Understanding molecular signaling cascades in neural disease using multi-resolution models

If the genome defines the program for the operations of a cell, signaling networks execute it. These cascades of chemical, cell-biological, structural, and trafficking events span milliseconds (e.g., synaptic release) to potentially a lifetime (e.g., stabilization of dendritic spines). In principle almost every aspect of neuronal function, particularly at the synapse, depends on signaling. Thus dysfunction of these cascades, whether through mutations, local dysregulation, or infection, leads to disease. The sheer complexity of these pathways is matched by the range of diseases and the diversity of their phenotypes. In this review, we discuss how to build computational models, how these models are essential to tackle this complexity, and the benefits of using families of models at different levels of detail to understand signaling in health and disease.

Dynamic modelling and tristability analysis of misfolded α-synuclein degraded via autophagy in Parkinson's disease

The widely-accepted hallmark pathology of Parkinson's disease (PD) is the presence of Lewy bodies with characteristic abnormal aggregated α-synuclein (αSyn). Growing physiological evidence suggests that there is a pivotal role for the autophagy-lysosome pathway (ALP) in the clearance of misfolded αSyn (αSyn∗). This work establishes a mathematical model for αSyn∗ degradation through the ALP. Qualitative simulations are used to uncover the tristable behavior of αSyn∗, i.e., the lower, medium, and upper steady states, which correspond to the healthy, critical, and disease stages of PD, respectively. Time series and codimension-1 bifurcation analysis suggest that the system shows tristability dynamics. Furthermore, variations in the key parameters influence the tristable dynamic behavior, and the distribution of tristable regions is exhibited more comprehensively in codimension-2 bifurcation diagrams. In addition, robustness analysis demonstrates that tristability is a robust property of the system. These results may be valuable in therapeutic strategies for the prevention and treatment of PD.

Dynamics of a model for the degradation mechanism of aggregated α-synuclein in Parkinson's disease

Accumulation of the misfolded synaptic protein α-synuclein (αSyn^*) is a hallmark of neurodegenerative disease in Parkinson's disease (PD). Recent studies suggest that the autophagy lysosome pathway (ALP) including both the Beclin1-associated and mTOR-signaling pathways is involved in the αSyn^* clearance mechanism. In this study, a mathematical model is proposed for the degradation of αSyn^* by ALP with the crosstalk element of mTOR. Using codimension-1 bifurcation analysis, the tri-stability of αSyn^* is surveyed under three different stress signals and, in addition, consideration is given to the regulatory mechanisms for the Beclin1- and mTOR-dependent rates on αSyn^* degradation using the codimension-1 and-2 bifurcation diagrams. It was found that, especially under internal and external oxidative stresses (S ₁), the bistable switch of the aggregation of αSyn^* can be transformed from an irreversible to a reversible condition through the ALP degradation pathways. Furthermore, the robustness of the tri-stable state for the stress S ₁ to the parameters related to mTOR-mediated ALP was probed. It was confirmed that mTOR-mediated ALP is important for maintaining the essential dynamic features of the tri-stable state. This study may provide a promising avenue for conducting further experiments and simulations of the degradation mechanism of dynamic modeling in PD.

Power Failure of Mitochondria and Oxidative Stress in Neurodegeneration and Its Computational Models

The brain needs more energy than other organs in the body. Mitochondria are the generator of vital power in the living organism. Not only do mitochondria sense signals from the outside of a cell, but they also orchestrate the cascade of subcellular events by supplying adenosine-5'-triphosphate (ATP), the biochemical energy. It is known that impaired mitochondrial function and oxidative stress contribute or lead to neuronal damage and degeneration of the brain. This mini-review focuses on addressing how mitochondrial dysfunction and oxidative stress are associated with the pathogenesis of neurodegenerative disorders including Alzheimer's disease, amyotrophic lateral sclerosis, Huntington's disease, and Parkinson's disease. In addition, we discuss state-of-the-art computational models of mitochondrial functions in relation to oxidative stress and neurodegeneration. Together, a better understanding of brain disease-specific mitochondrial dysfunction and oxidative stress can pave the way to developing antioxidant therapeutic strategies to ameliorate neuronal activity and prevent neurodegeneration.

