Localized Axolemma Deformations Suggest Mechanoporation As

bioRxiv preprint doi: https://doi.org/10.1101/816108; this version posted October 23, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder. All rights reserved. No reuse allowed without permission.

1 Localized axolemma deformations 2 suggest mechanoporation as axonal injury trigger 3 4 Annaclaudia Montanino1, Marzieh Saeedimasine2, Alessandra Villa2, Svein Kleiven1 5 6 1 Division of Neuronic Engineering, Royal Institute of Technology (KTH), Huddinge, 7 Sweden 8 2 Department of Biosciences and Nutrition, Karolinska Institutet (KI), Huddinge, Sweden 9 10 11 Running title: Axolemma deformations in axonal injury 12 13 Abstract 14 Traumatic brain injuries are a leading cause of morbidity and mortality worldwide. With 15 almost 50% of traumatic brain injuries being related to axonal damage, understanding the 16 nature of cellular level impairment is crucial. Experimental observations have so far led to the 17 formulation of conflicting theories regarding the cellular primary injury mechanism. 18 Disruption of the axolemma, or alternatively cytoskeletal damage has been suggested mainly 19 as injury trigger. However, mechanoporation thresholds of generic membranes seem not to 20 overlap with the axonal injury deformation range and microtubules appear too stiff and too 21 weakly connected to undergo mechanical breaking. Here, we aim to shed a light on the 22 mechanism of primary axonal injury, bridging finite element and molecular dynamics 23 simulations. Despite the necessary level of approximation, our models can accurately 24 describe the mechanical behavior of the unmyelinated axon and its membrane. More 25 importantly, they give access to quantities that would be inaccessible with an experimental 26 approach. We show that in a typical injury scenario, the axonal cortex sustains deformations 27 large enough to entail pore formation in the adjoining lipid bilayer. The observed axonal 28 deformation of 10-12% agree well with the thresholds proposed in the literature for axonal 29 injury and, above all, allow us to provide quantitative evidences that do not exclude pore 30 formation in the membrane as a result of trauma. Our findings bring to an increased 31 knowledge of axonal injury mechanism that will have positive implications for the prevention 32 and treatment of brain injuries. 33 34 35 Keywords: Mechanoporation, Axolemma, Axonal injury, Membrane permeability, 36 Traumatic brain injury, Finite Element 37 38 Number of words: Abstract (240 words), Manuscript (9683 words) 39 Number of Figures: 7 Figures + 1 Table 40 41 42 43 44 45 46 47 48

1 1 Introduction 2 Traumatic brain injury (TBI) is defined as “an alteration in brain function, or other evidence 3 of brain pathology, caused by an external force”.1 In 2013 approximately 2.8 million TBI- 4 related emergency department visits, hospitalization, and deaths occurred in the United 5 States.2 In a recent study reporting the epidemiology of TBI in Europe, Peeters and coworkers 6 analyzed data from 28 studies on 16 European countries and reported an average mortality 7 rate of ≈ 11 per 100,000 population over an incidence rate of 262 per 100,000 population per 8 year.3 Diffuse axonal injury (DAI), a multifocal damage to white matter axons, is the most 9 common consequence of TBIs of all severities including mild TBIs or concussions.4 Invisible 10 to conventional brain imaging, DAI can only be histologically diagnosed and its hallmark is 11 the presence of axonal swellings or retraction balls observable under microscopic 12 examination.5 13 14 Considerable research effort has been put into the understanding of the primary effects of 15 trauma onto the neurons. To define an axonal injury trigger, nervous tissues and neuronal 16 cultures have been subjected to dynamic loads leading to several hypotheses regarding the 17 cell injury mechanism. Mechanoporation (i.e. the generation of membrane pores due to 18 mechanical deformation) of the axolemma has been historically put forward as primary 19 axonal injury mechanism.6–11 Although such a mechanism was initially proposed to affect the 20 somatic plasmalemma, it was more recently associated with both the somata and neural 21 processes.12,13 Assessing the occurrence of such a mechanism is particularly important in 22 cases of mild/moderate TBIs, where cells’ abnormalities – but not immediate death- are 23 coupled with functional alterations.14 Disruption of the axolemma has been inferred 24 observing changes in membrane permeability due to mechanical stretch supposedly leading 25 to increased intra axonal calcium concentration, however this has been questioned by some 26 studies.15–17 27 28 Experimental studies using oriented cell cultures have instead put forward microtubule 29 disruption as cell injury trigger having observed cytoskeletal damage and tau protein 30 accumulation at the site of axonal swelling.18,19 These studies have further motivated the 31 development of models (both analytical and computational) having the microtubule bundle as 32 a focus.20–25 In our previous work, however, we have shown with a finite element model of 33 the entire axon that, especially when including detachment of tau protein elements, 34 deformations in the microtubules did not pass the suggested microtubule failure thresholds.26 35 On the contrary, we found that, as a result of axonal stretching and of microtubules 36 distancing, very high strain localization formed on the axonal membrane. However, we were 37 unable to say whether these could lead to axolemmal damage or not. 38 39 Up to date, studies assessing poration thresholds – both experimental and computational ones 40 - have not been axon-specific and therefore might not reflect axolemmal behavior. Previous 41 experimental studies have in fact focused on areal deformations of red blood cells (RBCs).27 42 Molecular simulations studies have investigated mechanoporation by deforming two-to-four 43 component lipid bilayer biaxially.28–30 Given the slenderness of the axons, however, during 44 stretch-injury one can expect the axolemma to deform mainly along the axial direction. Not 45 only loading mode specificity, but also material specificity might also play a key role in the 46 understanding of axonal injury. Among others, lipid composition is known to affect 47 membranes’ biomechanical properties.31 For example, experimental studies have established 32,33 48 areal failure thresholds (εA <10%) based on RBC’s or giant lipid vesicles’ membranes. It 49 has however been shown that these thresholds do not apply to the axons’ membrane: when

