Microsecond molecular dynamics studies of cholesterol-mediated myelin sheath degeneration in early Alzheimer's disease

Abstract

Cholesterol-mediated perturbations of membrane structural integrity are key early events in the molecular pathogenesis of Alzheimer's disease (AD). In AD, protein misfolding (proteopathy) and pro-inflammatory conditions (immunopathy) culminate in neuronal death, a process enabled by altered membrane biophysical properties which render neurons more susceptible to proteopathic and immunopathic cytotoxicities. Since cholesterol is a principal neuronal membrane lipid, normal cholesterol homeostasis is central to membrane health; also, since increased cholesterol composition is especially present in neuronal myelin sheath (i.e. brain “white matter”), recent studies have not surprisingly revealed that white matter atrophy precedes the conventional biomarkers of AD (amyloid plaques, tau tangles). Employing extensive microsecond all-atom molecular dynamics simulations, we investigated biophysical and mechanical properties of myelin sheath membrane as a function of cholesterol mole fraction (χ_CHL). Impaired χ_CHL modulates multiple bilayer properties, including surface area per lipid (APL), chain order, number and mass density profiles, area compressibility and bending moduli, bilayer thickness, lipid tilt angles, H-bonding interactions and tail interdigitation. The increased orientational ordering of both palmitoyl and oleoyl chains in model healthy myelin sheath (HMS) membranes illustrates the condensing effect of cholesterol. With an increase in χ_CHL, number density profiles of water tend to attain bulk water number density more quickly, indicating shrinkage in the interfacial region with increasing χ_CHL. The average tilt value is 11.5° for the C10–C13 angle in cholesterol and 64.2° for the P–N angle in POPC lipids in HMS. These calculations provide a molecular-level understanding of myelin sheath susceptibility to pathology as an early event in the pathogenesis of AD.

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1. Introduction

Alzheimer's disease (AD) is a devastating neurodegenerative disorder traditionally characterized by the accumulation of extracellular β-amyloid (Aβ) plaques and intracellular hyperphosphorylated tau protein neurofibrillary tangles.¹ The underlying mechanisms of AD-related cellular damage and cognitive decline remain unelucidated despite decades of research.^2,3 In recent years, increasing evidence has suggested that demyelination of neurons occurs very early in the pathogenesis of AD, even before plaque and tangle deposition.^4–8 Understanding the biomolecular mechanism of this demyelination may provide insights regarding new druggable targets for AD.

Myelin is a multilamellar membrane structure that functions as an electrical insulator surrounding the neuronal axon in the white matter of the central nervous system (CNS); it is critical for efficient and fast conduction of nerve impulses.^9,10 Myelin sheath homeostasis in brain is preserved by the coordinated working of oligodendrocyte progenitor cells (OPCs), microglia and astrocytes. Microglia phagocytose myelin debris and secrete signaling factors to promote the differentiation of OPCs to oligodendrocytes, whose main function is to generate myelin.^11,12 Astrocytes regulate myelination by supporting proliferation and migration of oligodendrocytes. However, due to various pathological, genetic and environmental factors, myelin regeneration–degeneration homeostasis is disrupted early during the pathogenesis of AD; in turn, this activates astrocytes and transforms microglia into a senescence phenotype.^13,14 Activation of M1-phenotype microglia triggers release of pro-inflammatory cytokines (e.g. IL6, IL10, IL1R1, TNF-α, IFNγ) and increases cellular stress thereby further activating the innate immune response. Oligodendrocytes, the myelin forming glial cells of the CNS, are damaged due to coupled proteopathic (plaques and tangles) and immunopathic distress.^15,16 Impaired oligodendrocytes result in decrease in myelin density and ultimately neuronal death leading to cognitive impairment (see Fig. 1).^4,5,17,18

Fig. 1 In a healthy neuronal myelin sheath (MS) with a normal cholesterol concentration, microglia exist in the M2 phenotype. M2 microglia trigger the release of anti-inflammatory cytokines and immunosuppressive responses. The composition of a healthy myelin sheath is preserved by the coordinated actions of oligodendrocytes, microglia and astrocytes. However, a damaged neuronal myelin sheath in AD, arising from either high or low cholesterol content, is characterized by activation of pro-inflammatory microglia (M1 phenotype) and astrocytes, as well as dysfunction of oligodendrocytes. Additional neuro-immunological changes are reflected by pro-inflammatory cytokines, concomitant protein misfolding of β-amyloid (Aβ) and tau (forming toxic oligomers and neurofibrillary tangles, respectively) and disordered cholesterol homeostasis. Also, abnormal interactions between neurotransmitters and misfolded proteins impair synaptic transmission, which is imperative for proper cellular functioning.

Accordingly, myelin damage initiates a cascade of molecular mechanisms which contribute to the ongoing AD pathology. Understanding the biochemical elements responsible for myelin degeneration is necessary to mitigate such effects. The major molecular constituent of myelin is cholesterol; cholesterol constitutes ∼10% of the dry weight of the whole brain with nearly 70% being in myelin.^19–21 Thus, brain, particularly the white matter, contains a disproportionate amount of cholesterol relative to other organs, and in a healthy brain, cholesterol homeostasis is maintained tightly.²²

An impaired cholesterol mole fraction (χ_CHL) in the myelin sheath adversely affects its biological function. High χ_CHL obstructs permeability of essential nutrients/ions across the myelin sheath, whereas low χ_CHL allows facile passage of unwanted molecules/impurities into the neuron. High cholesterol content released after myelin disruption also stimulates inflammasome activation resulting in a maladaptive immune response which initiates phagolysosomal-induced membrane rupture.²³ Tong et al. have shown that high χ_CHL is a trigger of white matter alterations and cognitive decline in a mouse model.²⁴ Low cholesterol likewise adversely impacts myelination since a relatively high cholesterol content is essential for normal myelin membrane growth.²⁵ Therefore, the cholesterol content of a myelin sheath membrane is rigorously regulated in a healthy brain; an altered χ_CHL in the myelin sheath membrane adversely affects membrane biophysical properties such as fluidity and permeability.^22,26

Published information regarding the effect of cholesterol content on the biophysical and structural properties of heterogeneous biological membranes is limited.²⁷ The impact of cholesterol content on lipid bilayers composed of POPC/PSM or POPE/PSM, typical constituents of eukaryotic cell membranes, has been methodically studied by Klauda and co-workers.^28–33 However, the eukaryotic bilayer models were limited to ternary lipid systems.^28,30,31 Villa and co-workers modelled neuronal axon, myelin sheath and the node of Ranvier employing all-atom, coarse-grained molecular dynamics simulations and finite element simulations to understand structural and mechanical properties of these bilayers.^34–36 However, they have not reported the effect of variation in cholesterol content on these biological bilayers.

Herein, we have investigated a series of model myelin sheath membranes containing six representative lipids based on experimental lipidomic data (as explained in the methods section), using all-atom molecular dynamics simulations to gain insights relevant to AD pathology. The effect of impaired membrane integrity from an altered cholesterol mole fraction in the heterogeneous myelin sheath membrane has also been investigated.

