A Stochastic Multiscale Model That Explains the Segregation of Axonal Microtubules and Neurofilaments in Neurological Diseases

Role of integrin and its potential as a novel postmortem biomarker in traumatic axonal injury

Traumatic axonal injury (TAI) accounts for a large proportion of the mortality of traumatic brain injury (TBI). The diagnosis of TAI is currently of limited use for medicolegal purposes. It is known that axons in TAI are diffusely damaged by secondary processes other than direct head injury. However, the physiopathological mechanism of TAI is still elusive. The present study used RGD peptide, an antagonist of the mechanotransduction protein integrin, to explore the role of integrin-transmitted mechanical signalling in the pathogenesis of rat TAI. The rats were subjected to a linearly accelerating load, and changes in beta-amyloid precursor protein (β-APP) expression, skeleton ultrastructure, skeleton protein neurofilament light (NF-L), and α-tubulin in the brainstem were observed, indicating that RGD could relieve the severity of axonal injury in TAI rats. In addition, the expression of β-integrin was stronger and centralized in the brainstem of the deceased died from TAI compared to other nonviolent causes. This study examined the pathophysiology and biomechanics of TAI and assessed the role of integrin in the injury of microtubules and neurofilaments in TAI. Thus, we propose that integrin-mediated cytoskeletal injury plays an important role in TAI and that integrin has the potential as a biomarker for TAI.

An age‐dependent mathematical model of neurofilament trafficking in healthy conditions

Neurofilaments (Nfs) are the major structural component of neurons. Their role as a potential biomarker of several neurodegenerative diseases has been investigated in past years with promising results. However, even under physiological conditions, little is known about the leaking of Nfs from the neuronal system and their detection in the cerebrospinal fluid (CSF) and blood. This study aimed at developing a mathematical model of Nf transport in healthy subjects in the 20–90 age range. The model was implemented as a set of ordinary differential equations describing the trafficking of Nfs from the nervous system to the periphery. Model parameters were calibrated on typical Nf levels obtained from the literature. An age‐dependent function modeled on CSF data was also included and validated on data measured in serum. We computed a global sensitivity analysis of model rates and volumes to identify the most sensitive parameters affecting the model’s steady state. Age, Nf synthesis, and degradation rates proved to be relevant for all model variables. Nf levels in the CSF and in blood were observed to be sensitive to the Nf leakage rates from neurons and to the blood clearance rate, and CSF levels were also sensitive to rates representing CSF turnover. An additional parameter perturbation analysis was also performed to investigate possible transient effects on the model variables not captured by the sensitivity analysis. The model provides useful insights into Nf transport and constitutes the basis for implementing quantitative system pharmacology extensions to investigate Nf trafficking in neurodegenerative diseases.

Modeling material transport regulation and traffic jam in neurons using PDE-constrained optimization

The intracellular transport process plays an important role in delivering essential materials throughout branched geometries of neurons for their survival and function. Many neurodegenerative diseases have been associated with the disruption of transport. Therefore, it is essential to study how neurons control the transport process to localize materials to necessary locations. Here, we develop a novel optimization model to simulate the traffic regulation mechanism of material transport in complex geometries of neurons. The transport is controlled to avoid traffic jam of materials by minimizing a pre-defined objective function. The optimization subjects to a set of partial differential equation (PDE) constraints that describe the material transport process based on a macroscopic molecular-motor-assisted transport model of intracellular particles. The proposed PDE-constrained optimization model is solved in complex tree structures by using isogeometric analysis (IGA). Different simulation parameters are used to introduce traffic jams and study how neurons handle the transport issue. Specifically, we successfully model and explain the traffic jam caused by reduced number of microtubules (MTs) and MT swirls. In summary, our model effectively simulates the material transport process in healthy neurons and also explains the formation of a traffic jam in abnormal neurons. Our results demonstrate that both geometry and MT structure play important roles in achieving an optimal transport process in neuron.

The Role of Protein Adduction in Toxic Neuropathies of Exogenous and Endogenous Origin

The peripheral (axonal) neuropathy associated with repeated exposure to aliphatic and aromatic solvents that form protein-reactive γ-diketones shares some clinical and neuropathological features with certain metabolic neuropathies, including type-II diabetic neuropathy and uremic neuropathy, and with the largely sub-clinical nerve damage associated with old age. These conditions may be linked by metabolites that adduct and cross-link neuroproteins required for the maintenance of axonal transport and nerve fiber integrity in the peripheral and central nervous system.

Cytoskeletal organization of axons in vertebrates and invertebrates

The maintenance of axons for the lifetime of an organism requires an axonal cytoskeleton that is robust but also flexible to adapt to mechanical challenges and to support plastic changes of axon morphology. Furthermore, cytoskeletal organization has to adapt to axons of dramatically different dimensions, and to their compartment-specific requirements in the axon initial segment, in the axon shaft, at synapses or in growth cones. To understand how the cytoskeleton caters to these different demands, this review summarizes five decades of electron microscopic studies. It focuses on the organization of microtubules and neurofilaments in axon shafts in both vertebrate and invertebrate neurons, as well as the axon initial segments of vertebrate motor- and interneurons. Findings from these ultrastructural studies are being interpreted here on the basis of our contemporary molecular understanding. They strongly suggest that axon architecture in animals as diverse as arthropods and vertebrates is dependent on loosely cross-linked bundles of microtubules running all along axons, with only minor roles played by neurofilaments.