1 undergoing osmotic shocks - which induce biaxial deformation of the axolemma- in fact the 34 2 axolemma could sustain areal strains εA > 20%) without rupturing. 3 4 Another peculiarity of the axonal membrane is that both in unmyelinated and myelinated 5 axons, protein channels span the lipid bilayer, making possible the propagation of the action 6 potential. In particular, voltage-gated sodium channels are the main responsible for the 7 continuous and saltatory conduction in unmyelinated and myelinated axons respectively. The 8 density of sodium channels in the axonal membrane has been reported to be in the range 5- 9 3000 channels/μm2. Lower densities of sodium channels are found in unmyelinated axons, 10 while higher densities are observed in nodal portions of myelinated axons. 35,36 These 11 channels have also been proposed to influence the injury response.37 Rigid inclusions 12 embedded in a lipid bilayer model have been shown to facilitate membrane disruptions while 13 stiffening the membrane-inclusion system.38 In this study, unmyelinated axons are 14 considered. These axons are, in fact, not only as numerous as myelinated ones in the human 15 brain,19 but have also been shown to be more vulnerable to mechanical strain than their 16 myelinated counterpart.39,40 These motivations have so far justified the usage of unmyelinated 17 axons as experimental injury models. Modelling an unmyelinated axon allows us to gain a 18 better insight of the basic axon injury mechanism, irrespective of more complex and ill- 19 defined boundary conditions - such as those that could be induced especially at the paranodal 20 junction by the attachment of myelin or other surrounding tissue. 21 22 It is apparent that, in order to describe the axonal injury mechanism, both axon-specific 23 boundary conditions and material properties should be taken into account. Therefore, to 24 provide mechanical insights into the initiation of axonal damage, we combined a finite 25 element (FE) model of a generic distal portion of an unmyelinated axon and a molecular- 26 based lipid bilayer model with fixed number of particles. In particular, the axonal model was 27 utilized to simulate typical stretch injury scenarios (Figure 1a, 1d). As a result of cellular- 28 level deformation, local deformations happening at the cortex level (Figure 1b, 1e) could be 29 extracted. These local deformations were then used as input for molecular simulations of the 30 axonal lipid bilayer (Figure 1c, 1f). In this way, membrane permeability or poration could be 31 quantified in dependence of applied axonal strain and strain rates. 32 33 2 Methods

34 2.1 Finite element (FE) framework 35 FE head models are commonly used by the scientific community, despite their level of 36 idealization, for the explanation they can provide of traumatic phenomena. Through FE 37 simulations it is in fact possible to simulate traumas and extract quantities that would 38 otherwise be inaccessible via an experimental setup. Similarly, the FE method has been used 39 to capture the mechanical behavior of cells and subcellular components.41–47 More recently, 40 FE models of the axon have been proposed to shed a light on the mechanism behind axonal 41 injury.25,26,48–50 42 43 In the present study a previously published and validated axon FE model was used (Figure 44 1a), which is a 8 μm long representative volume (RV) of an axon consisting of three main 45 compartments: a microtubule (MT) bundle, the neurofilament (NF) network and, finally, the 46 axolemma-cortex complex wrapping the entire structure.26 The axon model diameter (1.15 47 µm) was chosen to fall in the range of those from experiments to which it was originally 48 validated against. 51–53 The choice of its length was instead dictated by considerations related

1 to the average MT length. Given the average continuous length of MTs (4.02 µm),54 to 2 contain a unit length of the microtubule bundle the length of the axon RV was set to 8 µm. 3 Given its cross-section and the proposed MTs densities, 19 rows of MTs were included in the 4 axon RV, each containing two randomly placed discontinuities.55–57 5 6 In the MT bundle, solid elastic MTs are cross-linked by viscoelastic tau proteins, which are 7 modeled as discrete beams. These are assigned a failure threshold so that they stop carrying 8 the load as soon as they reach double their length.20 The NF network is modeled as a dense 9 mesh of viscoelastic beams filling up the axonal space and anchoring the MTs to the plasma 10 membrane.58 A detailed description of our literature-supported modeling choices can be 11 found in the supplementary material and in our previous publication.26 12 13 14

15 16 Figure 1: Schematic representation of the combined modelling approach. (a) Finite element axonal model 17 coated with a slightly transparent layer symbolizing the lipid bilayer (virtual). A quarter of the model was 18 removed to reveal the arrangement of the inner structures. A microtubules bundle (solid blue hollow cylinders 19 cross-linked by beam-like tau proteins) is located centrally, while the rest of the axonal space is filled with a 20 dense beam-meshed neurofilaments network (yellow). The cytoskeleton is wrapped in a thick shell layer 21 representing the axonal cortex (grey) (b) Single undeformed cortex element coated with a virtual lipid bilayer 22 linked to the corresponding undeformed molecular coarse grained model of the lipid bilayer (c). The lipid 23 content resembles the plasma membrane: (PC lipids are in blue, PE in yellow, CHOL in green, SM in orange, 24 PS in purple, GM in red, anionic lipids in pink, and the rest of lipids in gray, water is not visualized for clarity). 25 (d) Deformed axon finite element model (axonal deformation, εaxon) (e) Deformed cortex element (localized 26 deformation: εx=0.34, εy=0). (f) Visualization of the induced pore upon lipid bilayer deformation. 27 28 In a study focused on the assessment of RBC membrane mechanical behavior, Evans and 29 coworkers defined the lipid bilayer as "along for the ride" when the cell is deformed, meaning 30 that the cortex (or “matrix”) is the one resisting the applied deformation and influencing the 31 structural response.59 Assuming this to be true also for the axon, in the current study, the 32 axonal wrapping layer was assigned properties in line with those of the sole axonal cortex. 33 The axonal cortex has a unique periodic organization made of rigid actin rings connected by 34 flexible cylinders of spectrin.60 In our model the cortex is represented by a layer of fully 35 integrated shell elements with a thickness of 50 nm.61 These elements were assigned a shear 36 modulus G = 0.0016 MPa and a viscosity η =105 Pas.62,63 Mechanical properties of all the

