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

Abstract

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.

Keywords: axonal cytoskeleton; high strain rate; molecular dynamics; tau protein.

Figure 1

Stress vs. strain plot of single tau projection domain. Up to ~200% strain, the protein keeps unfolding, and after that a sharp rise in the slope is observed, suggesting the pure stretching of covalent bonds. Unfolding and stretching zones are shown in rectangular boxes.

Figure 2

(a) Simplified schematic for tau protein unfolding and stretching (ε_xx = tensile strain). Initially, there are multiple folding (which are distinct from each other). When loading is applied, the van der Waals force and electrostatic force between the folded portions are broken, and therefore the structure unfolds. At extreme strain, the structure becomes free of all the folds, and stretches to a relatively linear filament. (b) Initial single tau structure (strain = 0%), (c) tau protein being unfolded due to pulling at 10⁹ s⁻¹ (strain = 36%), (d) tau protein being stretched (strain = 206%, only the projection domain is shown for the convenience of visualization). Color legends: green: projection domain, red: MT binding region, blue: N terminus or tail, white, and the rest: inter-repeats between the MT binding regions. The enlarged snapshots are for the first ~1100 atoms for convenient visualization. Water molecules are not shown.

Figure 3

(a) Stress-strain plot of protein 2 projection domain for two different strain rates. At a lower strain rate, we observe the development of stress at a higher value and delayed separation, and vice versa. (b) Potential energy vs. time plot for the system.

Figure 3

(a) Stress-strain plot of protein 2 projection domain for two different strain rates. At a lower strain rate, we observe the development of stress at a higher value and delayed separation, and vice versa. (b) Potential energy vs. time plot for the system.

Figure 4

Stages observed during the pull of one protein in the dimerized tau model (for the strain rate of 2 × 10⁹ s⁻¹). (a) Initial stage (strain: 0%), (b) Unfolding of protein 2 (strain: 135%), (c) Stretching of protein 2 (strain: 177%), (d) Unfolding of protein 1 (strain: 325%), (e) stretching of protein 1 (strain: 345%), (f) Disentanglement of the overlapped projection domains of the tau proteins (strain: 430%), (g) Continued disentanglement (strain: 676%), (h) Sliding out of projection domain (strain: 750%), (i) Separation of proteins (strain: 758%). Color legends: Green: Projection domain of protein 2, Blue: projection domain of protein 1, Red: MT binding region (including the inter-repeats) for protein 1 and 2, Yellow: N terminal tails of protein 1 and 2.

Figure 5

(a) Stress vs. Strain graph for the projection domain of tau during the pulling at different strain rates. The stress-strain trends are similar for both the strain rates, although the separation occurs at different strains. (b) Potential energy vs. time plot for the single tau-MT system.

Figure 5

(a) Stress vs. Strain graph for the projection domain of tau during the pulling at different strain rates. The stress-strain trends are similar for both the strain rates, although the separation occurs at different strains. (b) Potential energy vs. time plot for the single tau-MT system.

Figure 6

Observation during the pulling of single tau towards the −x-direction (strain rate: 2 × 10⁹ s⁻¹) away from MT surface. (a) Initial stage (strain: 0%), (b) unfolding of tau projection domain (strain: 409%), (c) stretching of tau projection domain (strain: 698%), (d) stretching of MT binding region (strain: 968%), (e) onset of separation (strain: 1108%), (f) after complete separation (strain: 1128%). Color legends: Red, blue, green, and yellow: repeating helical units of MT, maroon: projection domain of tau, orange: MT binding site atoms of tau (including the inter-repeats), white: N terminus tail of tau.

Figure 7

(a) Stress vs. Strain graph for the projection domain of tau during the pulling at different strain rates. The separation occurs early for higher strain rate (~360%), and much later for lower strain rate (~825%). (b) Potential energy vs. time plot for the dimerized tau-MT system. As expected, potential energy drastically reduces at separation (~360% strain for 2 × 10⁹ s⁻¹, ~825% strain for 1 × 10⁹ s⁻¹). For both cases, the tau-tau bond is stronger than the tau-MT bond.

Figure 8

Observation during the dimerized tau pulling away from the MT surface (−x-direction, strain rate: 2 × 10⁹ s⁻¹). (a) Initial stage (strain: 0%), (b) unfolding and stretching of tau (strain: 250%), (c) onset of separation (strain: 350%), (d) after separation (strain: ~354%). Color legends: Red, blue, green, and yellow: repeating helical units of MT, maroon: projection domain of tau 1, orange: MT binding site atoms of tau 1(including the inter-repeats), light green: tail domain of tau 1, purple: projection domain of tau 2, light blue: MT binding site atoms of tau 2 (including the inter-repeats), black: tail domain of tau 2.