Viscoelastic Response of Neurofilaments: An Atomistic Simulation Approach

Viscoelastic damage evaluation of the axon

In this manuscript, we have studied the microstructure of the axonal cytoskeleton and adopted a bottom-up approach to evaluate the mechanical responses of axons. The cytoskeleton of the axon includes the microtubules (MT), Tau proteins (Tau), neurofilaments (NF), and microfilaments (MF). Although most of the rigidity of the axons is due to the MT, the viscoelastic response of axons comes from the Tau. Early studies have shown that NF and MF do not provide significant elasticity to the overall response of axons. Therefore, the most critical aspect of the mechanical response of axons is the microstructural topology of how MT and Tau are connected and construct the cross-linked network. Using a scanning electron microscope (SEM), the cross-sectional view of the axons revealed that the MTs are organized in a hexagonal array and cross-linked by Tau. Therefore, we have developed a hexagonal Representative Volume Element (RVE) of the axonal microstructure with MT and Tau as fibers. The matrix of the RVE is modeled by considering a combined effect of NF and MF. A parametric study is done by varying fiber geometric and mechanical properties. The Young’s modulus and spacing of MT are varied between 1.5 and 1.9 GPa and 20–38 nm, respectively. Tau is modeled as a 3-parameter General Maxwell viscoelastic material. The failure strains for MT and Tau are taken to be 50 and 40%, respectively. A total of 4 RVEs are prepared for finite element analysis, and six loading cases are inspected to quantify the three-dimensional (3D) viscoelastic relaxation response. The volume-averaged stress and strain are then used to fit the relaxation Prony series. Next, we imposed varying strain rates (between 10/sec to 50/sec) on the RVE and analyzed the axonal failure process. We have observed that the 40% failure strain of Tau is achieved in all strain rates before the MT reaches its failure strain of 50%. The corresponding axonal failure strain and stress vary between 6 and 11% and 5–19.8 MPa, respectively. This study can be used to model macroscale axonal aggregate typical of the white matter region of the brain tissue.

Shock-Induced Damage Mechanism of Perineuronal Nets

The perineuronal net (PNN) region of the brain’s extracellular matrix (ECM) surrounds the neural networks within the brain tissue. The PNN is a protective net-like structure regulating neuronal activity such as neurotransmission, charge balance, and action potential generation. Shock-induced damage of this essential component may lead to neuronal cell death and neurodegenerations. The shock generated during a vehicle accident, fall, or improvised device explosion may produce sufficient energy to damage the structure of the PNN. The goal is to investigate the mechanics of the PNN in reaction to shock loading and to understand the mechanical properties of different PNN components such as glycan, GAG, and protein. In this study, we evaluated the mechanical strength of PNN molecules and the interfacial strength between the PNN components. Afterward, we assessed the PNN molecules’ damage efficiency under various conditions such as shock speed, preexisting bubble, and boundary conditions. The secondary structure altercation of the protein molecules of the PNN was analyzed to evaluate damage intensity under varying shock speeds. At a higher shock speed, damage intensity is more elevated, and hyaluronan (glycan molecule) is most likely to break at the rigid junction. The primary structure of the protein molecules is least likely to fail. Instead, the molecules’ secondary bonds will be altered. Our study suggests that the number of hydrogen bonds during the shock wave propagation is reduced, which leads to the change in protein conformations and damage within the PNN structure. As such, we found a direct connection between shock wave intensity and PNN damage.

Effect of random fiber networks on bubble growth in gelatin hydrogels

In hydrodynamics, the event of dynamic bubble growth in a pure liquid under tensile pressure is known as cavitation. The same event can also be observed in soft materials (e.g., elastomers and hydrogels). However, for soft materials, bubble/cavity growth is either defined as cavitation if the bubble growth is elastic and reversible or as fracture if the cavity growth is by material failure and irreversible. In any way, bubble growth can cause damage to soft materials (e.g., tissue) by inducing high strain and strain-rate deformation. Additionally, a high-strength pressure wave is generated upon the collapse of the bubble. Therefore, it is crucial to identify the critical condition of spontaneous bubble growth in soft materials. Experimental and theoretical observations have agreed that the onset of bubble growth in soft materials requires higher tensile pressure than pure water. The extra tensile pressure is required since the cavitating bubble needs to overcome the elastic and surface energy in soft materials. In this manuscript, we developed two models to study and quantify the extra tensile pressure for different gelatin concentrations. Both the models are then compared with the existing cavitation onset criteria of rubber-like materials. Validation is done with the experimental results of threshold tensile pressure for different gelatin concentrations. Both models can moderately predict the extra tensile pressure within the intermediate range of gelatin concentrations (3-7% [w/v]). For low concentration (∼1%), the network's non-affinity plays a significant role and must be incorporated. On the other hand, for higher concentrations (∼10%), the entropic deformation dominates, and the strain energy formulation is not adequate.

Effect of Strain Rate on Single Tau, Dimerized Tau and Tau-Microtubule Interface: A Molecular Dynamics Simulation Study

Microtubule-associated protein (MAP) tau is a cross-linking molecule that provides structural stability to axonal microtubules (MT). It is considered a potential biomarker for Alzheimer's disease (AD), dementia, and other neurological disorders. It is also a signature protein for Traumatic Brain Injury (TBI) assessment. In the case of TBI, extreme dynamic mechanical energies can be felt by the axonal cytoskeletal members. As such, fundamental understandings of the responses of single tau protein, polymerized tau protein, and tau-microtubule interfaces under high-rate mechanical forces are important. This study attempts to determine the high-strain rate mechanical behavior of single tau, dimerized tau, and tau-MT interface using molecular dynamics (MD) simulation. The results show that a single tau protein is a highly stretchable soft polymer. During deformation, first, it significantly unfolds against van der Waals and electrostatic bonds. Then it stretches against strong covalent bonds. We found that tau acts as a viscoelastic material, and its stiffness increases with the strain rate. The unfolding stiffness can be ~50-500 MPa, while pure stretching stiffness can be >2 GPa. The dimerized tau model exhibits similar behavior under similar strain rates, and tau sliding from another tau is not observed until it is stretched to >7 times of original length, depending on the strain rate. The tau-MT interface simulations show that very high strain and strain rates are required to separate tau from MT suggesting Tau-MT bonding is stronger than MT subunit bonding between themselves. The dimerized tau-MT interface simulations suggest that tau-tau bonding is stronger than tau-MT bonding. In summary, this study focuses on the structural response of individual cytoskeletal components, namely microtubule (MT) and tau protein. Furthermore, we consider not only the individual response of a component, but also their interaction with each other (such as tau with tau or tau with MT). This study will eventually pave the way to build a bottom-up multiscale brain model and analyze TBI more comprehensively.