1 model components can be found in Table 1. In a recent study, fluid friction was observed at 2 the membrane-cortex interface with friction forces being proportional to the relative speed of 3 the two layers.61 Considering the axonal loading mode chosen for this investigation (i.e. pure 4 stretching), however, the relative movement between the two layers can be assumed to be 5 minimal. Hence, we assumed the lipid bilayer as fully tied to the cortex: any deformation 6 happening in the cortex plane would be directly transferred to the lipid bilayer. Therefore, in 7 the current study an explicit FE representation of the membrane was avoided (hence the 8 "virtual" representation in Figure 1) and deputed instead to a molecular dynamics 9 description. In practice, cortical deformations resulting from axonal injury simulations were 10 extracted and fed into coarse grained (CG) membrane or membrane-protein systems. 11 Axonal component Element type Material Microtubules Solid Linear elastic E=830 MPa ν=0.37 Cortex Shell G=0.0016 MPa η=1e5 Pas Tau proteins Discrete beam Linear viscoelastic K=5e-5 N/m μ=2.205e-4 Ns/m NFs elements Discrete beam Linear viscoelastic K=7.5e-5 N/m μ=1e-7 Ns/m Mts-NFs links Discrete beam Linear viscoelastic K=1e-6 N/m μ=1e-7 Ns/m 12 13 Table 1: Axon model material parameters. Young+s modulus (E), Poisson’s ratio (ν), shear modulus (G), 14 viscosity (η), spring stiffness (K), 1D viscosity coefficient (μ) (for references, see supplementary material) 15 16 2.2 Axonal injury simulations 17 To study axonal injury at the single-cell level it was deemed appropriate to consider the 18 axonal behavior under uniaxial deformation. It is generally accepted that strain is the main 19 mechanism behind axonal injury.64 Although at the tissue (i.e. brain) level strain presents 20 itself as a 3D tensor, to enforce experimental control, it is common to apply only one 21 deformation at a time, this being of compressive, tensile or shearing nature. It has previously 22 been shown with neuronal cultures that different loading modes might actually lead to 23 different mechanisms of injury.65 Specifically, in that study, Geddes-Klein and coworkers 24 found that stretching a primary cortical neuron culture uniaxially or biaxially (simultaneously 25 in two perpendicular directions) yielded different mechanisms behind the influx of calcium. 26 However, it should be considered that when deforming a network of cells - which are not 27 embedded in a matrix-, the network’s almost 1D structures, the single axons, will first re- 28 orientate in the direction of the load and then mostly stretch. 29 30 In an effort to investigate a general axonal behavior, rather than a particular one, 10 different 31 FE axon models were produced by altering the MT bundle geometry of the baseline model. 32 More specifically, every model was generated by randomly moving the MTs discontinuities 33 locations, while keeping the average MTs length of the original model. Symmetry conditions 34 were enforced on a quarter of a model and simulations were run with the latter condition. 35

1 Each axon FE model was subjected to a displacement-controlled uniaxial tensile deformation 2 (Figure 1d). Namely, each model was stretched up to a global strain εaxon = 30%. This 3 deformation range was chosen to cover all the axonal injury thresholds proposed so far in the 4 literature at either cellular or tissue level.66–70 The deformations were applied at strain rates 5 휀̇=1,10, 20, 40 /s, which are characteristic of axonal injury experiments.7,9,18 It is important to 6 note that our axon FE model represents an unmyelinated axon and hence can be compared 7 against in vitro injury model, which typically do not present myelinated axons. All 8 simulations were performed in LSDYNA using an implicit dynamic solver. The implicit 9 scheme was a necessary choice dictated by the element dimension, while the dynamic regime 10 was chosen to be able to capture strain-rate related inertia and material effects. Subsequently, st nd 11 for each simulation of 1,10, 20 and 40 /s strain rates the 1 and 2 principal strains ( 휀푥, 휀푦 ) 12 in the cortex plane were extracted as function of axonal strain.

