Mechanical Responses of a Single Myelin Layer: A Molecular Simulation Study.

The myelin sheath provides insulation to the brain's neuron cells, which aids in signal transmission and communication with the body. Degenerated myelin hampers the connection between the glial cells, which are the front row responders during traumatic brain injury mitigation. Thus, the structural integrity of the myelin layer is critical for protecting the brain tissue from traumatic injury. At the molecular level, myelin consists of a lipid bilayer, myelin basic proteins (MBP), proteolipid proteins (PLP), water and ions. Structurally, the myelin sheath is formed by repeatedly wrapping forty or more myelin layers around an axon. Here, we have used molecular dynamic simulations to model and capture the tensile response of a single myelin layer. An openly available molecular dynamic solver, LAMMPS, was used to conduct the simulations. The interatomic potentials for the interacting atoms and molecules were defined using CHARMM force fields. Following a standard equilibration process, the molecular model was stretched uniaxially at a deformation rate of 5 Å/ps. We observed that, at around 10% applied strain, the myelin started to cohesively fail via flaw formation inside the bilayers. Further stretching led to a continued expansion of the defect inside the bilayer, both radially and transversely. This study provides the cellular-level mechanisms of myelin damage due to mechanical load.

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.

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.

Mechanical behavior of actin and spectrin subjected to high strain rate: A molecular dynamics simulation study.

Recent nanoscopy and super-resolution microscopy studies have substantiated the structural contribution of periodic actin-spectrin lattice to the axonal cytoskeleton of neuron. However, sufficient mechanical insight is not present for spectrin and actin-spectrin network, especially in high strain rate scenario. To quantify the mechanical behavior of actin-spectrin cytoskeleton in such conditions, this study determines individual stretching characteristics of actin and spectrin at high strain rate by molecular dynamics (MD) simulation. The actin-spectrin separation criteria are also determined. It is found that both actin and spectrin have high stiffness when susceptible to high strain rate and show strong dependence on applied strain rate. The stretching stiffness of actin and forced unfolding mechanism of spectrin are in harmony with the current literature. Actin-spectrin model provides novel insight into their interaction and separation stretch. It is shown that the region vulnerable to failure is the actin-spectrin interface at lower strain rate, while it is the inter-repeat region of spectrin at higher strain rate.

Viscoelastic Response of Neurofilaments: An Atomistic Simulation Approach.

Existent literature has limitations regarding the mechanical behavior of axonal cytoskeletal components in a high strain rate scenario, which is mainly due to limitations regarding the structure of some components such as tau protein and neurofilaments (NF). This study performs molecular dynamics (MD) simulations on NFs to extract their strain rate-dependent behavior. It is found that they are highly stretchable and show multiple stages of unfolding. Furthermore, NFs show high tensile stiffness. Also, viscoelastic modeling shows that they correspond to simplified viscoelastic models. This study effectively enhances the existent axonal models focusing on axonal injury.

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.

Domain focused and residue focused phosphorylation effect on tau protein: A molecular dynamics simulation study.

Phosphorylation has been hypothesized to alter the ability of tau protein to bind with microtubules (MT), and pathological level of phosphorylation can incorporate formation of Paired Helical Filaments (PHF) in affected tau. Study of the effect of phosphorylation on different domains of tau (projection domain, microtubule binding sites and N-terminus tail) is important to obtain insight about tau neuropathology. In an earlier study, we have already obtained the mechanical properties and behavior of single tau and dimerized tau and observed tau-MT interaction for normal level of phosphorylation. This study attempts to obtain insights on the effect of phosphorylation on different domains of tau, using molecular dynamics (MD) simulation with the aid of CHARMM force field under high strain rate. It also determines the effect of residue focused phosphorylation on tau-MT interaction and tau accumulation tendency. The results show that for single tau protein, unfolding stiffness does not differ significantly due to phosphorylation, but stretching stiffness can be much higher than the normally phosphorylated protein. For dimerized tau protein, the stretching required to separate the protein forming the dimer is similar for phosphorylation in individual domains but is significantly less in case of phosphorylation in all domains. For tau-MT interaction simulations, it is found that for normal phosphorylation, the tau separation from MT occurs at higher strain for phosphorylation in projection domain and N-terminus tail, and earlier for phosphorylation in all domains altogether than the normal phosphorylation state. The residue focused phosphorylation study also shows that tau separates earlier from MT and shows stronger accumulation tendency at the phosphorylated state, while preserving the highly stretchable and flexible characteristic of tau. This study provides important insight on mechanochemical phenomena relevant to traumatic brain injury (TBI) scenario, where the result of mechanical loading and posttranslational modification as well as conformation decides the mechanical behavior.

