Mechanical Effects of Dynamic Binding between Tau Proteins on Microtubules during Axonal Injury

The viscoelastic nature of axons plays a key role in their selective vulnerability to damage in traumatic brain injury (TBI). Experimental studies have shown that although axons can tolerate 100% strain under slow loading rates, even strain as small as 5% can rupture microtubules (MTs) during the fast loading velocities relevant to TBI. Here, we developed a computational model to examine rate-dependent behavior related to dynamic interactions between MTs and the MT-associated protein tau under varying strains and strain rates. In the model, inverted pairs of tau proteins can dynamically cross-link parallel MTs via the respective MT-binding domain of each tau. The model also incorporates realistic thermodynamic breaking and reformation of the bonds between the connected tau proteins as they respond to mechanical stretch. With simulated stretch of the axon, the model shows that despite the highly dynamic nature of binding and unbinding events, under fast loading rates relevant to TBI, large tensile forces can be transmitted to the MTs that can lead to mechanical rupture of the MT cylinder, in agreement with experimental observations and as inferred in human TBI. In contrast, at slow loading rates, the progressive breaking and reformation of the bonds between the tau proteins facilitate the extension of axons up to ∼100% strain without any microstructural damage. The model also predicts that under fast loading rates, individual MTs detach from MT bundles via sequential breaking of the tau-tau bonds. Finally, the model demonstrates that longer MTs are more susceptible to mechanical rupture, whereas short MTs are more prone to detachment from the MT bundle, leading to disintegration of the axonal MT ultrastructure. Notably, the predictions from the model are in excellent agreement with the findings of the recent in vitro mechanical testing of micropatterned neuronal cultures.     

Micromechanical analysis of brain’s diffuse axonal injury

Computational models are important tools which help researchers understand traumatic brain injury (TBI). A mechanistic multi-scale numerical approach is introduced to quantify diffuse axonal injury (DAI), the most important mechanism of TBI, induced by a mechanical insult at micro-scale regions of the white matter or voxels where fiber orientations are the same. Using the mechanical properties of a single axon with a viscoelastic constitutive relation and its functional failure in terms of electrophysiological impairment, a numerical 2D micro-level lattice method is implemented to directly analyze the percentage of injured axons in a voxel containing a bundle of axons all with the same orientation under biaxial stretches. Reference micro-injury maps are then developed with the input parameters based on the principal strain or stretch values and their direction with respect to axons, which provide the percentage of injured axons in the voxel of interest as the output. The methodology is independent of any statistical analyses of the accident data and medical reports to derive probabilistic injury risk curves for DAI. Avoiding a structurally detailed full finite element head model, this study proposes a micro-mechanical approach which considers the anatomical structure of neural axons in the white matter together with their mechanical properties using a numerical lattice method to analyze the brain’s diffuse axonal injury. This work has the potential to help develop safer prevention tools and more effective diagnosis methods for DAI.     

Strains at the myotendinous junction predicted by a micromechanical model

The goal of this work was to create a finite element micromechanical model of the myotendinous junction (MTJ) to examine how the structure and mechanics of the MTJ affect the local micro-scale strains experienced by muscle fibers. We validated the model through comparisons with histological longitudinal sections of muscles fixed in slack and stretched positions. The model predicted deformations of the A-bands within the fiber near the MTJ that were similar to those measured from the histological sections. We then used the model to predict the dependence of local fiber strains on activation and the mechanical properties of the endomysium. The model predicted that peak micro-scale strains increase with activation and as the compliance of the endomysium decreases. Analysis of the models revealed that, in passive stretch, local fiber strains are governed by the difference of the mechanical properties between the fibers and the endomysium. In active stretch, strain distributions are governed by the difference in cross-sectional area along the length of the tapered region of the fiber near the MTJ. The endomysium provides passive resistance that balances the active forces and prevents the tapered region of the fiber from undergoing excessive strain. These model predictions lead to the following hypotheses: (i) the increased likelihood of injury during active lengthening of muscle fibers may be due to the increase in peak strain with activation and (ii) endomysium may play a role in protecting fibers from injury by reducing the strains within the fiber at the MTJ.     