2. Methods

2.1 Model membranes

A typical biological membrane contains ∼2000 diverse lipids resulting from variations in the head-groups and aliphatic chains of the different lipid species.^37–40 The most abundant lipids in a biological membrane are phosphatidylcholines (PC), phosphatidylethanolamines (PE), cholesterol (CHL), sphingomyelins (SM) and glycolipids. The model myelin sheath (MS) membrane systems studied in this work contain: cholesterol, 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoethanolamine (POPE), 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoserine (POPS), galactosylceramide (GalCer) and N-stearoyl sphingomyelin (SSM) as specific constituent lipids. The myelin sheath model has been developed based on experimental lipid composition data for cellular membranes provided by Alberts et al.⁴¹ and as justified by other literature studies.^34,42,43 Since the myelin sheath membrane is high in cholesterol, the effect of fluctuations in the mole fraction of cholesterol (χ_CHL) was studied by varying χ_CHL in the model MS systems in this work. The variation in the composition of other lipids (PC, SM and glycolipids) also affects myelin sheath degeneration. The effect of deficiency in phosphatidylcholine synthesis on myelination has not been reported in the literature. However, recent literature shows that choline homeostasis may regulate myelination during development and myelin repair.^44,45 No myelin degeneration was detected in sphingomyelin-deficient Sphingomyelin synthase 1 or Sphingomyelin synthase 2 knockout mice.^46,47 However, significant myelin recovery was seen in animals with inhibition or depletion of the enzymes responsible for sphingomyelin hydrolysis into phosphatidylcholine and ceramide; this suggests that optimal sphingomyelin content is a component of myelin regeneration.⁴⁸ Myelin sheath thinning with myelin splitting is observed in animals unable to synthesize galactosylceramide.^49,50 Also, mice with myelin deficient in galactosylceramide (2-hydroxlyated galactosylceramide and sulfatide) exhibited myelin degeneration by 18 months of age; mice having a low concentration of galactosylceramide sulfatide demonstrated disorganization of the uncompact myelin sheath domains.^51–55 Significantly decreased sphingomyelin, and increased phospholipid content have been demonstrated in the degenerated myelin sheath pathology of in multiple sclerosis.⁵⁶ Composition of healthy myelin sheath membrane and different MS bilayer systems studied in this work are provided in Table 1. Homogeneous bilayer systems with pure lipids and having equal mole fraction of lipids were also modelled to compare against experimental data and to dissect the effects of specific lipid species on various properties. The atomistic structures of POPC, POPE, POPS, SSM, GalCer and CHL are given in ESI.†

Table 1 Lipid composition of 26 membrane systems evaluated in this study, where N_total represents total number of lipids in the system and is kept constant in each simulation (100 per membrane leaflet). N_PC, N_PE, N_PS, N_CHL, N_SSM and N_GalCer represent numbers of POPC, POPE, POPS, cholesterol, sphingomyelin and galactosylceramide molecules, respectively. n_H2O and m_H2O are the total number of water molecules in the PBC box and the number of water molecules per lipid, respectively. χ_CHL is the mole fraction of membrane cholesterol. Each membrane system was equilibrated for a minimum of 1 μs. IUPAC nomenclature for the various lipids is provided in the footnote

Set	Bilayer system	N PC	N PE	N CHL	N SSM	N GalCer	N PS	n H2O	m H2O	χ CHL	Ions
											Na^+	Cl^−
Where lipid name abbreviations used are as follows: POPC = 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine; POPE = 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphoethanolamine; CHL = cholesterol; SSM = sphingosine-phosphorylcholine; GalCer = beta-D-galactosylceramide; POPS = 1-palmitoyl-2-oleoyl-sn-glycero-3-phospho-L-serine.
1	Healthy myelin sheath membrane and reference bilayer systems
	PC	200	0	0	0	0	0	10139	50.69	0	25	25
	PC:PE	100	100	0	0	0	0	9477	47.38	0	23	23
	PC:PE:CHL	66	66	68	0	0	0	8350	41.75	0.34	21	21
	PC:PE:CHL:SSM	50	50	50	50	0	0	8117	40.58	0.25	20	20
	PC:PE:CHL:GalCer	50	50	50	0	50	0	9405	47.02	0.25	25	25
	Healthy Myelin Sheath (HMS)	18	28	78	14	46	16	8883	44.41	0.39	40	24
2	Cholesterol variations in myelin sheath membrane composition
	MS_1	34	44	0	30	60	32	9961	49.81	0	58	26
	MS_2	32	42	8	28	60	30	9947	49.74	0.04	56	26
	MS_3	30	40	18	26	58	28	8939	44.70	0.09	51	23
	MS_4	28	38	28	24	56	26	9609	48.05	0.14	51	25
	MS_5	26	36	38	22	54	24	9560	47.80	0.19	49	25
	MS_6	24	34	48	20	52	22	9400	47.00	0.24	47	25
	MS_7	22	32	58	18	50	20	8969	44.85	0.29	44	24
	MS_8	20	30	68	16	48	18	9095	45.48	0.34	38	24
	MS_9	16	26	88	12	44	14	8620	43.10	0.44	37	23
	MS_10	14	24	98	10	42	12	8484	42.42	0.49	34	22
	MS_11	12	22	108	8	40	10	8322	41.61	0.54	32	22
	MS_12	10	20	118	6	38	8	8214	41.07	0.59	30	22
	MS_13	8	18	128	4	36	6	8014	40.07	0.64	28	22
	MS_14	6	16	138	2	34	4	7895	39.48	0.69	25	21
	MS_15	4	14	148	0	32	2	7673	38.37	0.74	23	21
	MS_16	2	12	158	0	28	0	7596	37.98	0.79	20	20
	MS_17	0	8	168	0	24	0	7404	37.02	0.84	20	20
	MS_18	0	4	178	0	18	0	7280	36.40	0.89	20	20
	MS_19	0	2	188	0	10	0	7202	36.01	0.94	20	20
	MS_20	0	0	198	0	2	0	7108	35.54	0.99	19	19

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The systems were modelled as a lipid bilayer with both leaflets having the same lipid composition with constant number of lipids (200) to avoid bias due to system size. The initial coordinates of the atomistic bilayers were constructed using the membrane-only generation option of Membrane Builder in CHARMM-GUI.^57,58 All lipids are predefined in the CHARMM-GUI. Galcer is the predefined glycolipid in the CHARMM-GUI within the Galactocerebrosides subgroup,⁵⁹ characterized by having β-D-galactose as a head-group (see Fig. S1, ESI†). An ion concentration of 0.15 M NaCl was added to the bilayer systems using distance as the ion placing method to mimic physiological conditions.