On the Molecular Level Cavitation in Soft Gelatin Hydrogel.

We have studied the molecular level cavitation mechanisms and bubble growth kinetics in soft gelatin hydrogel and water. The apparent difference in cavitation threshold pressure between that generates in pure water and that in gelatin hydrogel is considered. Gelatin, which is derived from collagen, is frequently used as a brain simulant material. In liquid, cavitation bubble is created when surrounding pressure drops below the saturation vapor pressure. In principle, a cavitation bubble should continue to grow as long as tensile pressure continues to increase in the system. In our study, using molecular dynamics simulation, we have investigated the pressure requirement for a nanoscale cavitation to grow in water and gel. First, we have modeled a gel like structure with a preexisting bubble of 5 nm radius. A control model containing a 5 nm bubble in pure water is also created. Then, we have applied hydrostatic tensile pressure at two different expansion rates in the gel and water models. The results show that a gel-like structure requires higher pressure for the cavitation to grow, and both gel and water models exhibit strain rate effect on the cavitation threshold pressure. We have also found that the cavitation collapse time is dominated by the viscosity of the medium.

Effects of Focal Axonal Swelling Level on the Action Potential Signal Transmission.

Focal axon swelling refers to localized swelling in axons that may occur because of trauma (e.g., traumatic brain injury) or neurodegenerative diseases (e.g., Alzheimer's disease). Since the swelling region can be many times larger than its original axon size, many researchers hypothesize that the swelling can alter the action potential (AP) signal. This article discusses the results of a series of newly developed computational studies to elucidate the possible intervention or blockage of AP signals due to swelling in the brain. We argue that the spherical geometry of the swelling site with its enlarged conducting interior causes the entering electric currents to spread evenly over the entire swelled membrane. As such, when the swelled surface becomes larger than the threshold size, the electric current will spread too thin to trigger the AP to spike. In this study, we have used a hybrid membrane model to simulate AP propagation across axons of different radii and swelling radii. We used an integrated model where a cylindrical symmetric 2D model is used to examine the electric current inside a spherical swelling site. In addition, two 1D models are used to capture the current flows along the upstream and downstream stretch before and after the swelling site. The parameters for this model are obtained from literature dedicated to modeling the experimental outcomes of mammal neurons. We observed two factors, which simultaneously affect AP transmission across a swelled axon: a) the axon radius and b) the ratio of the swelled and unswelled axon radii. In general, a thicker axon needs a smaller swelling size and axon ratio to block AP transmission. On the other hand, a thinner axon will reach the threshold at a larger swelling size and axon ratio. When only swelling size is considered, then thinner axons will block AP transmission at a smaller swelling radius. The AP transmission delay inside the swelled region determines whether the AP transmits forward or not. Notably, the blockage is worse if the AP fires at a high frequency. An increase in the charging and reset time due to swelling appears to be the main reason for the variation in axonal response.

Damage and Failure of Axonal Microtubule under Extreme High Strain Rate: An In-Silico Molecular Dynamics Study.