A mechanism for neurofilament transport acceleration through nodes of Ranvier

Neurofilaments are abundant space-filling cytoskeletal polymers in axons that are transported along microtubule tracks. Neurofilament transport is accelerated at nodes of Ranvier, where axons are locally constricted. Strikingly, these constrictions are accompanied by sharp decreases in neurofilament number, no decreases in microtubule number, and increases in the packing density of these polymers, which collectively bring nodal neurofilaments closer to their microtubule tracks. We hypothesize that this leads to an increase in the proportion of time that the filaments spend moving and that this can explain the local acceleration. To test this, we developed a stochastic model of neurofilament transport that tracks their number, kinetic state, and proximity to nearby microtubules in space and time. The model assumes that the probability of a neurofilament moving is dependent on its distance from the nearest available microtubule track. Taking into account experimentally reported numbers and densities for neurofilaments and microtubules in nodes and internodes, we show that the model is sufficient to explain the local acceleration of neurofilaments within nodes of Ranvier. This suggests that proximity to microtubule tracks may be a key regulator of neurofilament transport in axons, which has implications for the mechanism of neurofilament accumulation in development and disease.

Spatial pattern formation in reaction-diffusion models: a computational approach

Reaction-diffusion equations have been widely used to describe biological pattern formation. Nonuniform steady states of reaction-diffusion models correspond to stationary spatial patterns supported by these models. Frequently these steady states are not unique and correspond to various spatial patterns observed in biology. Traditionally, time-marching methods or steady state solvers based on Newton's method were used to compute such solutions. However, the solutions that these methods converge to highly depend on the initial conditions or guesses. In this paper, we present a systematic method to compute multiple nonuniform steady states for reaction-diffusion models and determine their dependence on model parameters. The method is based on homotopy continuation techniques and involves mesh refinement, which significantly reduces computational cost. The method generates one-parameter steady state bifurcation diagrams that may contain multiple unconnected components, as well as two-parameter solution maps that divide the parameter space into different regions according to the number of steady states. We applied the method to two classic reaction-diffusion models and compared our results with available theoretical analysis in the literature. The first is the Schnakenberg model which has been used to describe biological pattern formation due to diffusion-driven instability. The second is the Gray-Scott model which was proposed in the 1980s to describe autocatalytic glycolysis reactions. In each case, the method uncovers many, if not all, nonuniform steady states and their stabilities.

Intra- and intercellular transport of substances: Models and mechanisms

Non-equilibrium-statistical models of intracellular transport are built. The most significant features of these models are microscopic reversibility and the explicit considerations of the driving forces of the process - the ATP-ADP chemical potential difference. In this paper, water transport using contractile vacuoles, the transport and assembly of microtubules and microfilaments, the protein distribution within a cell, the transport of neurotransmitters from the synaptic cleft and the transport of substances between cells using plasmodesmata are discussed. Endocytosis and phagocytosis models are considered, and transport tasks and information transfer mechanisms inside the cell are explored. Based on an analysis of chloroplast movement, it was concluded that they have a complicated method of influencing each other in the course of their movements. The role of quantum effects in sorting and control transport mechanisms is also discussed. It is likely that quantum effects play a large role in these processes, otherwise reliable molecular recognition would be impossible, which would lead to very low intracellular transport efficiency.

A stochastic model that explains axonal organelle pileups induced by a reduction of molecular motors

Nerve cells are critically dependent on the transport of intracellular cargoes, which are moved by motor proteins along microtubule tracks. Impairments in this movement are thought to explain the focal accumulations of axonal cargoes and axonal swellings observed in many neurodegenerative diseases. In some cases, these diseases are caused by mutations that impair motor protein function, and genetic depletion of functional molecular motors has been shown to lead to cargo accumulations in axons. The evolution of these accumulations has been compared to the formation of traffic jams on a highway, but this idea remains largely untested. In this paper, we investigated the underlying mechanism of local axonal cargo accumulation induced by a global reduction of functional molecular motors in axons. We hypothesized that (i) a reduction in motor number leads to a reduction in the number of active motors on each cargo which in turn leads to less persistent movement, more frequent stops and thus shorter runs; (ii) as cargoes stop more frequently, they impede the passage of other cargoes, leading to local 'traffic jams'; and (iii) collisions between moving and stopping cargoes can push stopping cargoes further away from their microtubule tracks, preventing them from reattaching and leading to the evolution of local cargo accumulations. We used a lattice-based stochastic model to test whether this mechanism can lead to the cargo accumulation patterns observed in experiments. Simulation results of the model support the hypothesis and identify key questions that must be tested experimentally.