2.2 Molecular dynamics simulations

All MD simulations were performed using the NAMD package version 2.13 employing all-atom CHARMM36 lipid force field and the modified TIP3P model for explicitly representing solvent molecules.^60–65 An aqueous environment was mimicked for these simulations by employing periodic boundary conditions. For constraining covalent bonds containing a hydrogen atom at their equilibrium bond length, the SETTLE algorithm⁶⁶ for water and the SHAKE algorithm⁶⁷ for phospholipids was used. Long-range electrostatic interactions were computed using the Particle Mesh Ewald (PME) algorithm.⁶⁸ The van der Waals interactions were truncated at a cutoff distance of 12 Å and were modeled using a Lennard-Jones potential. The isobaric–isothermal (NPT) ensemble was generated with temperature and pressure maintained at 310 K (which is well above the melting points of phospholipids) and 1 atm, respectively. Constant temperature and pressure was maintained by employing Langevin dynamics with a damping coefficient of 1 ps^-1 and the Langevin piston Nosé–Hoover method^69,70 in which the pressure coupling is isotropic only in the x- and y directions, respectively. Different myelin sheath membrane and reference bilayer systems were first equilibrated using the CHARMM-GUI standard six-step equilibration process in Membrane Builder.^57,58 Each MS and reference bilayer systems were further equilibrated for a minimum of 1 μs; the total simulation time was approximately 26 μs. The graphs of area per lipid of different bilayer systems as a function of simulation time are given in ESI,† confirming that each bilayer system reached equilibrium before running production simulation trajectories. All bilayer systems reached equilibrium after approximately 800 ns of simulation time. The velocity-Verlet algorithm⁷¹ with a time step of 2 fs was used to generate MD trajectories and VMD version 1.9.3⁷² was used to visualize the systems. The last 200 ns part of equilibrated trajectory of each system was used for analysis.

2.3 Simulation analysis

To understand structural and biophysical properties of different myelin sheath membrane systems, we have calculated ten properties for each model membrane lipid bilayer: [1] area per lipid (APL) in the membrane including APL of each specific lipid as a function of χ_CHL in different MS systems, [2] bilayer thickness (D_HH), [3] number density profile of POPC, water (TIP3P) and cholesterol molecules, [4] mass density profiles of POPC, water (TIP3P) and cholesterol molecules, [5] Sn-1 and Sn-2 carbon order parameters, [6] area compressibility modulus (K_A), [7] bending modulus (K_c), [8] POPC and cholesterol lipid tilt angles, [9] lipid interdigitation and [10] H-bonding. The results are reported as an average value for the last 0.2 μs of 1 μs atomistic simulation trajectory There was minimum deviation in the results for different properties for the last 0.2 μs of 1 μs atomistic simulation trajectory as bilayer systems had already reached equilibrium. Results of different structural and mechanical properties of reference bilayer systems (given in Table 1) were compared against available experimentally determined values to validate simulation results. The x and y dimensions of the simulation box are multiplied and divided by total number of lipids present in one leaflet of the bilayer to calculate area per lipid (APL). Component surface area of different lipids was calculated by determining the X and Y coordinates of representative atoms for each lipid (e.g. O3 of Cholesterol, C2, C21, and C31 for phospholipids; as shown in Fig. S5 of ESI†). The X and Y coordinates of these selected representative atoms are projected onto a plane delimited by the simulation box. This plane is subsequently divided into polygons through a Voronoi diagram using the qvoronoi program within the Quickhull⁷³ package. The sum of all polygonal areas is the area of the simulation box, and summing areas of representative atoms gives the area per lipid for individual lipid components.

The thickness of the bilayer is calculated as the distance between the phosphate atom peaks in the mass density profile. Traditionally, orientational mobility of C–H bonds in lipid bilayers is calculated by C–H bond order parameter available from ²H NMR experiments (as C–D bond in ²H NMR).⁷⁴ Carbon order parameter (S_CD) is calculated as follows:

where θ_i presents the angle between the lipid bilayer normal and the molecular axis given C_i−1 and C_i+1 carbon atoms. The angular brackets represent molecular and temporal ensemble averages. The number and mass density profiles along the bilayer normal for water, POPC and cholesterol were computed by dividing the equilibrated simulation cell along the z-direction into bins of width 0.1 Å. The time-averaged number and mass of the water, POPC and cholesterol located in each bin was computed. The area compressibility modulus (K_A) and bending modulus (K_c) for different MS and reference bilayer systems were calculated using eqn (2) and (3) to understand the effect of cholesterol on the bilayer's mechanical properties.In eqn (2), k_B represents the Boltzmann constant, T is the average temperature of the system throughout the simulation, 〈A〉_eq and 〈δA〉_eq² are the average area per lipid and mean square fluctuation of the bilayer surface area at equilibrium respectively. N is the total number of lipids in each bilayer leaflet.

The bending modulus (K_c) was calculated using eqn (3).⁷⁵

where h represents the thickness of bilayer and h₀ is 1 nm. We used the polymer-brush model proposed by Evans et al.⁷⁶ to describe coupling between the two leaflets of a lipid bilayer. This model relates K_A to K_cvia the membrane mechanical thickness and a β parameter that represents the strength of coupling of the two leaflets; for lipid bilayers, β = 24.

To identify lipid interdigitation and the mass overlap between the upper and lower leaflets of the bilayer as a function χ_CHL, the lipid interdigitation tool in Membplugin⁷⁷ (an extension of VMD) was used. The degree of acyl chain interdigitation is calculated using a correlation-based fraction which gives the width of overlapping bilayer regions (W_ρ) in nm, fraction of mass overlap (I_ρ) and contacts between two leaflets (I_c). I_ρ represents zero to complete mass overlap between lipid leaflets and varies within 0 ≤ I_ρ ≤ 1. I_c gives number of heavy atoms in contact with opposite leaflet within a default cutoff range of 4 Å. To examine orientation of cholesterol molecules in the MS and reference membrane systems, we calculated the angle between the cholesterol vector (defined by the carbon atom bonded to the hydroxyl group (OH) and the carbon atom bonded to the acyl tail of the cholesterol) and the bilayer normal (z-axis). Further explanation of tilt angle definition employed for POPC and cholesterol is given in the results section. Analyses were performed using VMD and TCL scripts written in-house. VMD software was used for graphical representations.

3. Results and discussion

Myelin sheath composition is specialized and different from other types of biological membranes. One of the most distinct features of myelin sheath membrane is its enrichment with a variety of lipids such as cerebrosides, phospholipids and particularly cholesterol. The white matter concentration of cerebrosides is directly proportional to myelin content.⁴¹ In this work, a model myelin sheath membrane and different myelin sheath membrane bilayer systems with varying cholesterol mole fraction (χ_CHL) have been studied as discussed in methods section.