As a major cytoskeleton element of the axon, the breaking of microtubules (MTs) has been considered as a major cause of the axon degeneration. High strain rate loading is considered as one of the key factors in microtubule breaking. Due to the small size of microtubule, the real-time behavior of microtubule breaking is hard to capture. This study employs fully-atomistic molecular dynamics (MD) simulation to determine the failure modes of microtubule under different loadings conditions such as, unidirectional stretching, bending and hydrostatic expansion. For each loading conditions, MT is subjected to extreme high strain rate (108-109 s-1) loading. We argue that such level of high strain rate may be realized during cavitation bubble implosion. For each loading type, we have determined the critical energy for MT rupture. The associated rupture mechanisms are also discussed. We observed that the stretching has the lowest energy barrier to break the MT at the nanosecond time scale. Moreover, the breakage between the dimers starts at ~16% of total strain when stretched, which is much smaller compared to the reported strain-at-failure (50%) for lower strain rate loading. It suggests that MT fails at a significantly smaller strain states when loaded at higher strain rates.

On the atomistic-based continuum viscoelastic constitutive relations for axonal microtubules.

Mechanical response of brain's interior during traumatic brain injury is primarily governed by the cytoskeleton (CSK) and occurs over multiple length scales starting from the axonal substructure level. The axonal cytoskeleton can be viewed as a nanofiber reinforced nanocomposite structure where nano-fibrous microtubules (MTs) are arranged in staggered arrays and cross-linked by Tau proteins. Each MT is made of thirteen laterally connected protofilaments (PFs), each of which is formed via linear polymerization of αß-heterodimer protein called tubulin. Recent studies suggest that the unique viscoelastic nature of axons governs the damage during traumatic brain injury. To understand how the internal substructures of axon influences the viscoelastic mechanical behavior of axon from a theoretical perspective, the viscoelastic properties of MTs need to be properly described. Since viscosity is a bulk property, the measurement methods are fairly consistent. On the other hand, the reported experimentally measured elastic properties of MTs vary by several orders of magnitude due to limitations of experimental tools. Alternatively, many have attempted to determine MT properties using theoretical and computational methods at different length scales ranging between the atomistic and the continuum level. The atomistic approaches capture the dynamics and interactions of a material at the atomic or atomic cluster level but these methods are computationally expensive and can model only a very small physical scale. On the other hand, the continuum theories lack finer scale details. Here, we present an atomistic-based continuum viscoelastic constitutive relation for microtubules (MTs) based on the interatomic potential for proteins and continuum homogenization method. The interaction potential includes both van der Waals and electrostatic interactions between the protein molecules. The calculated Young's modulus of 3.385 GPa agrees reasonably well with the range of experimentally measured value without any parameter fitting. We have then investigated the viscoelastic response of MT based on the estimated viscosity using atomistic simulation and evaluated Young's modulus using our method. The current theory suggests that MT behaves like a viscoelastic material when applied loading rate is extremely high, otherwise it acts like an elastic solid material.

Cavitation nucleation in gelatin: Experiment and mechanism.

Dynamic cavitation in soft materials is becoming increasingly relevant due to emerging medical implications such as the potential of cavitation-induced brain injury or cavitation created by therapeutic medical devices. However, the current understanding of dynamic cavitation in soft materials is still very limited, mainly due to lack of robust experimental techniques. To experimentally characterize cavitation nucleation under dynamic loading, we utilize a recently developed experimental instrument, the integrated drop tower system. This technique allows quantitative measurements of the critical acceleration (acr) that corresponds to cavitation nucleation while concurrently visualizing time evolution of cavitation. Our experimental results reveal that acr increases with increasing concentration of gelatin in pure water. Interestingly, we have observed the distinctive transition from a sharp increase (pure water to 1% gelatin) to a much slower rate of increase (∼10× slower) between 1% and 7.5% gelatin. Theoretical cavitation criterion predicts the general trend of increasing acr, but fails to explain the transition rates. As a likely mechanism, we consider concentration-dependent material properties and non-spherical cavitation nucleation sites, represented by pre-existing bubbles in gels, due to possible interplay between gelatin molecules and nucleation sites. This analysis shows that cavitation nucleation is very sensitive to the initial configuration of a bubble, i.e., a non-spherical bubble can significantly increase acr. This conclusion matches well with the experimentally observed liquid-to-gel transition in the critical acceleration for cavitation nucleation. STATEMENT OF SIGNIFICANCE: From a medical standpoint, understanding dynamic cavitation within soft materials, i.e., tissues, is important as there are both potential injury implications (blast-induced cavitation within the brain) as well as treatments utilizing the phenomena (lithotripsy). In this regard, the main results of the present work are (1) quantitative characterization of cavitation nucleation in gelatin samples as a function of gel concentration utilizing well-controlled mechanical impacts and (2) mechanistic understanding of complex coupling between cavitation and liquid-/solid-like material properties of gel. The new capabilities of testing soft gels, which can be tuned to mimic material properties of target organs, at high loading rate conditions and accurately predicting their cavitation behavior are an important step towards developing reliable cavitation criteria in the scope of their biomedical applications.