The Spectrum of Mechanism-Oriented Models and Methods for Explanations of Biological Phenomena

Developing and improving mechanism-oriented computational models to better explain biological phenomena is a dynamic and expanding frontier. As the complexity of targeted phenomena has increased, so too has the diversity in methods and terminologies, often at the expense of clarity, which can make reproduction challenging, even problematic. To encourage improved semantic and methodological clarity, we describe the spectrum of Mechanism-oriented Models being used to develop explanations of biological phenomena. We cluster explanations of phenomena into three broad groups. We then expand them into seven workflow-related model types having distinguishable features. We name each type and illustrate with examples drawn from the literature. These model types may contribute to the foundation of an ontology of mechanism-based biomedical simulation research. We show that the different model types manifest and exert their scientific usefulness by enhancing and extending different forms and degrees of explanation. The process starts with knowledge about the phenomenon and continues with explanatory and mathematical descriptions. Those descriptions are transformed into software and used to perform experimental explorations by running and examining simulation output. The credibility of inferences is thus linked to having easy access to the scientific and technical provenance from each workflow stage.

Intermediate filament accumulation can stabilize microtubules in Caenorhabditis elegans motor neurons

Neural circuits utilize a coordinated cellular machinery to form and eliminate synaptic connections, with the neuronal cytoskeleton playing a prominent role. During larval development of Caenorhabditis elegans, synapses of motor neurons are stereotypically rewired through a process facilitated by dynamic microtubules (MTs). Through a genetic suppressor screen on mutant animals that fail to rewire synapses, and in combination with live imaging and ultrastructural studies, we find that intermediate filaments (IFs) stabilize MTs to prevent synapse rewiring. Genetic ablation of IFs or pharmacological disruption of IF networks restores MT growth and rescues synapse rewiring defects in the mutant animals, indicating that IF accumulation directly alters MT stability. Our work sheds light on the impact of IFs on MT dynamics and axonal transport, which is relevant to the mechanistic understanding of several human motor neuron diseases characterized by IF accumulation in axonal swellings.

Abnormal neurofilament inclusions and segregations in dorsal root ganglia of a Charcot-Marie-Tooth type 2E mouse model

Charcot-Marie-Tooth (CMT) disease or hereditary motor and sensory neuropathy is the most prevalent inherited peripheral neuropathy and is associated with over 90 causative genes. Mutations in neurofilament light polypeptide gene, NEFL cause CMT2E, an axonal form of CMT that results in abnormal structures and/or functions of peripheral axons in spinal cord motor neurons and dorsal root ganglion neurons. We have previously generated and characterized a knock-in mouse model of CMT2E with the N98S mutation in Nefl that presented with multiple inclusions in spinal cord neurons. In this report, we conduct immunofluorescence studies of cultured dorsal root ganglia (DRG) from Nefl^N98S/+ mice, and show that inclusions found in DRG neurites can occur in embryonic stages. Ultrastructural analyses reveal that the inclusions are disordered neurofilaments packed in high density, segregated from other organelles. Immunochemical studies show decreased NFL protein levels in DRG, cerebellum and spinal cord in Nefl^N98S/+ mice, and total NFL protein pool is shifted toward the triton-insoluble fraction. Our findings reveal the nature of the inclusions in Nefl^N98S/+ mice, provide useful information to understand mechanisms of CMT2E disease, and identify DRG from Nefl^N98S/+ mice as a useful cell line model for therapeutic discoveries.

A systems biology-led insight into the role of the proteome in neurodegenerative diseases

INTRODUCTION

Multifactorial disorders are the result of nonlinear interactions of several factors; therefore, a reductionist approach does not appear to be appropriate. Proteomics is a global approach that can be efficiently used to investigate pathogenetic mechanisms of neurodegenerative diseases.

AREAS COVERED

Here, we report a general introduction about the systems biology approach and mechanistic insights recently obtained by over-representation analysis of proteomics data of cellular and animal models of Alzheimer's disease, Parkinson's disease and other neurodegenerative disorders, as well as of affected human tissues. Expert commentary: As an inductive method, proteomics is based on unbiased observations that further require validation of generated hypotheses. Pathway databases and over-representation analysis tools allow researchers to assign an expectation value to pathogenetic mechanisms linked to neurodegenerative diseases. The systems biology approach based on omics data may be the key to unravel the complex mechanisms underlying neurodegeneration.

Multi-class and multi-scale models of complex biological phenomena

Computational modeling has significantly impacted our ability to analyze vast (and exponentially increasing) quantities of experimental data for a variety of applications, such as drug discovery and disease forecasting. Single-scale, single-class models persist as the most common group of models, but biological complexity often demands more sophisticated approaches. This review surveys modeling approaches that are multi-class (incorporating multiple model types) and/or multi-scale (accounting for multiple spatial or temporal scales) and describes how these models, and combinations thereof, should be used within the context of the problem statement. We end by highlighting agent-based models as an intuitive, modular, and flexible framework within which multi-scale and multi-class models can be implemented.