A total of 26 model membrane systems with different lipid composition were studied in this work as given in Table 1. The mole fraction of cholesterol was varied in healthy myelin sheath membrane for studying the effect of altered cholesterol concentration. Reference bilayer systems composed of only phospholipids (PC, PC : PE) or phospholipids : cholesterol (PC : PE : CHL, PC : PE : CHL : SSM, PC : PE : CHL : GalCer, where different lipids and cholesterol are in equal proportion in different bilayer systems), have been also studied in order to compare results against available experimental data. The lipid bilayer compositions for reference bilayer systems are also given in Table 1.

The final snapshots of 1 μs equilibrated reference bilayer systems, healthy myelin sheath (HMS), and myelin sheath bilayers with varying χ_CHL are shown in Fig. 2–4, respectively.

Fig. 2 Final equilibration snapshots of reference lipid bilayer systems (as given in Table 1) having varying cholesterol mole fraction (χ_CHL), with POPC (purple), POPE (orange), POPS (cyan), cholesterol (red), SSM (green), GalCer (silver), sodium ions (blue spheres), chloride ions (red spheres) and water (pink dots). All lipid bilayers were equilibrated for a minimum of 1 μs.

Fig. 3 Final equilibration snapshot of a healthy myelin sheath membrane (as given in Table 1) with POPC (purple), POPE (orange), POPS (cyan), cholesterol (red), SSM (green), GalCer (silver), sodium ions (blue spheres), chloride ions (red spheres) and water (pink dots). All lipid bilayers were equilibrated for a minimum of 1 μs.

Fig. 4 Final equilibration snapshots of different myelin sheath membrane systems (as given in Table 1) having varying cholesterol mole fraction (χ_CHL), with POPC (purple), POPE (orange), POPS (cyan), cholesterol (red), SSM (green), GalCer (silver), sodium ions (blue spheres), chloride ions (red spheres) and water (pink dots). All lipid bilayers were equilibrated for a minimum of 1 μs.

3.1 Lateral bilayer area and bilayer thickness

The reference bilayer and myelin sheath bilayer systems converged at 800 ns equilibration time. Graphs depicting the convergence of area per lipid (APL) as a function of simulation time are provided in the ESI.† Average APL and thickness D_HH for reference, HMS and different myelin sheath (MS) bilayer systems with varying χ_CHL are given in Table 2.

Table 2 Average area per lipid (APL) and thickness (D_HH) of studied bilayer systems as a function of mole fraction of membrane cholesterol (χ_CHL) at 310 K

Set	Bilayer system	χ CHL	APL (Å^2)	D HH (Å)
1	Reference bilayer systems
	PC	0	65.35 ± 1.10	38.10 ± 0.53
	PC:PE	0	60.49 ± 1.02	40.89 ± 0.57
	PC:PE:CHL	0.34	45.70 ± 0.54	45.75 ± 0.45
	PC:PE:CHL:SSM	0.25	44.96 ± 0.55	47.20 ± 0.40
	PC:PE:CHL:GalCer	0.25	43.74 ± 0.45	47.23 ± 0.45
2	Myelin sheath (MS) membrane systems
	MS_1	0	46.17 ± 0.27	47.73 ± 0.24
	MS_2	0.04	46.63 ± 0.29	47.67 ± 0.23
	MS_3	0.09	46.70 ± 0.57	47.26 ± 0.38
	MS_4	0.14	44.30 ± 0.26	48.04 ± 0.21
	MS_5	0.19	44.42 ± 0.48	47.79 ± 0.33
	MS_6	0.24	43.80 ± 0.33	47.69 ± 0.27
	MS_7	0.29	42.26 ± 0.26	47.34 ± 0.23
	MS_8	0.34	42.64 ± 0.29	46.76 ± 0.34
	Healthy myelin sheath (HMS)	0.39	42.33 ± 0.33	46.99 ± 0.30
	MS_9	0.44	41.28 ± 0.22	47.03 ± 0.28
	MS_10	0.49	41.04 ± 0.23	46.38 ± 0.28
	MS_11	0.54	40.08 ± 0.19	45.62 ± 0.29
	MS_12	0.59	40.18 ± 0.21	45.99 ± 0.40
	MS_13	0.64	39.89 ± 0.22	45.04 ± 0.38
	MS_14	0.69	39.59 ± 0.19	43.84 ± 0.54
	MS_15	0.74	38.73 ± 0.18	43.58 ± 0.61
	MS_16	0.79	38.78 ± 0.19	43.07 ± 0.79
	MS_17	0.84	38.41 ± 0.15	43.01 ± 1.03
	MS_18	0.89	38.19 ± 0.16	41.17 ± 1.39
	MS_19	0.94	38.07 ± 0.16	39.47 ± 2.02
	MS_20	0.99	37.80 ± 0.14	39.07 ± 0.89

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In general, APL decreases with an increase in χ_CHL in reference and myelin sheath membrane bilayer systems. For reference systems, APL follows the trend: PC:PE:CHL:GalCer ∼ PC:PE:CHL:SSM < PC:PE:CHL < PC:PE < PC; whereas bilayer thickness exhibits an opposite trend: PC:PE:CHL:GalCer ∼ PC:PE:CHL:SSM > PC:PE:CHL >PC:PE ∼ PC. In reference bilayers, increasing χ_CHL from 0 to 0.34, decreases APL by 33% and increases thickness by 23%, which is consistent with NMR data.⁷⁸ The calculated PC bilayer APL is 65.35 ± 1.10 Ų at 310 K which agrees with experimental APL values of 63, 62 and 66 Ų at 297, 323 and 310 K, respectively.^79–81 Also, the calculated pure PC bilayer thickness is 38.10 Å at 310 K as given in Table 2 which compares well with an experimental D_HH of 37.0 Å at 303 K.⁸² PC:PE:CHL:SSM and PC:PE:CHL:GalCer systems have slightly lower APLs than PC:PE:CHL, which suggest that both SSM and GalCer lipids have similar condensing effects and this condensing effect is slightly higher than cholesterol molecules.

The effect of varying cholesterol content on APL and D_HH in different myelin sheath membranes was also studied. Table 2 presents APL and D_HH values for 21 different myelin sheath membrane systems containing a model healthy myelin sheath membrane system. In general, APL decreases with increasing χ_CHL. In particular, as we increase χ_CHL from 0 to 0.99 in different MS systems, APL decreases by approximately 18%. Previous experimental and theoretical investigations on the condensing effects of cholesterol also correlate with this finding.^83–86D_HH does not follow any discernible trend with increasing χ_CHL in the lower cholesterol range until χ_CHL becomes close to that of the HMS membrane. There is a slight decrease in D_HH values on further increasing χ_CHL.

