centrifugation and replacing the supernatant with phosphate saline buffer (PBS). The cells were exposed to osmotic stress by mixing hematocrit with lysis buffer (3% PBS buffer, pH 8) at a volume fraction of 5%. The lysis buffer was pre-chilled to ≈4°C and the reaction tube was immediately stored on ice to prevent a fast re-closing of the ruptured cells. Hemoglobin and other cellular compartments were removed through multiple washing steps, as demonstrated in [32]. The protocol results in a white pellet containing empty RBC vesicles, commonly known as RBC ghosts. These RBC ghosts were suspended in heavy water (D 2 O) in the case of the NSE experiment: the supernatant was removed from the pellet and the tube was refilled with D 2 O. The sample was centrifuged at 20,000 g for 20 minutes and the resulting supernatant was subsequently replaced with D 2 O. This step was repeated twice. This buffer exchange was omitted when preparing the samples for the XDS experiment. The resulting ghost solution was then tip sonicated 20 times for 5 s each at a power of 100 W. The reaction tube was placed on ice during sonication to prevent the sample from overheating. Afterwards, the tube was centrifuged for 15 min at ≈20,000 g. This additional centrifugation step was found to be an efficient method for removing remaining undesired structures from the solution: The supernatant consists of a solution of large unilamellar vesicles (LUV, diameter: 199 nm, PID = 0.1) while any larger structures sediment into a pellet. This supernatant has an approximate concentration of ≈14 mg/ml [33] and will be hereafter referred to as the membrane solution. Multi-lamellar, solid supported membranes were prepared for the X-ray experiments. Membranes from the membrane solution were applied onto single-side polished silicon wafers. 100 mm diameter, 300 μm thick silicon wafers were pre-cut into 10 × 10 mm2 chips. The wafers were treated with a solution of 15 ml sulfuric acid and 5 ml hydrogen peroxide (Piranha solution) resulting in a hydrophilic surface. Each wafer was then thoroughly rinsed with ≈50 ml of ultra pure water (18.2 MΩ⋅cm) and placed on a hot plate (37°C) in a 3-dimensional orbital shaker. 100 μl of the membrane solution was pipetted slowly onto the wafer. The sample was covered with a tilted lid of a petri dish and to allow the membrane solution to slowly dry within ≈12 h. The dried wafers were further incubated prior to the experiment at 97% relative humidity and 37°C for 72 h by placing the samples in a sealed container with a saturated K 2 SO 4 solution. This allows the membranes to assemble into an oriented multilamellar structure. Assuming an average area per lipid of 0.5 nm and an average molar mass per lipid of 700 g/mol permits determining the average mass per leaflet to be 400 μg. A total membrane mass of 1.4 g/wafer thus results in of roughly 3,000 stacked membranes in a sample 18 μm thick. The membrane solution suspended in D 2 O were used for the neutron spin-echo experiments to create a strong scattering contrast between the protonated RBC cm and the surrounding solution. The liposome solution was brought to a final concentration of 20 mg/ml. First the sample was centrifuged at 20,000 g for 20 minutes and the supernatant replaced by D 2 O. This process was repeated twice. ≈6 ml of this solution was filled in custom made sample holders provided by the NIST Center for Neutron Research (NCNR). All samples were sealed prior to the shipment to the National Institute of Standards and Technology (NIST) in Gaithersburg, MD, USA. The vesicle diameter was measured using dynamic light scattering (DLS) prior to shipment and a diameter of 199 nm (polydispersity index = 0.1) was determined. Small Angle Neutron Scattering (SANS) experiments were performed at NIST simultaniously to the NSE experiments. The DLS results explain the SANS spectrum that was measured prior to the NSE experiment and is shown in S2 Fig in S1 File. Importantly, the SANS data showed no multilamellar peak confirming that the vesicles have a unilamellar structure. We note that we can not fully exclude effects of the preparation protocol on the RBC cm s bending rigdity. An increased bending rigidity in stomatocytes has been reported previously [9] and it was speculated that this originated in changes of the lipid bilayer’s composition. Our simulations are critical as they provide a deeper insight into the effects of the lipid composition on the RBC cm bending rigidity. The bending modulus of the asymmetric membrane was very close to values determined on symmetrized membranes models. Even the complete loss of polyunsaturated lipids or cholesterol increased the bending modulus to only 13 k B T. This demonstrates that even such extreme changes would result in bending moduli that are still significantly lower than values measured on synthetic lipid bilayers.