Tissue-level thresholds for axonal damage in an experimental model of central nervous system white matter injury

In vivo, tissue-level, mechanical thresholds for axonal injury were determined by comparing morphological injury and electrophysiological impairment to estimated tissue strain in an in vivo model of axonal injury. Axonal injury was produced by dynamically stretching the right optic nerve of an adult male guinea pig to one of seven levels of ocular displacement (Nlevel = 10; Ntotal = 70). Morphological injury was detected with neurofilament immunohistochemical staining (NF68, SM132). Simultaneously, functional injury was determined by the magnitude of the latency shift of the N35 peak of the visual evoked potentials (VEPs) recorded before and after stretch. A companion set of in situ experiments (Nlevel = 5) was used to determine the empirical relationship between the applied ocular displacement and the magnitude of optic nerve stretch. Logistic regression analysis, combined with sensitivity and specificity measures and receiver operating characteristic (ROC) curves were used to predict strain thresholds for axonal injury. From this analysis, we determined three Lagrangian strain-based thresholds for morphological damage to white matter. The liberal threshold, intended to minimize the detection of false positives, was a strain of 0.34, and the conservative threshold strain that minimized the false negative rate was 0.14. The optimal threshold strain criterion that balanced the specificity and sensitivity measures was 0.21. Similar comparisons for electrophysiological impairment produced liberal, conservative, and optimal strain thresholds of 0.28, 0.13, and 0.18, respectively. With these threshold data, it is now possible to predict more accurately the conditions that cause axonal injury in human white matter.     

Multiscale mechanics of the cervical facet capsular ligament,with particular emphasis on anomalous fiber realignment prior to tissue failure

The facet capsular ligaments encapsulate the bilateral spinal facet joints and are common sources of painful injury due to afferent innervation. These ligaments exhibit architectural complexity, which is suspected to contribute to the experimentally observed lack of co-localization between macroscopic strain and microstructural tissue damage. The heterogeneous and multiscale nature of this ligament, combined with challenges in experimentally measuring its microscale mechanics, hinders the ability to understand sensory mechanisms under normal or injurious loading. Therefore, image-based, subject-specific, multiscale finite-element models were constructed to predict the mechanical responses of the human cervical facet capsular ligament under uniaxial tensile stretch. The models precisely simulated the force–displacement responses for all samples (\(\textit{R}^{2}=0.99\pm 0.01\)) and showed promise in predicting the magnitude and location of peak regional strains at two different displacements. Yet, there was a loss of agreement between the model and experiment in terms of fiber organization at large tissue stretch, possibly due to a lack of accounting for tissue failure. The mean fiber stretch ratio predicted by the models was found to be significantly higher in regions that exhibited anomalous fiber realignment experimentally than in regions with normal realignment (\(\textit{p}<0.002\)). The development of microstructural abnormalities was associated with the predicted fiber-level stretch (\(\textit{p}<0.009\)), but not with the elemental maximum principal stress or maximum principal strain by logistic regression. The multiscale models elucidate a potential mechanical basis for predicting injury-prone tissue domains and for defining the relationships between macroscopic ligament stretch and microscale pathophysiology in the subfailure regime.     

The Axonal Membrane Protein Caspr, a Homologue of Neurexin IV, Is a Component of the Septate-like Paranodal Junctions That Assemble during Myelination

We have investigated the potential role of contactin and contactin-associated protein (Caspr) in the axonal–glial interactions of myelination. In the nervous system, contactin is expressed by neurons, oligodendrocytes, and their progenitors, but not by Schwann cells. Expression of Caspr, a homologue of Neurexin IV, is restricted to neurons. Both contactin and Caspr are uniformly expressed at high levels on the surface of unensheathed neurites and are downregulated during myelination in vitro and in vivo. Contactin is downregulated along the entire myelinated nerve fiber. In contrast, Caspr expression initially remains elevated along segments of neurites associated with nascent myelin sheaths. With further maturation, Caspr is downregulated in the internode and becomes strikingly concentrated in the paranodal regions of the axon, suggesting that it redistributes from the internode to these sites. Caspr expression is similarly restricted to the paranodes of mature myelinated axons in the peripheral and central nervous systems; it is more diffusely and persistently expressed in gray matter and on unmyelinated axons. Immunoelectron microscopy demonstrated that Caspr is localized to the septate-like junctions that form between axons and the paranodal loops of myelinating cells. Caspr is poorly extracted by nonionic detergents, suggesting that it is associated with the axon cytoskeleton at these junctions. These results indicate that contactin and Caspr function independently during myelination and that their expression is regulated by glial ensheathment. They strongly implicate Caspr as a major transmembrane component of the paranodal junctions, whose molecular composition has previously been unknown, and suggest its role in the reciprocal signaling between axons and glia.     