Fig. 5 visualizes the trends of APL and D_HH with variation in χ_CHL in various bilayer systems. There is a sharp decrease in APL as we introduce cholesterol into the lipid bilayers as compared to PC and PC:PE reference bilayers, as shown in Fig. 5. APL decreases with an increase in χ_CHL, where HMS corresponds to the APL of a model healthy myelin sheath membrane. For the HMS bilayer, APL is 42.33 Ų. Similar to the sharp decrease in APL upon introduction of cholesterol into phospholipid bilayers, there is a sharp increase in thickness of bilayers as well with increasing χ_CHL. However, a clear monotonic trend is not observed in thickness of MS bilayers in lower ranges, but at higher χ_CHL, we observed a decrease in D_HH values. The thickness of a healthy myelin sheath membrane is 46.99 Å, which is highlighted on the D_HH curve presented in Fig. 5. The deviation of APL and D_HH from HMS values corresponding to altered χ_CHL in MS bilayers impairs their biological functions (possibly leading to the implications observed in neurological disorders).

Fig. 5 Area per lipid (APL) and bilayer thickness (D_HH) for POPC bilayer (PC), healthy myelin sheath (HMS) and different model bilayer systems (given in Table 1) as a function of cholesterol composition at 310 K.

3.2 Component surface areas

Table 3 presents APL values of individual lipids in modelling different reference, HMS and MS membrane systems. Phospholipids (i.e., POPC, POPE and POPS) have higher APLs compared to other lipids (i.e., sphingomyelin (SM) and ceramide (Cer)). In eukaryotic membranes, POPC lipids are the main phospholipid constituents (∼50%), whereas POPS lipids are the most abundant anionic phospholipid. A pure POPC bilayer has an APL of 65.17 Ų, which decreases to approximately 57–60 Ų range in different reference and MS systems. Cholesterol has an usually low APL compared to phospholipids. For the MS_20 bilayer system, with an χ_CHL of 0.99, the APL value is 37.90 Ų, which agrees well with the experimental value of 40 Ų for pure cholesterol. SSM and GalCer lipids also experience condensing effects at higher χ_CHL. Compared to other lipids in different bilayer systems, cholesterol molecules expand considerably with increasing χ_CHL fluctuating in a 30–38 Ų range.

Table 3 The component APL (Ų) of specific lipid types in bilayer systems at 310 K

Set	Bilayer system	χ CHL	POPC (Å^2)	POPE (Å^2)	CHL (Å^2)	SSM (Å^2)	GalCer (Å^2)	POPS (Å^2)
1	Reference bilayer systems
	PC	0	65.168
	PC:PE	0	61.159	59.879
	PC:PE:CHL	0.34	54.612	54.044	28.263
	PC:PE:CHL:SSM	0.25	59.668	57.557	30.518	31.043
	PC:PE:CHL:GalCer	0.25	56.884	54.328	31.410		33.628
2	Myelin sheath (MS) membrane systems
	MS_1	0	56.404	57.993		29.716	33.750	57.872
	MS_2	0.04	59.160	57.310	29.033	34.186	35.341	57.374
	MS_3	0.09	58.736	61.994	32.336	33.466	36.069	60.156
	MS_4	0.14	57.690	57.473	30.325	31.109	32.596	60.826
	MS_5	0.19	63.993	62.441	31.639	30.319	34.195	59.590
	MS_6	0.24	58.136	59.697	31.931	31.608	37.333	59.756
	MS_7	0.29	58.385	58.298	31.305	33.894	33.072	59.179
	MS_8	0.34	57.980	55.610	33.886	34.875	34.743	59.030
	Healthy Myelin Sheath (HMS)	0.39	58.398	60.979	34.624	31.915	34.452	59.054
	MS_9	0.44	63.100	64.239	32.778	32.845	32.385	59.936
	MS_10	0.49	60.852	60.639	35.003	37.338	32.618	59.937
	MS_11	0.54	59.526	60.803	34.798	36.648	33.425	63.229
	MS_12	0.59	62.199	57.197	36.274	26.877	32.944	66.236
	MS_13	0.64	61.064	60.929	36.430	32.954	34.491	60.235
	MS_14	0.69	64.620	60.609	36.851	25.781	33.743	60.438
	MS_15	0.74	64.883	62.268	36.775		32.926	60.149
	MS_16	0.79	64.887	64.028	37.382		33.882
	MS_17	0.84		63.793	37.893		33.144
	MS_18	0.89		64.600	37.936		34.470
	MS_19	0.94		64.782	37.894		36.095
	MS_20	0.99			37.903		31.800

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Optimal cholesterol content in biological membranes facilitates both passive diffusion and active transmembrane transport of molecules.^87–89 Alterations in the APL values of constituent membrane lipids alters their physical properties thereby altering optimal transmembrane molecular diffusion and related cellular functions.

3.3 Orientation ordering of lipid tails

The variation of deuterium order parameter values for the carbon atoms of the palmitoyl (sn-1) and unsaturated oleoyl (sn-2) tails of POPC lipids for reference and myelin sheath systems at different χ_CHL is shown in Fig. 6–9.

Fig. 6 Change in orientation ordering of the carbon atoms of the palmitoyl tail of POPC lipid molecules in pure POPC, healthy myelin sheath (HMS) membrane and reference bilayer systems as given in Table 1. The experimental order parameters for a pure POPC bilayer at 310 K from Seelig et al.⁷⁴ are plotted for comparison against calculated results.

Fig. 7 Change in orientation ordering of the carbon atoms of the oleoyl tail of POPC lipid molecules in pure POPC, healthy myelin sheath (HMS) membrane and reference bilayer systems as given in Table 1. The experimental order parameters for pure POPC bilayer at 310 K from Seelig et al.⁷⁴ are also plotted for comparison against calculated results.

Fig. 8 Change in orientation ordering of the carbon atoms of the palmitoyl tail of POPC lipid molecules in healthy myelin sheath (HMS) membrane and different myelin sheath membrane systems with varying composition of cholesterol as given in Table 1.

Fig. 9 Change in orientation ordering of the carbon atoms of the oleoyl tail of POPC lipid molecules in axonal plasma (AP) membrane and different axonal membrane systems with varying composition of cholesterol as given in Table 1.

The experimental sn-1 and sn-2 SCD results from Seelig et al.⁷⁴ for POPC have been reproduced with the CHARMM36m force field computed POPC bilayer S_CD, as shown in Fig. 6 and 7, respectively. The order parameter profiles become higher for both palmitoyl (sn-1) and unsaturated oleoyl (sn-2) tails of POPC lipids with the addition of cholesterol in reference and healthy myelin sheath (HMS) membrane systems, as shown in Fig. 6 and 7 respectively. The ordering effect of GalCer lipids is higher than SSM lipids. Noticeably, myelin sheath membranes have a higher content of GalCer lipids as compared to SSM lipids; therefore, they are inherently biased towards attaining higher order and structure compared to other biological lipid membranes. High content of GalCer lipids in myelin sheath membrane increases its structural order, thereby reducing its permeability which helps in maintaining its crucial function of providing insulation for electrical signal propagation along neuronal axons. The order parameter profile for HMS (with χ_CHL = 0.39) is highest for C4–C10 carbon atoms for palmitoyl tails and C2–C12 for oleoyl tails as compared to other reference bilayers systems, as shown in Fig. 6 and 7. In other words, the increase in the orientational ordering of both palmitoyl and oleoyl chains is higher in HMS membranes compared to other reference bilayers, which illustrates the condensing effect of cholesterol. Lipid bilayer systems with higher χ_CHL tend to pack more tightly resulting in elevated thickness. These finding are also supported with the decrease in the lateral APL and increase in thickness of the reference and HMS with addition of cholesterol, as discussed in Table 2.