X-ray diffraction X-ray scattering experiments were performed using a rotating anode instrument equipped with a Rigaku HyPix-3000 2-dimensional semiconductor detector. Details of the experimental setup and protocol can be found in the Supplementary Material. The membrane bending modulus κ and the membrane interaction modulus B were determined from measurements of the diffuse scattering when the membranes were well-hydrated from water vapor close to 100% relative humidity. The analysis was similar to previous studies [16–20, 34], although the different experimental setup required a modification that is detailed in Supplementary Material. All measurements were conducted at 37°C. Basically, the q || dependence of the intensity I(q z , q || ) is proportional to a constant times the so-called structure or interference factor S(q z , q || ). (The constant is related to the electron density profile which is not of concern in this paper and is a simple linear fitting parameter for each q z .) For obtaining moduli, the focus is the structure factor [34], (1) where d is the average repeat spacing of the membranes in the stack, J 0 is the zero order Bessel function [34], H z (z, L z , σ z ) and H r (r, L r , σ r ) account for finite domain sizes within the sample; L r and L z are the average domain sizes with variances σ r and σ z in the lateral and out-of-plane directions [34]. The height-height pair correlation function δu n (r) follows from Eq (9) that defines κ and B (2) in which the Caillé η c parameter [35] and an in-plane correlation length ξ are related to the bending modulus κ and the membrane interaction modulus B by (3) This model was fit simultaneously to the intensities at q z = 2.0q 1 and q z = 2.5q 1 to obtain values of κ and B with results shown in Fig 1C. Further details of the numerical calculation of the structure factor in Eq (1) are described in the Supplementary Material. PPT PowerPoint slide

PNG larger image

TIFF original image Download: Fig 1. A Schematic of a stack of fluctuating membranes and the geometry of specular (q || = 0) and off-specular (q || ≠ 0) X-ray scattering. B q-space X-ray intensity map of a solid supported RBC cm membrane stack, measured at 37°C. Two orders of lamellar peaks surrounded by diffuse X-ray intensity are visible. The white lines show the locations and ranges of the data used for fits. C Off-specular intensities at q z = 2q 1 and q z = 2.5q 1 , normalized to the respective X-ray intensity at q || = 0.01 Å−1). Fits of the structure factor S(q z , q || ) following Eq (1) are shown as solid lines. Error bars represents the ± standard deviation. Intensity measured in proximity of a lamellar peak is orders of magnitude higher than intensity measured in between lamellar peaks. Since errors in scattering experiments scale with the square root of counted X-ray photons, the relative error is consequently smaller in proximity of a lamellar peak than between lamellar peaks. https://doi.org/10.1371/journal.pone.0269619.g001 Only two lamellar repeat spacing peaks were detected for solid supported RBC cm , limiting the analysis of the membrane fluctuations to the low-q z regime. The observed diffuse X-ray signal is secondarily sensitive to the domain size [16, 34], so the primary fit was repeated for different values of L r and the fit with the smallest ξ2 was found for L r = 500 Å. The direct application of the XDS method gives values of κ ≈2 k B T that we believe are too small. The main reason is that molecular tilt was not included in Eq (9) because our experimental setup gave too low signal/noise to provide a meaningful fit to an extra parameter. Inclusion of tilt generally increases κ by 25% to 50% as the tilt modulus K t varies from 90 mN/m to 50 mN/m when κ is of order 20 k B T [36]. However, our simulations suggest that K t is only about 4 mN/m for the RBC cm . In order to estimate how much κ of the RBC cm would increase if the XDS data were strong enough to fit for K t , we prepared several sets of emulated structure factor data with different values of κ emu , all with the simulated value of K t . We then fit these emulations with the tilt independent XDS analysis program used for actual data to obtain κ fit values. The emulated data that returned κ fit closest to the value of 2 k B T had a value of κ emu that was about 6 k B T. This is the value shown as the large end of the range in Table 1. Importantly, the structure factor for the emulated data had very weak peaks for orders three and higher, in agreement with the primary data shown in Fig 1. Those intensities are a product of the structure factor and the form factor squared; the latter could also have extinctions, but invoking extinctions is not necessary to account for the absence of higher order peaks which comes about just from the effect of small values of the elastic moduli on the structure factor. Our fitting routine was tested on a POPC bilayer. The observed 2-dimensional X-ray scattering pattern is shown in S3A Fig in S1 File and the corresponding diffuse profiles are depicted in S3B Fig in S1 File including fits to the data. The determined bending modulus of (20.8±1) k B T is in good agreement with the earlier 20.3 k B T [37] and the more recent tilt independent value of 19.2 k B T [38], which further supports the use of this analysis for the RBC cm .