Viscoelasticity of Tau Proteins Leads to Strain Rate-Dependent Breaking of?Microtubules during Axonal Stretch Injury: Predictions from a Mathematical Model

The unique viscoelastic nature of axons is thought to underlie selective vulnerability to damage during traumatic brain injury. In particular, dynamic loading of axons has been shown to mechanically break microtubules at the time of injury. However, the mechanism of this rate-dependent response has remained elusive. Here, we present a microstructural model of the axonal cytoskeleton to quantitatively elucidate the interaction between microtubules and tau proteins under mechanical loading. Mirroring the axon ultrastructure, the microtubules were arranged in staggered arrays, cross-linked by tau proteins. We found that the viscoelastic behavior specifically of tau proteins leads to mechanical breaking of microtubules at high strain rates, whereas extension of tau allows for reversible sliding of microtubules without any damage at small strain rates. Based on the stiffness and viscosity of tau proteins inferred from single-molecule force spectroscopy studies, we predict the critical strain rate for microtubule breaking to be in the range 22–44 s⁻¹, in excellent agreement with recent experiments on dynamic loading of micropatterned neuronal cultures. We also identified a characteristic length scale for load transfer that depends on microstructural properties and have derived a phase diagram in the parameter space spanned by loading rate and microtubule length that demarcates those regions where axons can be loaded and unloaded reversibly and those where axons are injured due to breaking of the microtubules.     

Viscoelasticity of Tau Proteins Leads to Strain Rate-Dependent Breaking of Microtubules during Axonal Stretch Injury: Predictions from a Mathematical Model

The unique viscoelastic nature of axons is thought to underlie selective vulnerability to damage during traumatic brain injury. In particular, dynamic loading of axons has been shown to mechanically break microtubules at the time of injury. However, the mechanism of this rate-dependent response has remained elusive. Here, we present a microstructural model of the axonal cytoskeleton to quantitatively elucidate the interaction between microtubules and tau proteins under mechanical loading. Mirroring the axon ultrastructure, the microtubules were arranged in staggered arrays, cross-linked by tau proteins. We found that the viscoelastic behavior specifically of tau proteins leads to mechanical breaking of microtubules at high strain rates, whereas extension of tau allows for reversible sliding of microtubules without any damage at small strain rates. Based on the stiffness and viscosity of tau proteins inferred from single-molecule force spectroscopy studies, we predict the critical strain rate for microtubule breaking to be in the range 22–44 s⁻¹, in excellent agreement with recent experiments on dynamic loading of micropatterned neuronal cultures. We also identified a characteristic length scale for load transfer that depends on microstructural properties and have derived a phase diagram in the parameter space spanned by loading rate and microtubule length that demarcates those regions where axons can be loaded and unloaded reversibly and those where axons are injured due to breaking of the microtubules.     

Caspr2, a new member of the neurexin superfamily, is localized at the juxtaparanodes of myelinated axons and associates with K+ channels

Rapid conduction in myelinated axons depends on the generation of specialized subcellular domains to which different sets of ion channels are localized. Here, we describe the identification of Caspr2, a mammalian homolog of Drosophila Neurexin IV (Nrx-IV), and show that this neurexin-like protein and the closely related molecule Caspr/Paranodin demarcate distinct subdomains in myelinated axons. While contactin-associated protein (Caspr) is present at the paranodal junctions, Caspr2 is precisely colocalized with Shaker-like K+ channels in the juxtaparanodal region. We further show that Caspr2 specifically associates with Kv1.1, Kv1.2, and their Kvbeta2 subunit. This association involves the C-terminal sequence of Caspr2, which contains a putative PDZ binding site. These results suggest a role for Caspr family members in the local differentiation of the axon into distinct functional subdomains.     