Effect of Shock-Induced Cavitation Bubble Collapse on the damage in the Simulated Perineuronal Net of the Brain.

The purpose of this study is to conduct modeling and simulation to understand the effect of shock-induced mechanical loading, in the form of cavitation bubble collapse, on damage to the brain's perineuronal nets (PNNs). It is known that high-energy implosion due to cavitation collapse is responsible for corrosion or surface damage in many mechanical devices. In this case, cavitation refers to the bubble created by pressure drop. The presence of a similar damage mechanism in biophysical systems has long being suspected but not well-explored. In this paper, we use reactive molecular dynamics (MD) to simulate the scenario of a shock wave induced cavitation collapse within the perineuronal net (PNN), which is the near-neuron domain of a brain's extracellular matrix (ECM). Our model is focused on the damage in hyaluronan (HA), which is the main structural component of PNN. We have investigated the roles of cavitation bubble location, shockwave intensity and the size of a cavitation bubble on the structural evolution of PNN. Simulation results show that the localized supersonic water hammer created by an asymmetrical bubble collapse may break the hyaluronan. As such, the current study advances current knowledge and understanding of the connection between PNN damage and neurodegenerative disorders.

3D structural integrity and interactions of single-stranded protein-binding DNA in a functionalized nanopore.

Biomarker-binding nucleotide sequences, like aptamers, have gained recent attention in cancer cell isolation and detection works. Self-assembly and 3D conformation of aptamers enable them to selectively capture and bind diseased cells and related biomarkers. One mode of utilizing such an extraordinary selective property of the aptamers is by grafting these in nanopores. Coating the inside walls of the nanopore with biomarker specific ligands, like DNA, changes the statistics of the dynamic translocation events. When the target protein passes through the nanopore, it interacts with ligand coated inside the nanopore, and the process alters the overall potential energy profile which is essentially specific to the protein detected. The fundamental goal in this process is to ensure that these detection motifs hold their structure and functionality under applied electric field and experimental conditions. We report here all-atom molecular dynamics simulations of the effects of external electric field on the 3D conformation of such DNA structures. The simulations demonstrate how the grafted moieties affect the translocation time, velocity, and detection frequency of the target molecule. We also investigated a novel case of protein translocation, where DNA is prebound to the protein. As model, a thrombin-specific G-quartet and thrombin pair was used for this study.

Atomistic simulation and measurement of pH dependent cancer therapeutic interactions with nanodiamond carrier.

In this work, we have combined constant-pH molecular dynamics simulations and experiments to provide a quantitative analysis of pH dependent interactions between doxorubicin hydrochloride (DOX) cancer therapeutic and faceted nanodiamond (ND) nanoparticle carriers. Our study suggests that when a mixture of faceted ND and DOX is dissolved in a solvent, the pH of this solvent plays a controlling role in the adsorption of DOX molecules on the ND. We find that the binding of DOX molecules on ND occurs only at high pH and requires at least ∼10% of ND surface area to be fully titrated for binding to occur. As such, this study reveals important mechanistic insight underlying an ND-based pH-controlled therapeutic platform.