13 2.3 Setting up the membrane molecular model 14 The membrane was modeled as a molecular-based lipid bilayer (two leaflets of lipids) and 15 was described by a CG model where groups of atoms (3-4 heavy atoms) are united into beads 16 which interact with each other by means of empirical potentials. The MARTINI2.2 force 17 field together with the non-polar water model was used.71–73 The axolemma is characterized 18 by having phosphatidylcholine (PC), phosphatidylethanolamine (PE), cholesterol (CHOL), 19 glycolipid, (and for some studies also sphingomyelin (SM)) as the main components (Table 20 S1). To mimic the axolemma’s lipid composition, the mammalian plasma membrane model 21 deposited on MARTINI webpage (http://www.cgmartini.nl/) was used.74 In the membrane 22 model, 63 different types of lipids were distributed asymmetrically between two leaflets 23 (Figure 1c). The outer leaflet has a higher level of saturation of the tails and contains PC 24 (36%), PE (6%), CHOL (31%), SM (19%), glycolipid (GM) (6%), and other lipids (2%). The 25 inner leaflet, which has a higher level of polyunsaturation, contains PC (17%), PE (25%), 26 CHOL (29%), SM (9%), phosphatidylserine (PS) (11%), anionic lipids phosphatidylinositol 27 (PIP) (2%), and other lipids (7%). Note that the reported values are in mol %. Full details of 28 the membrane model can be found in the work by Ingolfsson and coworkers.74 The bilayer 29 (containing a total of 6700 lipids) was placed in a cubic box (42*42*12 nm) and solvated by 30 about 100,000 CG water beads and NaCl was added to mimic the ionic strength at 31 physiological condition (150 mM NaCl). 32 33 2.4 Setting up of membrane-protein molecular model 34 Sodium channel protein type subunit alpha (Nav1.1) was used to represent the family of 35 voltage-gated ion channels embedded in the axonal membrane.75 The three-dimensional (3D) 36 structure for the homo sapiens Nav1.1 has not been resolved experimentally, however, the 37 encoding gene is known (SCN1A gene).76 Thus we built the 3D structure using homology 38 modeling and Phyre2 server was used.77 Among the available sodium channels, the best 39 sequence alignment (100% confidence and 48% sequence identity) was found with putative 78 40 sodium channel from American cockroach, NavPaS (PDB ID: 5X0M). The cryo-electron 41 microscopy structure of NavPaS has been used as template. The missing N-terminal and C- 42 terminal domains, 1-2 and 3-4 linkers were modeled using the software Modeller.79 43 The so obtained 3D structure for Nav1.1 is composed of a single polypeptide chain that folds 44 into four homologous repeats (Figure 2), each one containing six transmembrane segments. 45 The protein was oriented in the lipid bilayer using Positioning of Proteins in Membrane 46 (PPM) method.80 The structure was first minimized in the PC bilayer at the atomistic level 47 (using CHARMM36 force field81) using 5000 steps of steepest descent minimization and then 48 equilibrated for 200 ns.

1 The obtained atomistic structure was used to build the protein CG model. Martinize protocol 2 together with ElNeDyn were used to convert the atomistic Nav1.1 structure into a coarse- 3 grained model.82,83 One protein was embedded in the 42x42 nm2 CG membrane (Figure 2), 4 that corresponds to a density of 567 ion channels/μm2 . 5

6 7 Figure 2: (a) Three dimensional structure of Nav1.1 protein embedded in the lipid bilayer. Protein is shown by 8 secondary structure elements (α-helix in magenta, β-sheet in yellow, turn in cyan, and coil in black). Phosphate 9 atoms of lipid head group are shown in blue. (b) CG model of Nav1.1 protein in the plasma membrane model. 10 Protein is shown in black VDW representation. For lipid color code see Figure 1. 11 12 2.5 Molecular Dynamics (MD) simulations 13 MD simulations are widely used to provide a three-dimensional description of lipid bilayers 14 and proteins at the molecular level and their evolution in time, from which time-dependent 15 and independent properties can be evaluated.84 All MD simulations were performed using the 16 GROMACS simulation package, version 2016.85 Simulations have been performed in NPT 17 ensemble (constant number of particles, constant pressure, and constant temperature) and 18 NPzAT ensemble (constant number of particles, constant pressure along z, Pz , constant 19 bilayer area, and constant temperature). The temperature of the systems was kept at 310 K 20 using velocity rescale thermostat with a time constant of 1ps.86 Semi-isotropic Parrinello- 21 Rahman barostat was applied to couple the pressure to 1 bar with a time constant of 12 ps 22 (compressibility of 3e-4 bar-1).87 Periodic boundary conditions were applied. A time step of 23 20 fs was used. The Verlet cutoff scheme was used. Non-bonded interactions were calculated 24 using a cut-off of 1.1 nm.88 The reaction field potential was used to treat long range 25 electrostatic interactions using a switching distance of 1.1 nm.89 26 27 NPT simulations were performed to equilibrate the membrane structure in absence of 28 deformation. To generate the starting structures for deformed lipid bilayers, we deformed the 29 bilayer using unsteady stretching algorithm with a stretching speed c=5 m/s. The so-obtained 30 deformed system was then simulated at constant bilayer area for 2 µs to generate an ensemble 31 of configurations that describes the membrane at the selected strain. The simulations were 32 extended up to 5 µs for strains larger than 30 %. During the simulations an elastic bond force 33 constant of 500 kJ.mol-1.nm-2 was applied to the protein atom pairs within a 0.9 nm cut-off 34 (ElNeDyn).83 That means that the protein is simulated as a semi-rigid body. The analysis was 35 performed on the last 1μs of production runs. The errors were calculated by block averaging 36 over 5 blocks. All the figures were rendered using Visual Molecular Dynamics software.90 As 37 criteria to detect pore formation in the lipid bilayer, we use the jump in the surface tension. 38 After the detection of the pore, simulations were extended of 5 to 9 µs to check whether 39 spondaneous sealing occurred in the simulation time scale (microseconds). 40 41 2.6 Permeability coefficient

1 The transport of substances across a lipid membrane is a biological process of vital 2 importance. Small molecules, such as water molecules or drugs, can be transported into the 3 membrane in a passive or active way. A passive transport proceeds via an entropy-driven, 4 nonspecific diffusion process of the molecule across the membrane. Permeability or leakage 5 of a small molecule should give a measure of the structural stability of the membrane since it 6 should reflect lipid packing at the membrane core. Membrane permeation can be described by 7 a so called "solubility-diffusion mechanism" (see review by Shinoda91 for details) and 8 quantified by the membrane permeability coefficient, Pm. The Pm of a water molecule is 92,93 9 proportional to its oil/water partition coefficient (Koil/water). 10 11 First, we calculated the membrane/water partition coefficient for water at equilibrium and at 12 different strains. We do that by calculating the average number of water molecules (1 CG 13 water bead = 4 water molecules) in the bilayers within a distance of 0.52 nm from the lipid 14 tails on 1 µs molecular simulations. The partition coefficient for water is 퐾mem/water = [solute]mem 15 , where [solute] denotes the concentration of water molecules in the lipid bilayers [solute]water 16 and water solution, respectively. [water]mem is obtained by dividing the average number of 17 water molecules by the lipid bilayers volume, while for the water concentration in water the 18 experimental value (55.5 mol/L) was used. The membrane volume was corrected to account 19 for the presence of the protein. Knowing that logPm is proportional to logKmem/water , we then 20 estimated how membrane strain influences its permeability.