Robust human body model injury prediction in simulated side impact crashes

This study developed a parametric methodology to robustly predict occupant injuries sustained in real-world crashes using a finite element (FE) human body model (HBM). One hundred and twenty near-side impact motor vehicle crashes were simulated over a range of parameters using a Toyota RAV4 (bullet vehicle), Ford Taurus (struck vehicle) FE models and a validated human body model (HBM) Total HUman Model for Safety (THUMS). Three bullet vehicle crash parameters (speed, location and angle) and two occupant parameters (seat position and age) were varied using a Latin hypercube design of Experiments. Four injury metrics (head injury criterion, half deflection, thoracic trauma index and pelvic force) were used to calculate injury risk. Rib fracture prediction and lung strain metrics were also analysed. As hypothesized, bullet speed had the greatest effect on each injury measure. Injury risk was reduced when bullet location was further from the B-pillar or when the bullet angle was more oblique. Age had strong correlation to rib fractures frequency and lung strain severity. The injuries from a real-world crash were predicted using two different methods by (1) subsampling the injury predictors from the 12 best crush profile matching simulations and (2) using regression models. Both injury prediction methods successfully predicted the case occupant's low risk for pelvic injury, high risk for thoracic injury, rib fractures and high lung strains with tight confidence intervals. This parametric methodology was successfully used to explore crash parameter interactions and to robustly predict real-world injuries.     

Internodal specializations of myelinated axons in the central nervous system

We have examined the localization of contactin-associated protein (Caspr), the Shaker-type potassium channels, Kv1.1 and Kv1.2, their associated beta subunit, Kvbeta2, and Caspr2 in the myelinated fibers of the CNS. Caspr is localized to the paranodal axonal membrane, and Kv1.1, Kv1.2, Kvbeta2 and Caspr2 to the juxtaparanodal membrane. In addition to the paranodal staining, an internodal strand of Caspr staining apposes the inner mesaxon of the myelin sheath. Unlike myelinated axons in the peripheral nervous system, there was no internodal strand of Kv1.1, Kv1.2, Kvbeta2, or Caspr2. Thus, the organization of the nodal, paranodal, and juxtaparanodal axonal membrane is similar in the central and peripheral nervous systems, but the lack of Kv1.1/Kv1.2/Kvbeta2/Caspr2 internodal strands indicates that the oligodendrocyte myelin sheaths lack a trans molecular interaction with axons, an interaction that is present in Schwann cell myelin sheaths.     

Predicting the order in which contacts are broken during single molecule protein stretching experiments

We combine two methods to enable the prediction of the order in which contacts are broken under external stretching forces in single molecule experiments. These two methods are Gō-like models and elastic network models. The Gō-like models have shown remarkable success in representing many aspects of protein behavior, including the reproduction of experimental data obtained from atomic force microscopy. The simple elastic network models are often used successfully to predict the fluctuations of residues around their mean positions, comparing favorably with the experimentally measured crystallographic B-factors. The behavior of biomolecules under external forces has been demonstrated to depend principally on their elastic properties and the overall shape of their structure. We have studied in detail the muscle protein titin and green fluorescent protein and tested for ten other proteins. First, we stretch the proteins computationally by performing stochastic dynamics simulations with the Gō-like model. We obtain the force-displacement curves and unfolding scenarios of possible mechanical unfolding. We then use the elastic network model to calculate temperature factors (B-factors) and compare the slowest modes of motion for the stretched proteins and compare them with the predicted order of breaking contacts between residues in the Gō-like model. Our results show that a simple Gaussian network model is able to predict contacts that break in the next time stage of stretching. Additionally, we have found that the contact disruption is strictly correlated with the highest force exerted by the backbone on these residues. Our prediction of bond-breaking agrees well with the unfolding scenario obtained with the Gō-like model. We anticipate that this method will be a useful new tool for interpreting stretching experiments.     