The palmitoyl (sn-1) and oleoyl (sn-2) POPC S_CD parameters for HMS and different myelin sheath membranes, as a function of χ_CHL′ are presented in Fig. 8 and 9, respectively, which show that altering χ_CHL of MS membranes enables palmitoyl and oleoyl chains of POPC to assume either higher or lower order than HMS. In general, both palmitoyl and oleoyl POPC S_CD parameters increase with an increase of χ_CHL in different MS membrane systems. However, substantial fluctuations in order parameters are observed for C2–C12 carbon atoms in palmitoyl chain and C3–C8 and C12–C16 of oleoyl chains. Modified order of lipid chains as a function of χ_CHL in different myelin sheath membranes compared to normal myelin sheath (HMS) adversely affects both its structural and functional properties. Lower order in membrane lipids increases fluidity and permeability, thereby enabling transmembrane permeation of toxic or unwanted molecules. Conversely, higher than normal order deleteriously hinders diffusion of essential ions/nutrients through the lipid bilayer.

3.4 Distribution of water, POPC and CHL along bilayer normal axis

Distribution of water, POPC and cholesterol along the bilayer normal (z-axis) for reference systems, model healthy myelin sheath (HMS) membrane, and different myelin sheath (MS) systems was studied by computing atomic number density profiles, as shown in Fig. 10. Fig. 10(a and b), present number density profiles of water molecules for reference and MS systems, respectively. The bilayers can be divided into three regions. First, the hydrophobic region rich in lipid tails in which no water molecule is present. Secondly, the bulk region at which the density of water meets the water bulk density (i.e., ∼0.9979 g cm⁻³ = 33.4 H₂O nm⁻³); the bulk water density is represented by a dotted black line in Fig. 10(a and b), for both myelin sheath and reference systems. Thirdly, the interfacial region, sandwiched between the hydrophobic and bulk regions; in the interfacial region, the number density of water is characterized by 0 < ρ < 33.4. In Fig. 10(a), both pure PC and PC:PE bilayers have sigmoidal number density curves. However, with the introduction of cholesterol in pure PC and PC:PE bilayers, the number density curves start to deviate from their sigmoidal shape and to show a slight curvature. This slight curvature in the middle of the water number density curves is also observed in health myelin sheath and other MS bilayer systems. The number density profiles of water tend to attain bulk water number density much more quickly with an increase in mole fraction of cholesterol in lipid bilayers; for example, Δρ (within 1.0 < z < 2.0) for MS_1 (χ_CHL = 0), healthy myelin sheath membrane (χ_CHL = 0.39) and MS_18 (χ_CHL = 0.89) are 6.27, 11.86, 28.63 H₂O nm⁻³ respectively. This suggests that there is a shrinkage in the interfacial region with increasing χ_CHL, thereby potentially impacting various biophysical processes occurring at the lipid–water interface of bilayers. Therefore, the increase of cholesterol results in higher water density and the interfacial region endeavours to attain a bulk-like environment. In other words, high cholesterol content decreases APL of lipids and increases water number density in the interfacial region. Magnetic resonance imaging (MRI) provides clinical images of cerebral atrophy for assessing neurodegeneration in AD as a function of brain volume/cerebrospinal fluid [CSF] index.⁹⁰ The atomistic details of the increased number density of water in the cholesterol rich membrane presented in this work is compatible with this MRI-based cerebral atrophy characterization.

Fig. 10 Number density profile of water (a and b), POPC (c and d) and cholesterol (e and f) along the bilayer normal for reference, HMS and different myelin sheath membrane systems at varying χ_CHL values. The bulk density of water is represented by a dashed black line at 33.4 H₂O nm⁻³ in the water number density profile.

Fig. 10(c and d) represent POPC number density profiles of reference, model healthy myelin sheath and different myelin sheath membranes. In both reference and MS systems bilayers, the number density profiles shift towards the interfacial region having higher ‘z’ values on the x-axis. This indicates that lipids are more exposed to the interfacial water region as we decrease the mole fraction of cholesterol in the bilayer, possibly interrupting interfacial biochemical processes occurring at the membrane–water interface. Fig. 10(e and f) show that with an increase in the cholesterol mole fraction in both MS and reference systems, the number density profile peaks become sharper and higher. The number density profiles for different MS systems with mole fractions of cholesterol below 0.34 exhibit a comparatively smoother profile. This indicates that with increasing χ_CHL, the lipid membrane is compressed in the lateral direction (i.e. APL decreases) and elongated in the transverse direction (i.e. D_HH increases).

3.5 Mass density profile

Mass density profiles of water, POPC and cholesterol are plotted in Fig. 11. The distribution of mass of various molecules along the membrane z axis is evaluated through mass density profiles for various species. Fig. 11(a) and (b) show that with an increase in χ_CHL the mass density profile of water attains bulk water density much sooner as compared to HMS or bilayers with higher χ_CHL. The presence of a high volume of water molecules at bulk water density (∼1000 kg m⁻³) in cholesterol rich bilayer systems indicates that the mass distribution of water molecules is substantially perturbed as the cholesterol content is altered within the myelin sheath membrane.

Fig. 11 Mass density profile of water (a and b), POPC (c and d) and cholesterol (e and f) along the bilayer normal for reference, HMS and different myelin sheath membrane systems at varying χ_CHL values.

Fig. 11(c and d) show mass density profiles of POPC along the bilayer normal for reference and different myelin sheath systems. As χ_CHL is increased, the peaks in the POPC mass density profiles are diminished and become smoother. This shows that at lower χ_CHL, POPC head groups become more exposed at the lipid-water interface. Also, the width and height of the minima at the center of the bilayer corresponding to the low density region is dependent upon the χ_CHL. The mass density profiles of cholesterol, for both reference and MS systems, are given in Fig. 11(e and f) respectively. The density profiles are smoother for the MS bilayer with lower χ_CHL and have two distinct peaks near interfacial regions as χ_CHL is increased. Mass density profile peaks also shift slightly towards the interfacial region at higher. This clearly shows that alterations in the cholesterol content in the myelin sheath have significant impact on the intensities of the peaks. For the MS bilayers with χ_CHL higher than 0.34, these peaks become more prominent, indicating that the introduction of cholesterol yields enhanced structuring and bilayer stiffness.