21 3 Results 22 In this study, axonal injury was simulated deforming a FE model of the axons of a quantity 23 εaxon . Cortex principal strains (εx, εy) were then extracted and applied in cascade to a 24 molecular model of the plasma membrane and the structural outcome on the latter was 25 observed . As evidenced by Figure 3 - which shows the distribution of 1st Principal Green 26 Lagrange strains along the cortex shell-layer for one of the 10 tested models for 5% < εaxon 27 <15%- when the axon is stretched (0< εaxon <30 %), due to its composite nature, the 28 deformation pattern along the axonal cortex is not homogeneous. Areas of strain 29 concentration on the cortex evidently form throughout axonal deformation. The magnitude of 30 this strain concentration is dependent both on the applied strain (different columns in Figure 31 3) and strain rate (different rows in Figure 3). It can be observed that, for example, an 32 applied axonal strain as low as 5% corresponds to a local maximum strain which is twice as 33 high. The more εaxon increases, the more this localization of strains in the cortex is 34 pronounced. Moreover, on each column it is possible to observe, for the same axonal strain, 35 the influence of strain rate (1, 10 and 40 /s) on the local deformation level. Here it is possible 36 to notice that higher strain rates do not lead to higher local maximum strains for εaxon<10%. 37 However, at higher axonal strains the intuitive order is re-established: higher strain rates lead 38 ultimately to higher cortex-level deformations (Figure S2). 39 40 To better understand this behavior, the average results of 10 different models are reported in 41 Figure 4 together with the standard deviations for each tested strain rate. In this plot the st 42 cortex maximum 1 Principal Green-Lagrange strains (εx) are reported as a function of the 43 applied axonal strains. What can be noted is, first, the increased standard deviation with 44 higher rates. In addition, one can notice that for strain rates of 1 /s and 10 /s the curves follow 45 the same path until εaxon ≈ 7% and then diverge. Interestingly, as previously noted, the 46 response for a strain rate of 40 /s is on average lower than that of 1 /s and 10 /s until εaxon ≈ nd 47 12% and εaxon ≈ 20% respectively. 2 Principal Green-Lagrange strains (εy) in the cortex

1 plane were consistently found to be at least 6 orders of magnitude inferior to εx, therefore 2 they were set to zero when input into MD simulations. 3

4 5 6 Figure 3: Fringe plots showing the 1st Principal Green-Lagrange strain along the axonal cortex as a result of 5, 7 10, and 15 % axonal strains in the first, second and third column respectively. In the first, second and third row 8 results for strain rates of 1, 10 and 40 /s are reported. The range was set between 0 and 40% for visualization 9 purposes. 10 11 To understand the effect of axonal deformation on the membrane integrity, we used MD 12 simulations and a molecular based-lipid bilayer to describe the axonal membrane. First, to 13 verify that the membrane models resemble the mechanical feature of natural membrane, the 14 area compressibility modulus was estimated for small areal strain values (less than 0.05). A 15 value of 303±6 mN/m and 352±3 mN/m, respectively in absence and presence of Nav1.1 16 protein, was obtained (Figure S3) – which is in agreement with the area compressibility 17 modulus measured for red blood cell membranes (375±60 mN/m) at 37°C by Waugh and 18 Evan.94 The agreement allows us to move forward and use the model to investigate the effect 19 of local deformation on the bilayer structure. A selected number of cortex strains εx (Figure 20 4) were input into the membrane and membrane-protein system, while the membrane model 21 was kept undeformed in the y-direction (εy=0). 22 23 We monitored the bilayer structural features (i.e. pore formation, interdigitation, and water 24 permeability) at different local strains. Figure 5 depicts how the occurrence of pore 25 formation is detected. Namely, this event corresponds to a jump in the surface tension. 26 Figure 6 summarizes which molecular-level event is to be expected at each axonal strain εaxon 27 (and related maximum cortex strain, εx) for a plasma bilayer model with and without 28 embedded protein. The lipid bilayer can withstand the applied strain value of εx = 34% , 29 corresponding to εaxon = 10-12 %. At higher strains pore formation is observed. When Nav1.1 30 is embedded in the membrane, poration occurs at a larger cortex strain (εx = 47 %), 31 corresponding to εaxon = 12-15 %.