Neutron spin-echo spectroscopy Neutron Spin-Echo (NSE) experiments were performed using the NGA-NSE spectrometer at the NIST Center for Neutron Research (NCNR) in Gaithersburg, MD, USA [39]. While XDS measures nearly instantaneous snapshots of the disorder caused by the fluctuations, NSE measures the relaxation rates of those fluctuations which are affected by transport properties like viscosity as well as the static bending modulus. Measurements were performed at q = 0.0523 Å−1, 0.0664 Å−1, 0.0794 Å−1 and 0.0959 Å−1 using neutron wavelengths of λ = 8 Å and 11 Å, with a wavelength spread Δλ/λ≈0.18, providing access to Fourier times ranging from 0.01 ns to 100 ns. Temperature was controlled to 37°C by a recirculation bath within an accuracy of ±1°C. Data were corrected for instrumental resolution and solvent background using the DAVE software package [40]. Eq (12) relates the effective bending modulus to the customary bending modulus κ. The most important step to obtaining the true bending modulus κ is to relate K A to κ. The relation (4) where 2D c is the thickness of the hydrocarbon region, has been used [23] for NSE experiments on pure lipid bilayers. (We note that [23] incorrectly calls Eq (4) the polymer brush model. Instead, the factor 48 assumes uncoupled uniform monolayers, and the polymer brush model would replace 48 by 24.) Assuming Eq (4) and Eq (12), Eq (11) can be written as (5) It is often assumed that the neutral surface h (defined as the location in each monolayer where stretching is decoupled from bending [41]) is close to the boundary D c of the hydrocarbon chains and the head group, in which case h/D c = 1. Previous studies of the electron density of red blood cell membranes report a head-head group distance (membrane thickness) of 46 Å [32, 42]. Using these results, the thickness of the hydrophobic core is estimated to be 2D c = 36 Å. Using the uncoupled monolayer model results in a value of κ = (15±1.6) k B T. Pan et al. [19] pointed out that conventional models, the uncoupled monolayer model in Eq (4), the coupled monolayer model, and the polymer brush model, did not account for κ and K A data as cholesterol was added to lipid bilayers. Evan Evans provided an alternative theory [19] that assumed a stiff region in both uncoupled monolayers with a length of δ = 9 Å. This resulted in (6) Consequently, (7) Using h = D c and δ = 9 Å, the result for this cholesterol model is κ = (4.1±0.4) k B T when no diffusion correction was made and κ = (7±0.4) k B T when a diffusion correction was made; this is the range of values we display in Table 1 for our NSE results. This analysis also makes a direct connection to the area compressibility K A via Eq (6). Using κ = 4 k B T gives K A = 250 mN/m which is close to the values for single component saturated and unsaturated lipid bilayers [11]. In contrast, for the intact RBC K A = 500 mN/m [43], but this should be the sum of the area compressibility K A of the RBC cm and of the spectrin network because the K A of a composite membrane is the sum of the two parallel substituents [44]. This implies K A = 260 mN/m for the spectrin network. If instead, we use our larger κ = 7 k B T this gives 438 mN/m for the RBC cm , leaving 62 mN/m for the spectrin network, so either value is reasonable. In contrast, Eq (4) only gives 62 mN/m for the RBC cm membrane K A , which is smaller by far than any known lipid bilayer. It has been previously discussed [45] that vesicle diffusion can contribute a correction factor of exp(−Dq2t) to Eq (10), where the diffusion constant D can be estimated from the mean size of the vesicles. While diffusion dominates NSE relaxation for qR ≪25, its influence becomes considerably smaller for our mean vesicle radius (R = 200 nm) and the experimental q range, so its effect is often ignored [23]. We have therefore analyzed our data with and without a diffusion correction factor and thus obtain the range of values of κ shown in Table 1.