3.6 Area compressibility modulus (K_A) and bending rigidity modulus (K_c)

The results for the area compressibility modulus (K_A) and for bending rigidity modulus (K_c), as a function of χ_CHL′ for reference and healthy myelin sheath membrane bilayer systems are presented in Table 4. The experimental data for K_A and K_c for pure POPC and POPC:CHL employing different measuring techniques are also summarized in Table 4 for comparison. The calculated area compressibility modulus of pure POPC is 251 mN m⁻¹; experimentally, K_A is reported to be 180 – 330 mN m⁻¹ at 25 °C using infrared measurements and 208–237 mN m⁻¹ at 21 °C using micropipette aspiration methods.^75,91 The area compressibility modulus increases with an increase in χ_CHL in reference bilayer systems. Different experimental studies also report an increase in K_A values with an increase of cholesterol content in lipid bilayers.^92,93 POPC bilayer experimental bending rigidity data (shown in Table 4) demonstrate large variations in experimental K_c values depending upon measurement technique and experimental conditions. The calculated K_c value for a pure POPC bilayer employing the polymer-brush model proposed by Evans et al.⁷⁶ is 15.16 × 10⁻²⁰ J (as given in Table 4), which is compatible with an experimental K_c value at 310 K.^42,75 With increasing χ_CHL in reference bilayer systems, bending rigidity increases and follows the trend: PC:PE:CHL:GalCer > PC:PE:CHL:SSM ∼ PC:PE:CHL > PC:PE ∼ PC. Galcer lipids induce more bending rigidity as compared to SSM lipids. Experimentally, POPC/cholesterol bilayers exhibit strong stiffening with increasing χ_CHL as determined via micropipette aspiration⁹⁴ and neutron spin echo and dynamic light scattering⁹⁵ techniques. Fig. 12 shows that both the area compressibility modulus (K_A) and bending rigidity modulus (K_c) increase with an increase in cholesterol mole fraction for different myelin sheath membrane systems. Chakraborty et al.⁹⁶ have noted similar observations as an effect of increasing cholesterol mole fraction. Cholesterol increases the compressibility and bending modulus by reducing average area per lipid. The points corresponding to area compressibility modulus and bending rigidity modulus for health myelin sheath bilayer system are labelled as HMS in Fig. 12. In summary, higher χ_CHL increases the compressibility modulus and bending rigidity of myelin sheath membranes. The tilt and interdigitation deformations of lipids along with fluctuations in membrane thickness modulates the overall elasticity of cholesterol-doped membranes.

Table 4 Area compressibility modulus (K_A) and bending modulus (K_c) for different membrane bilayer systems at 310 K

System	χ CHL	K A (mN m^−1)		K c × 10^−20 (J)
		This work	Exp. literature data	This work	Exp. literature data
PC	0	251.19	180–330^91	15.160	Temp.	Experimental technique	K c × 10^−20 (J)
					24	Fluctuation analysis	14.6^97
					20	Fluctuation analysis	15.99 ± 0.31^98
					25	Fluctuation analysis	21.1 ± 0.4^99
					30	X-ray scattering	8.5^100
					25	Micropipette aspiration	21.1 ± 0.4^94
					30	Fluctuation analysis	10^101
					22	Fluctuation analysis	12.9 ± 0.4^102
					24	Fluctuation analysis	3.9 ± 0.9^103
					22	Neutron spin echo and dynamic light scattering	7.7 ± 0.8^95
					20	Fluctuation analysis	14.48 ± 0.19^98
					20	Fluctuation analysis	12.55 ± 0.33^98
					24	Electro-deformation	5.8 ± 1.2^103
PC:PE	0	253.81	—	16.825
PC:PE:CHL:GalCer	0.25	418.84	—	37.291
PC:PE:CHL:SSM	0.25	351.77	—	31.280
PC:PE:CHL	0.34	364.26	—	30.392

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Fig. 12 Area compressibility modulus (K_A) and bending modulus (K_c) for different myelin sheath membrane bilayer systems as a function of χ_CHL at 310 K. The results are calculated using average area at equilibrium and its variance following eqn (2) and (3) given in methods section.

3.7 P–N vector angle distribution for POPC, tilt angle of cholesterol and lipid interdigitation in model myelin sheath membranes

Changing cholesterol concentration in lipid bilayer membranes modulates the angular orientation of the various lipids and cholesterol. Fig. 13 represents variation in the P–N angle distribution function P(θ) for POPC lipid molecules and variation of the C10–C13 angle distribution function P(θ) for cholesterol molecules for different myelin sheath membrane and reference bilayer systems as a function of χ_CHL at 310 K. With the increase of mole fraction of cholesterol in different myelin sheath membrane model systems, the tilt angles of POPC and cholesterol are shifted towards lower values. The angle distribution for the phosphorous–nitrogen (P–N) vector of the phosphocholine head group and the C10–C13 vector for cholesterol become narrower as χ_CHL increases, indicating that cholesterol molecules become more ordered and align more towards the bilayer normal.

Fig. 13 The variation in the P–N angle distribution function P(θ) of POPC lipid molecules and the variation of C10–C13 angle distribution function P(θ) for cholesterol molecules for different myelin sheath membrane and reference bilayer systems as a function of χ_CHL at 310 K. The definition of the P–N angle in POPC lipids and the C10–C13 angle in cholesterol is shown.

The average P–N angle for POPC lipids and average C10–C13 cholesterol tilt angle as a function of cholesterol mole function for different model myelin sheath membrane systems are given in Table 5. Table 5 data show that increasing χ_CHL is inversely correlated with POPC and cholesterol tilt angles. Decrease in POPC and cholesterol tilt angles with higher χ_CHL is primarily a result of the decrease in APL and corresponding increase in lipid order and thickness. Increased APL and reduced chain order at lower χ_CHL allow more space for angular tilting. The average tilt value of the C10–C13 angle in cholesterol is 11.5° and 64.2° for the P–N angle in POPC lipids in a healthy myelin sheath membrane.

Table 5 The average P–N angle for POPC lipid and average cholesterol tilt angle, fraction of contacts and mass overlap and interdigitation within lipid bilayers systems at 310 K. The standard deviation in the results over the 0.2 μs simulation trajectory is also given

S. no.	Bilayer	χ CHL	P–N angle (deg)	C13-C10 angle (deg)	Interdigitation of bilayer leaflets i.e. width of overlapping regions Wρ (nm)	Fraction of mass overlap (Iρ)	Fraction of contacts (Ic)
			PC	Cholesterol
1	MS_1	0	59.775 ± 3.845	—	0.311 ± 0.037	0.174 ± 0.012	0.026 ± 0.002
2	MS_3	0.11	66.327 ± 4.628	11.786 ± 0.714	0.337 ± 0.037	0.169 ± 0.012	0.025 ± 0.002
3	MS_5	0.19	63.925 ± 4.884	11.291 ± 1.014	0.335 ± 0.046	0.168 ± 0.017	0.024 ± 0.003
4	HMS	0.39	64.225 ± 5.923	11.516 ± 0.741	0.262 ± 0.036	0.150 ± 0.013	0.026 ± 0.003
5	MS_12	0.59	64.579 ± 7.656	10.510 ± 0.502	0.268 ± 0.033	0.158 ± 0.014	0.028 ± 0.003
6	MS_16	0.79	57.417 ± 12.075	9.603 ± 0.413	0.324 ± 0.042	0.177 ± 0.017	0.033 ± 0.004
7	MS_20	0.99	—	9.782 ± 0.374	0.326 ± 0.026	0.207 ± 0.011	0.046 ± 0.004

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At lower χ_CHL, interdigitation of lipid bilayers decreases with an increase in cholesterol content. The interdigitation of bilayer leaflets increases as we further increase χ_CHL. The increase in thickness at lower concentrations is driven by acyl-chain ordering, whereas the decrease at higher concentrations is caused by an increase in interdigitation between the ordered lipid tails.