1 2 Figure 4: Maximum 1st Principal Green-Lagrange strains in the axonal corex as a function of axonal strain. 3 Lines represent the average over 10 models and the shaded areas represent the standard deviations. Results are 4 shown for strain rates 1,10, 20, and 40 /s. In the second row (center), the means for the different strain rates are 5 shown in the same plot to ease the visual comparison. Finally, in the second row (right), iso-strain curves are 6 reported, which show the maximum 1st Principal Green-Lagrange strains in the cortex as a function of the 7 applied strain rate. 8

9 10 Figure 5: Surface tension and corresponding lipid bilayer structure at εx=0.34 as a function of simulation steps. 11 12

1 2 3 Figure 6: Axonal strains and corresponding maximum local strains (mean values over a family of 10 different 4 FE axonal models) together with strain rates . * indicates the local deformations for which molecular dynamics 5 simulations have been performed. Top panel refers to the membrane model and bottom panel to the membrane- 6 protein model. ΔPm indicates how water permeability increases with respect to the equilibrium value (at local 7 strain=0). max corresponds to 40 % in the membrane model and 51% in the membrane-protein system. 8 9 Figure 7 shows an example of the observed bilayer disruption in absence and presence of 10 Nav1.1 protein (MovieS1, Movie S2). We observed that the membrane rupture occurs at 11 slightly larger local strain in presence of the protein. The presence of the Nav1.1 protein 12 therefore not only renders the membrane more resistant to deformation but also to rupture. In 13 addition, it was observed that before poration, the bilayers start to form interdigitated states 14 (Figure S4). Interdigitation occurs at εx > 27 % in absence of protein and εx > 34 % in 15 presence of protein, corresponding to εaxon =9%-11% and εaxon =10-12%, respectively (Figure 16 6). Interestingly, poration both in presence and absence of protein takes place in bilayer 17 regions lacking ganglioside lipids (Figure 7). Ganglioside-type lipids are mainly found in the 18 outer leaflet of the membrane and are known to make the lipid bilayer more resistant to 19 deformation due to the interactions between sugar headgroups.30 20

1 2 3 Figure 7: Lipid bilayers disruption. Left panels: snapshot at 680ns at εx=0.34 in absence of Nav1.1. Right 4 panels: snapshot at 27 ns for εx=0.47 in presence of Nav1.1. (in black). Top panels show the upper leaflets, low 5 panels show the lower leaflets. For lipids color code see Figure 1. 6 7 To quantify that the molecular models indeed reproduce membrane partitioning, we 8 calculated the membrane/water partition coefficient for water at equilibrium (logKmem/water = - 9 1.73). The presence of the protein has almost no effect on the partition coefficient 10 (logKmem/water = -1.75). At the increase of εaxon, water partitioning between aqueous solution 11 and lipid bilayers increases proportionally to εx (Figure S5). Given the aforementioned 12 proportionality between the partition coefficient Kmem/water and the permeability Pm, the latter 13 can be quantified as a function of strain. In particular, starting from equilibrium state, water 14 permeability increases up to 40 % (51 % in presence of protein) before pore formation. 15 Figure 6 coloring describes the change in water permeability for the the lipid bilayers with 16 and without protein channel at the increase of εaxon for different strain rates. 17 18 4 Discussion 19 The biomechanics of TBI has been the focus of considerable research effort for many years 20 now. Nevertheless, the underlying injury mechanism leading to cellular impairment is yet to 21 be explained. The use of in-silico models can provide better understanding of the mechanical 22 cues determining cells’ condition immediately after a mechanical insult. In this study, for the 23 first time, we were able to provide direct mechanical evidence of the possible onset of 24 mechanoporation as a result of the mechanical insult. More specifically, bridging finite 25 element and molecular dynamics simulations, we could determine at which level of axonal 26 strain the lipid bilayer sustains local deformations high enough to induce pore formation. 27 28 Several studies so far have stressed the need of taking into account axonal direction and 29 kinematics when studying injury at the tissue level both in experimental set-ups and 30 computational models. 95–97 It has indeed been assessed from tissue or cell cultures that 31 deformations applied to a tissue do not necessarily coincide with those sustained by the 32 embedded axons. In fact, in both tissue models -such as the optic nerve or organotypic slices- 33 and cell cultures non-affine deformations might arise. Similarly, at the cellular scale, which 34 is the focus of the current study, the applied axonal strains εaxon do not directly transfer to the 35 axonal membrane, due to the axonal composite nature. Despite being often assumed as a

1 homogeneous viscoelastic entity, the axon presents dramatic heterogeneities in deformation 2 along its length when stretched.98 Evidence of this is also the localized axonal length increase 3 (up to 65%) that was observed as a result of axonal stretch.19 The morphological response to 4 stretch injury – such as the appearing of undulations and periodical swellings– clearly hints at 5 an heterogeneity in the axonal response to tensile injury loads. This is confirmed by the 6 localization of membrane strains that we observed with our model (Figure 3). This 7 localization is directly related to the point of weakest connectivity of the microtubule 8 bundle.24,99 9 10 Especially when considering that our axonal finite element model is just an 8 μm-long 11 representative volume of the axon, one should imagine such a strain localization taking place 12 periodically along a periodical repetition of our model. The periodical swelling, which is 13 characteristic of axonal injury, could therefore be explained by the heterogeneous 14 deformations that are revealed by our model. 15 Recently, an experimental work has tried to quantify axonal membrane strains induced by the 16 deformation applied to a cell culture as a whole.100 Differences between applied strains and 17 membrane strains were reported. However, it must be noted that these discrepancies may 18 mostly be due to the non-alignment between applied load and axons’ directions within the 19 culture. Moreover, membrane strains were calculated from the level of separation of fiducial 20 membrane markers whose initial distance is not reported. Hence, a direct comparison 21 between our results and these data cannot be made. 22 23 In our results maximum cortex strains clearly appear as a nonlinear function of axonal strain 24 (Figure 3). Less intuitive is however the relation with strain rate. Due to the viscoelastic (and 25 hence rate-dependent) properties of tau proteins and of the cortex itself, at axonal strains 26 lower than 12%, the cortex deforms less at strain rate 40 /s rather than at 1 /s or 10 /s. Similar 27 observations were reported in previous studies based on numerical and analytical models of 28 the sole microtubule bundle.24,25,99 In those studies, simulations of the microtubule bundle 29 undergoing stretch revealed a higher resilience of the microtubule bundle at higher stretch 30 rates. Whether this emerging property is reflected by experimental models of axonal injury 31 has, to the best of our knowledge, not been established yet. 32 33 To assess the influence of the chosen material properties on maximum cortex strains and on 34 this rate-related phenomenon, a sensitivity study was conducted with one of the ten 35 geometries (Figure S1 in Supplementary material). The results indicate that, while 36 neurofilament and cortex properties minimally affect cortex strains, tau protein viscosity 37 does, particularly at rate 40 /s. Changes in tau proteins’ viscosity yield similar results at rate 1 38 and 10 /s. However, at rate 40 /s increasing or decreasing the viscosity of 100%, delays or 39 anticipates, respectively, the crossing of the mechanoporation threshold. A purely elastic 40 behavior for these elements (null viscosity) re-establishes the intuitively expected order: 41 cortex maximum deformation increases with increasing rate. Although the differences by 42 means of maximum cortex strains are minimal, a rate dependent or stress-based failure 43 criterion for the tau protein (or of other filaments) could be more appropriate and might alter 44 this non intuitive relation between poration and strain rate. Alternatively, a surface tension- 45 based poration criterion could be investigated. 46 47 Local deformations of the axonal cortex were used as input to MD simulations of the lipid 48 bilayer to establish model-informed axonal injury thresholds. Combining the axonal and 49 membrane level we show that poration occurs in a range of axonal strains going from 10% to 50 15%. These values are in agreement with previously established axonal injury