Fiber kinematics of small intestinal submucosa under biaxial and uniaxial stretch

Improving our understanding of the design requirements of biologically derived collagenous scaffolds is necessary for their effective use in tissue reconstruction. In the present study, the collagen fiber kinematics of small intestinal submucosa (SIS) was quantified using small angle light scattering (SALS) while the specimen was subjected to prescribed uniaxial or biaxial strain paths. A modified biaxial stretching device based on Billiar and Sacks (J. Biomech., 30, pp. 753-7, 1997) was used, with a real-time analysis of the fiber kinematics made possible due to the natural translucency of SIS. Results indicated that the angular distribution of collagen fibers in specimens subjected to 10% equibiaxial strain was not significantly different from the initial unloaded condition, regardless of the loading path (p=0.31). Both 10% strip biaxial stretch and uniaxial stretches of greater than 5% in the preferred fiber direction led to an increase in the collagen fiber alignment along the same direction, while 10% strip biaxial stretch in the cross preferred fiber direction led to a broadening of the distribution. While an affine deformation model accurately predicted the experimental findings for a biaxial strain state, uniaxial stretch paths were not accurately predicted. Nonaffine structural models will be necessary to fully predict the fiber kinematics under large uniaxial strains in SIS.     

Juxtaparanodal clustering of Shaker-like K+ channels in myelinated axons depends on Caspr2 and TAG-1

In myelinated axons, K+ channels are concealed under the myelin sheath in the juxtaparanodal region, where they are associated with Caspr2, a member of the neurexin superfamily. Deletion of Caspr2 in mice by gene targeting revealed that it is required to maintain K+ channels at this location. Furthermore, we show that the localization of Caspr2 and clustering of K+ channels at the juxtaparanodal region depends on the presence of TAG-1, an immunoglobulin-like cell adhesion molecule that binds Caspr2. These results demonstrate that Caspr2 and TAG-1 form a scaffold that is necessary to maintain K+ channels at the juxtaparanodal region, suggesting that axon-glia interactions mediated by these proteins allow myelinating glial cells to organize ion channels in the underlying axonal membrane.     

Current playground surface test standards underestimate brain injury risk for children

Playgrounds surface test standards have been introduced to reduce the number of fatal and severe injuries. However, these test standards have several simplifications to make it practical, robust and cost-effective, such as the head is represented with a hemisphere, only the linear kinematics is evaluated and the body is excluded. Little is known about how these simplifications may influence the test results. The objective of this study was to evaluate the effect of these simplifications on global head kinematics and head injury prediction for different age groups. The finite element human body model PIPER was used and scaled to seven different age groups from 1.5 up to 18 years old, and each model was impacted at three different playground surface stiffness and three head impact locations. All simulations were performed in pairs, including and excluding the body. Linear kinematics and skull bone stress showed small influence if excluding the body while head angular kinematics and brain tissue strain were underestimated by the same simplification. The predicted performance of the three different playground surface materials, in terms of head angular kinematics and brain tissue strain, was also altered when including the body. A body and biofidelic neck need to be included, together with suitable head angular kinematics based injury thresholds, in future physical or virtual playground surface test standards to better prevent brain injuries.     

Myelinating Schwann cells determine the internodal localization of Kv1.1, Kv1.2, Kvβ2, and Caspr

We examined the localization of Caspr and the K⁺ channels Kv1.1 and Kv1.2, all of which are intrinsic membrane proteins of myelinated axons in the PNS. Caspr is localized to the paranode; Kv1.1, Kv1.2 and their β2 subunit are localized to the juxtaparanode. Throughout the internodal region, a strand of Caspr staining is flanked by a double strand of Kv1.1/Kv1.2/Kvβ2 staining. This tripartite strand apposes the inner mesaxon of the myelin sheath, and forms a circumferential ring that apposes the innermost aspect of Schmidt-Lanterman incisures. The localization of Caspr and Kv1.2 are not disrupted in mice with null mutations of the myelin associated glycoprotein, connexin32, or Kv1.1 genes. At all of these locations, Caspr and Kv1.1/Kv1.2/Kvβ2 define distinct but interrelated domains of the axonal membrane that appear to be organized by the myelin sheath.     