Molecular dynamics simulations MD simulations were performed on a GPU accelerated computer workstation using GROMACS Version 5.1.4. An RBC cm model was designed using the CHARMM-GUI membrane-builder (http://charmm-gui.org/) [46, 47] and the Martini force-field 2.2 [47]. The system represents a membrane patch of ≈34 nm × 34 nm with about 2,500 lipid molecules on each leaflet and 37 water molecules per lipid corresponding to a well hydrated state of the membrane. The lipid composition of the membrane patch was adjusted to match the experimental lipidomic findings of RBC [48]. Each lipid species was mapped to available models in the Martini force-field as described in [49]: First, an error coefficient was calculated for every available model lipid. This error value is composed of an error of saturation E sat and an error of tail length E tail . E sat was chosen to be the difference in tail saturation between the model and the experimental lipid. In the same way E tail was defined as the difference in tail length. For instance, given an experimental Lipid: 18:2–14:1; a corresponding Martini lipid 18:1–16:1 would result in an error value of E = E sat + E tail = 1 + 2 = 3. The Martini lipid with the smallest error value was then used for each experimental lipid respectively. The cholesterol concentration was taken from [50] who reported that cholesterol accounts for a mole fraction of 50% of the RBC cm . The RBC cm is known to be asymmetric, with phosphatidylserine (PS) and phosphatidylethanolamine (PE) lipids preferably located on the inner leaflet. This asymmetry between different lipid species was adjusted by using values for the compositional asymmetry published in previous coarse grained plasma membrane simulations [51]. For a given species the simulated lipid population was split among both leaflets to match the relative experimental findings. For instance, phosphatidylcholine (PC) lipids were reported to be split in a ratio of 3:1 between the upper and lower leaflet. Thus from all simulated PC lipids 75% were placed in the upper and 25% were placed in the lower leaflet. Details about the exact lipid composition of each model can be found in the S1 Data. S5 Fig in S1 File visualizes the relative concentrations of lipid species in the membrane model. Simulations were equilibrated for 80 ns in the NPT ensemble (constant pressure and temperature), and then run for 5 μs. Prior to each simulation run, the system was allowed to equilibrate for simulated 5 ns. The simulation used a 1 fs time step, a short range van der Waal cutoff of 1.1 nm and a potential-shift-verlet coulomb modifier. Periodic boundary conditions were applied to all spacial directions. We note that periodic boundary conditions discretize the wave-vectors and result in a low-Q limit of the accessible fluctuation spectrum Q min = 2π/L, where L is the box size. Neighbor lists were updated in intervals of 20 steps. The temperature coupling was controlled by a v-rescale thermostat at a constant pressure of 1 bar using Parrinello-Rahman semi-isotropic weak coupling (τ = 12 ps; compressibility β = 3 ⋅ 10−4 bar−1). The fluctuation spectrum of the membrane was determined as detailed in the Supplementary Material. The spectrum is governed by a dependency according to the Helfrich–Canham (HC) theory plus a dependency due to tilt [52]. We use with the in-plane component Q || to distinguish between the Fourier space of the sample and the scattering vector . The bending modulus was determined by fitting the lower Q || -regime (Q || <0.2 Å−1) to (8) The MD simulations were conducted in the absence of any proteins in order to specifically study the influence of the lipid membrane on the bending modulus. The analysis of the XDS experiment is based on smectic elastic theory and does not include potential protein induced local curvature. Simulating a bilayer in the absence of proteins thus allows a direct comparison between both methods and provides insight into the contribution of the lipid bilayer to the RBC cm bending rigidity. The simulated value of κ essentially agrees with those from XDS and NSE. This suggests that κ can in first order be well approximated by the properties of just the lipid membrane. Determining the bending modulus in asymmetric membranes is non-trivial due to potentially induced curvature resulting from an uneven area per lipid in both leaflets [53]. Simulations on membrane patches with symmetrized upper and lower leaflet were used to verify the results from the asymmetric simulation. The resulting fluctuation spectra are presented in S4 Fig in S1 File. We find values of 5 k B T and 6 k B T, respectively which confirms the results that we obtained for the asymmetric membrane.

Dynamic light scattering The size distribution of the liposomes was measured by dynamic light scattering (DLS) using a Brookhaven 90Plus particle analyzer running Particle Solutions Software (Version 2.6, Brookhaven Instruments Corporation) with a 659 nm laser and a 90° detection angle. Each measurement was performed at a count rate between 200 and 500 kilocounts/s for 2 min. The scattering signal at the position of the detector fluctuates due to the diffusion of liposomes in the solution. The instrument directly measures the diffusion constant D of the liposomes by fitting the cross-correlation function of the time signal measured by the detector. This is related to the particle size via the Stokes-Einstein relation: , where η is the dynamic viscosity of the solution, k B is the Boltzmann constant, T is the sample temperature and r is the radius of the LUVs, assumed to be spherical. All measurements were performed at 25°C on 1 ml of sample containing ≈20 mg/ml of RBC liposomes.

[END]
---
[1] Url: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0269619

Published and (C) by PLOS One
Content appears here under this condition or license: Creative Commons - Attribution BY 4.0.

via Magical.Fish Gopher News Feeds:
gopher://magical.fish/1/feeds/news/plosone/