1 thresholds.18,66–70 Thresholds obtained from experimental tissue injury models cover a 2 slightly higher range of axonal strains.68,69 However, this is probably due to the influence of 3 axonal tortuosity and the alternation between an affine/non-affine regime.95,96 Namely, when 4 deforming the tissue experimentally, at least initially, part of the tissue deformation goes into 5 straightening of the axons. Only later the axons themselves sustain a deformation. 6 7 Several studies have so far tried to assess axonal injury by means of permeability.6,9,10,12,16,101 8 Cell-impermeant macromolecules, such as horseradish peroxidase or Lucifer Yellow, are 9 commonly injected in the extracellular space, prior to the application of a mechanical insult 10 to cell culture or the organ itself. The presence of these molecules in the intra-cellular space 11 post-injury has been proposed as an indicator of pore formation in the axolemma. These 12 changes are studied as a function of the magnitude of the applied strain and strain rate. 13 However, most often results are representative of the entire culture (consisting of non-aligned 14 axons) and not of the single cell. Hence, they cannot be compared with our results that 15 instead relate axonal strains to permeability changes in a localized membrane volume. In a 16 study by Kilinc and coworkers,10 however, permeability was observed in individual axons. In 17 particular, membrane permeability in injured axons was found to be twice as high as in 18 control axons. This is in agreement with our results showing that changes in water 19 permeability can be expected to be higher than 40 % (51 % in presence of embedded 20 proteins) at the onset of poration. Nevertheless, our results show that changes in permeability 21 can be expected even below the poration threshold, namely at axonal strains lower than 10-15 22 %. Interestingly, in a previous study by Yuen and coworkers,70 which utilized an aligned cell 23 culture system, pathological axonal alterations were observed at strains starting from 18,66– 24 εaxon=5% – a value that is more than twice as low as established axonal injury thresholds. 25 69 Based on our molecular simulations insight, this might be indeed justified by alterations in 26 axolemma permeability pre-poration. 27 28 At this stage, we would like to stress that it is only the combination between these two 29 models (the axonal and molecular-based membrane model) that allowed us to achieve such a 30 good agreement with experimental injury thresholds. In particular, ignoring the composite 31 nature of the axonal model, one would be tempted to assume that the strains sustained by the 32 membrane are equivalent to the tensile strains sustained by the axon. In this scenario, 33 according to our results (Figure 6), poration would occur at εx=εaxon  [0.34,0.51]. These 34 strain values are considerably higher than those so far proposed for axonal injury. Our 35 modeling effort was first aimed at an accurate representation of the axon passive mechanical 36 response to provide axon-specific boundary conditions to simulate molecular-level membrane 37 simulation. Secondly, an accurate representation of the membrane lipid content was deemed 38 necessary to assess features such as membrane permeability and poration given that lipid 39 content is known to have an influence on membrane's mechanical properties.28,30,31,33 40 Notably, considering the strain concentrations revealed by the axonal model with a different 41 lipid bilayer model would have yielded different results. Pure phospholipidic bilayers, in fact, 42 have been reported not to rupture until 0.68 von Mises strain.29 43 44 5 Limitations 45 Although our modeling approach brings new insights into the axonal injury mechanism, here 46 we want to address some limitations. Firstly, it must be noted that no active molecular 47 mechanism was considered in our axonal injury simulations. This was deemed a fair 48 approximation given that the aim of this work is to assess injury events that happen in 49 fractions of seconds, whereas biomolecular mechanisms, such as polarization/depolarization, 50 neurofilaments transport etc. live in the seconds-time scale. In light of this, our results are to