Modeling of microstructural kinematics during simple elongation of central nervous system tissue

Damage to axons and glial cells in the central nervous system (CNS) white matter is a nearly universal feature of traumatic brain injury, yet it is not clear how the tissue mechanical deformations are transferred to the cellular components of the CNS. Defining how cellular deformations relate to the applied tissue deformation field can both highlight cellular populations at risk for mechanical injury, and define the fraction of cells in a specific population that will exhibit damage. In this investigation, microstructurally based models of CNS white matter were developed and tested against measured transformations of the CNS tissue microstructure under simple elongation. Results show that axons in the unstretched optic nerves were significantly wavy or undulated, where the measured axonal path length was greater than the end-to-end distance of the axon. The average undulation parameter--defined as the true axonal length divided by the end-to-end length--was 1.13. In stretched nerves, mean axonal undulations decreased with increasing applied stretch ratio (lambda)--the mean undulation values decreased to 1.06 at lambda = 1.06, 1.04 at lambda = 1.12, and 1.02 at lambda = 1.25. A model describing the gradual coupling, or tethering, of the axons to the surrounding glial cells best fit the experimental data. These modeling efforts indicate the fraction of the axonal and glial populations experiencing deformation increases with applied elongation, consistent with the observation that both axonal and glial cell injury increases at higher levels of white matter injury. Ultimately, these results can be used in conjunction with computational simulations of traumatic brain injury to aid in establishing the relative risk of cellular structures in the CNS white matter to mechanical injury.     

Molecular domains of myelinated axons

Myelinated axons are organized into specific domains as the result of interactions with glial cells. Recently, distinct protein complexes of cell adhesion molecules, Na(+) channels and ankyrin G at the nodes, Caspr and contactin in the paranodes, and K(+) channels and Caspr2 in the juxtaparanodal region have been identified, and new insights into the role of the paranodal junctions in the organization of these domains have emerged.     

An axonal strain injury criterion for traumatic brain injury

Computational models are often used as tools to study traumatic brain injury. The fidelity of such models depends on the incorporation of an appropriate level of structural detail, the accurate representation of the material behavior, and the use of an appropriate measure of injury. In this study, an axonal strain injury criterion is used to estimate the probability of diffuse axonal injury (DAI), which accounts for a large percentage of deaths due to brain trauma and is characterized by damage to neural axons in the deep white matter regions of the brain. We present an analytical and computational model that treats the white matter as an anisotropic, hyperelastic material. Diffusion tensor imaging is used to incorporate the structural orientation of the neural axons into the model. It is shown that the degree of injury that is predicted in a computational model of DAI is highly dependent on the incorporation of the axonal orientation information and the inclusion of anisotropy into the constitutive model for white matter.     

A micromechanical model to predict damage and failure in biological tissues. Application to the ligament-to-bone attachment in the human knee joint

Computational models are developed in injury biomechanics to assess lesions in biological tissues based on mechanical measurements. The linear mechanics of fracture theory (LMFT) is a common approach to establish injuries based on thresholds (such as force or strain thresholds) which are straightforward to implement and computationally efficient. However, LMFT does not apply to non-linear heterogeneous materials and does not have the ability to predict failure onset. This paper proposes the cohesive zone model theory (CZMT) as an alternative. CZMT focuses on the development of behaviour laws for crack initiation and propagation at an interface that apply within a fibrous material or at the interface between materials. With the view of evaluating CZMT for biological tissues, the model developed by Raous et al. [1999. A consistent model coupling adhesion, friction and unilateral contact. Comput. Methods Appl. Mech. Eng., 177, 383–399] was applied to the ligament-to-bone interface in the human knee joint. This model accounts for adhesion, friction and damage at the interface and provides a smooth transition from total adhesion to complete failure through the intensity of adhesion variable. A 2D finite element model was developed to mimic previous experiments, and the model parameters were determined using a dichotomy method. The model showed good results by its ability to predict damage. The extension to a 3D geometry, with an inverse problem approach, is, however, required to better estimate the model parameters values. Although it is computationally costly, CZMT supplements the improvements achieved in microimaging techniques to support the development of micro/macro approaches in biomechanical modelling.