3.8 Hydrogen bonds

To understand the local interactions between different lipid molecules, we have studied hydrogen bonding for different lipids in MS and reference atomistic bilayers. The average number of H-bonds between water and a corresponding lipid or cholesterol molecule is given in Table 6. A POPC bilayer forms an average of 7.35 H-bonds with water molecules; little variation is observed in POPC–water H-bonding in the PC:PE:CHL bilayer (∼7 H-bonds) despite the addition of 35% cholesterol mole fraction. This indicates that the incorporation of hydrophobic cholesterol into the zwitterionic POPC bilayer brings only slight change to the surface chemistry of the bilayer.

Table 6 Average number of H-bonds between water and corresponding lipid and cholesterol molecules present in different reference and myelin sheath membrane systems with varying χ_CHL

Bilayer system	χ CHL	POPC–water	POPE–water	CHOL–water	GalCer–water	SSM–water	POPS–water
Reference bilayer systems
PC	0	7.35
PC:PE	0	6.91	5.65
PC:PE:CHL	0.34	7.02	5.93	1.30
PC:PE:CHL:GalCer	0.25	6.42	5.46	1.19	5.26
PC:PE:CHL:SSM	0.25	6.78	5.45	1.05		7.38
Myelin sheath (MS) membrane systems
MS_1	0	10.35	9.10		9.68	12.78	19.51
MS_5	0.19	13.79	11.33	1.91	10.33	14.02	19.83
HMS	0.39	14.35	12.06	2.41	11.88	12.28	19.06
MS_12	0.59	16.14	12.53	2.90	13.32	13.55	20.58
MS_16	0.79	17.52	12.71	3.29	14.60
MS_20	0.99			3.72	16.49

---

POPC contains only H-bond accepting groups (i.e. phosphoryl oxygens and ester group oxygens), whereas POPE, SSM and GalCer lipids have both H-bond acceptor and donor groups. SSM and PC lipids have a similar phosphocholine head group; however, due to the presence of a sphingo chain, SSM lipids contain an amide group, a free hydroxyl group at the C3 carbon, and a trans double bond between C4 and C5. The OH and NH groups of SSM lipids can act both as a H-bond donor and acceptor, whereas the carbonyl oxygen in the acyl chain acts as a H-bond acceptor. The sugar hydroxyl groups of GalCer can also be involved in hydrogen-bond formation with water.

Cholesterol participates in H-bonding with water at the lipid–water interface via its hydroxyl group. In different myelin sheath membrane systems, the number of H-bonds per lipid or cholesterol molecule increases with an increase in the cholesterol mole fraction. Cholesterol acts effectively as a spacer between lipid molecules, enabling more hydrated lipid headgroups.^104,105 This increase in H-bonding contributes to the rise in order parameters and compressibility moduli in different MS systems. Water–cholesterol and water–lipid interactions therefore become important in the dynamic balance of forces within the membrane. Finally, it plays a role in determining one of the key structural features of a membrane – namely elasto-mechanical properties. This alteration in H-bonding interaction of lipids and cholesterol with water, as χ_CHL increases in MS bilayer systems, leads to the formation of local defects in the lipid−water interfacial region which allows restriction of permeation of water/ions into the interior of the bilayer – ultimately disturbing molecular integration within the myelin sheath membrane.

4. Conclusions

Cholesterol-mediated perturbations in neuronal membrane homeostasis and structural integrity are key early events in the molecular pathogenesis of AD. Protein misfolding (proteopathy) and pro-inflammatory conditions (immunopathy) culminate in neuronal death by necrotic and apoptotic mechanisms, both of which are facilitated by altered membrane properties which render neurons more susceptible to cytotoxic insult. Since cholesterol is one of the principal neuronal membrane lipids, normal cholesterol biochemistry is central to membrane health; also, since increased cholesterol composition is present in the myelin sheath (i.e. brain “white matter”), it is not surprising that recent studies have revealed subtle white matter atrophy preceding the conventional pathological biomarkers of AD (amyloid plaques and tau tangles) – contradicting the historical misconception that AD is exclusively a grey matter disease.

To permit an improved understanding of the early molecular events of AD and to enable a biophysical understanding of the role of altered cholesterol concentration upon neuronal membrane homeostasis, we performed an extensive series of molecular modelling experiments of varying cholesterol concentrations in model myelin sheath membranes. Specifically, molecular dynamics simulations of model myelin sheath membranes with varying concentrations of cholesterol were performed to understand the effects of impaired χ_CHL on myelin sheath biophysical and mechanical properties to ascertain whether these altered properties increase vulnerability of myelin membranes to proteopathic and immunopathic attack. High χ_CHL introduces substantial myelin sheath thickening concurrent with a decrease in area per lipid molecule. This effect is a result of a cholesterol induced straightening of lipid hydrocarbon tails in the direction normal to the membrane plane. Altered cholesterol content not only modulates the tilting angles of different membrane lipids (e.g. POPC) but also changes their bilayer orientation, thereby altering multiple biophysical processes at the membrane interface including increased permeability to oligopeptide insertion. This molecular level understanding of myelin sheath membrane properties as a function of cholesterol content provides useful insights into the preliminary stages of neuronal susceptibility during the early pre-clinical phases of AD.

Author contributions

The manuscript was written through contributions of both authors. All authors have given approval to the final version of the manuscript.

Conflicts of interest

The authors declare no competing financial interest.

Acknowledgements

The authors thank the Krembil Foundation for financial support. D. F. W. thanks the Canada Research Chair program for support as a Tier I CRC in Protein Misfolding Diseases. The authors acknowledge SciNet and Compute Canada for providing additional computing facilities.

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Footnote

† Electronic supplementary information (ESI) available: Fig. S1–S4 of APL, component APL and bilayer thickness for healthy myelin sheath membrane (HMS) as a function of equilibration and production time; the average P–N angle for POPC, POPE, POPS, SSM lipids and average cholesterol tilt angle (C13–C10) of reference membrane systems at 310 K; the average fraction of contacts and mass overlap, interdigitation within lipid bilayers systems of reference membrane systems; Structure of various lipids and cholesterol molecules used in bilayer systems. See DOI: 10.1039/d1cp03844c

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