1 be seen as insights into the possible mechanistic events related to primary injury, rather than 2 damage evolution towards secondary axotomy. 3 4 It is also important to stress that our model represents a generic portion within the distal axon 5 of an unmyelinated neuron. Several studies have so far proposed specific axonal sites such as 6 the nodal, paranodal, internodal segments as primary sites of injury.102–104 Few studies have 7 also highlighted the susceptibility to injury of the axon initial segment (AIS), the parasomatic 8 region where action potentials are initiated.105–107 Due to the differences in the cytoskeleton 9 of the AIS and the distal axon, however, our results cannot be generalized to this segment. 10 11 Microtubules failure was discarded as injury trigger in our previous publication.26 12 Nevertheless, primary effects on other filaments might still subsist. For example, 13 neurofilament (NF) compaction was reported to occur as a direct effect of the mechanical 14 insult by Meythaler and coworkers.108 However, a larger body of evidence suggests NFs 15 compaction to be associated it with axolemmal permeability changes.109–111 Our model 16 includes a representation of the NFs network, whose morphological and material 17 characteristics are reported in the supplementary material. Nevertheless, we are persuaded 18 that the current representation of this network in our FE model, despite being reasonable as a 19 bulk, cannot reveal local phenomena related to injury. The lack of experimental information 20 in fact prevented us from assigning specific properties to filament backbone and side-arms as 21 well as failure properties for their connections. Hence, a priori, we cannot exclude that 22 damage to this component of the model takes place. 23 24 At this point, it is to note that our model accounts for the effect of an embedded protein on 25 the membrane structural features, but does not account for possible protein structural change 26 at different strains, since the protein is described as a semi-rigid body. Nav1.1 was chosen as 27 a representative example of one of the axolemma ion channels, however our protein- 28 membrane system does not account for the inhomogeneity of proteins distribution along the 29 axolemma. Future studies could aim at assessing the potential effect of protein deformability, 30 compositions or distributions on axolemma stretch susceptibility. 31 32 Moreover, the molecular systems used in this study do not account for the recruitment of 33 lipids, which has previously been discussed as a strategy put in place by the neurons to 34 reduce the build-up in membrane tension. 34,112 Such a mechanism was however observed in 35 experiments applying a “gentle” osmotic perturbation rather than very fast deformations as 36 those simulated in this study. Hence, although such a mechanism should be taken into 37 account when studying the evolution of axonal injury, it is here deemed not to affect our 38 considerations. 39 40 Further method specific limitations have been previously addressed for both the axonal model 41 and for molecular simulations of membranes.26,113 What we would like to address at this stage 42 are possible alternatives to the methodology that was presented here to bridge the axon finite 43 element and membrane molecular descriptions. An alternative to our approach could have 44 been to describe also the lipid bilayer at the continuum (axonal) level and derive tensions 45 (pressures) to be subsequently input into the molecular system. However, extracting 46 continuum properties from molecular systems is a nontrivial problem and underlies several 47 assumptions.114–118 Equating the strains at the two different length scales, on the contrary, 48 allowed us to prescind from a continuum description of the lipid bilayer that would have been 49 otherwise affected by several other assumptions. Another option is to directly apply strain 50 rates (1, 10, and 40 1/s) to the molecular-based membrane model. However, at the moment, it

1 is computationally unfeasible to obtain results at such time scale in a reasonable time frame. 2 Applying local strain directly to the simulation allowed us to overcome the time scale issue. 3 4 The current models were used in cascade to investigate the response to a purely uniaxial 5 stretch injury. Although this can be comparable to a controlled in vitro loading mode, it does 6 not directly correlate with the in vivo scenario. Strains in the brain are in fact represented by a 7 3D tensor. Current finite element head models resolve, with slightly different methods, this 8 tensor in the fiber direction and use this one-dimensional quantity as injury predictor.119–122 In 9 future studies, the uniaxial condition could be dropped to study how an axonal model 10 embedded in a matrix responds to a complete strain tensor. As a result of the different 11 boundary conditions the axonal model and its axolemma might undergo deformations which 12 are different from those observed in the present study. 13 14 6 Conclusions 15 In this study we successfully applied a top-to-bottom approach to better characterize the onset 16 of axonal injury. By bridging continuum and molecular descriptions, we have provided 17 quantitative evidences showing that mechanoporation of the axolemma is an event that 18 cannot be excluded in a typical axonal injury scenario. In addition, we showed that pre- 19 poration strain levels were characterized by an increased water permeability and 20 interdigitated states. All in all, our study results provide increased knowledge of the axonal 21 injury mechanism and have therefore potential positive implications for the development or 22 optimization of neuroprotective measures targeting membrane integrity in the treatment of 23 axonal injuries and brain injuries in general. 24 25 7 Acknowledgments: The authors thank the Swedish Research Council (VR-2016-05314), 26 the European Union Horizon 2020 Research and Innovation Framework Programme under 27 the Marie Skłodowska-Curie (grant agreement No. 642662), and the Swedish National 28 Infrastructure for Computing (SNIC2017-1-491 and SNIC2018-3-548) for the support. 29 30 8 Author Contribution statement: AM, MS, AV and SK designed the study. AM 31 performed and analyzed the finite element simulations, while MS and AV performed and 32 analyzed the molecular dynamics simulation. AM, MS and AV prepared the manuscript. All 33 authors critically reviewed the manuscript. 34 35 9 Author Disclosure Statement: No competing financial interests exist. 36 37 38 [Supplementary Material] 39 40 41 References: 42 1. Menon, D.K., Schwab, K., Wright, D.W., and Maas, A.I. (2010). Position statement: 43 Definition of traumatic brain injury. Arch. Phys. Med. Rehabil. 91, 1637–1640. 44 2. Taylor, C.A., Bell, J.M., Breiding, M.J., and Xu, L. (2017). Traumatic Brain Injury- 45 Related Emergency Department Visits, Hospitalizations, and Deaths - United States, 46 2007 and 2013. MMWR. Surveill. Summ. 66, 1–16. 47 3. Peeters, W., van den Brande, R., Polinder, S., Brazinova, A., Steyerberg, E.W., 48 Lingsma, H.F., and R., M.A.I. (2015). Epidemiology of traumatic brain injury in 49 Europe. Acta Neurochir. (Wien). 157, 1683–1696. 50 4. Johnson, V.E., Stewart, W., and Smith, D.H. (2013). Axonal pathology in traumatic

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