Influence of energy deficiency on the subcellular processes of Substantia Nigra Pars Compacta cell for understanding Parkinsonian neurodegeneration

Parkinson's disease (PD) is the second most prominent neurodegenerative disease around the world. Although it is known that PD is caused by the loss of dopaminergic cells in substantia nigra pars compacta (SNc), the decisive cause of this inexorable cell loss is not clearly elucidated. We hypothesize that "Energy deficiency at a sub-cellular/cellular/systems level can be a common underlying cause for SNc cell loss in PD." Here, we propose a comprehensive computational model of SNc cell, which helps us to understand the pathophysiology of neurodegeneration at the subcellular level in PD. The aim of the study is to see how deficits in the supply of energy substrates (glucose and oxygen) lead to a deficit in adenosine triphosphate (ATP). The study also aims to show that deficits in ATP are the common factor underlying the molecular-level pathological changes, including alpha-synuclein aggregation, reactive oxygen species formation, calcium elevation, and dopamine dysfunction. The model suggests that hypoglycemia plays a more crucial role in leading to ATP deficits than hypoxia. We believe that the proposed model provides an integrated modeling framework to understand the neurodegenerative processes underlying PD.

How Repair-or-Dispose Decisions Under Stress Can Initiate Disease Progression

Glia, the helper cells of the brain, are essential in maintaining neural resilience across time and varying challenges: By reacting to changes in neuronal health glia carefully balance repair or disposal of injured neurons. Malfunction of these interactions is implicated in many neurodegenerative diseases. We present a reductionist model that mimics repair-or-dispose decisions to generate a hypothesis for the cause of disease onset. The model assumes four tissue states: healthy and challenged tissue, primed tissue at risk of acute damage propagation, and chronic neurodegeneration. We discuss analogies to progression stages observed in the most common neurodegenerative conditions and to experimental observations of cellular signaling pathways of glia-neuron crosstalk. The model suggests that the onset of neurodegeneration can result as a compromise between two conflicting goals: short-term resilience to stressors versus long-term prevention of tissue damage.

ROS networks: designs, aging, Parkinson's disease and precision therapies

How the network around ROS protects against oxidative stress and Parkinson's disease (PD), and how processes at the minutes timescale cause disease and aging after decades, remains enigmatic. Challenging whether the ROS network is as complex as it seems, we built a fairly comprehensive version thereof which we disentangled into a hierarchy of only five simpler subnetworks each delivering one type of robustness. The comprehensive dynamic model described in vitro data sets from two independent laboratories. Notwithstanding its five-fold robustness, it exhibited a relatively sudden breakdown, after some 80 years of virtually steady performance: it predicted aging. PD-related conditions such as lack of DJ-1 protein or increased α-synuclein accelerated the collapse, while antioxidants or caffeine retarded it. Introducing a new concept (aging-time-control coefficient), we found that as many as 25 out of 57 molecular processes controlled aging. We identified new targets for "life-extending interventions": mitochondrial synthesis, KEAP1 degradation, and p62 metabolism.

Network Simulations Reveal Molecular Signatures of Vulnerability to Age-Dependent Stress and Tau Accumulation

Alzheimer’s disease (AD) is the leading cause of dementia and one of the most common causes of death worldwide. As an age-dependent multifactorial disease, the causative triggers of AD are rooted in spontaneous declines in cellular function and metabolic capacity with increases in protein stressors such as the tau protein. This multitude of age-related processes that cause neurons to change from healthy states to ones vulnerable to the damage seen in AD are difficult to simultaneously investigate and even more difficult to quantify. Here we aimed to diminish these gaps in our understanding of neuronal vulnerability in AD development by using simulation methods to theoretically quantify an array of cellular stress responses and signaling molecules. This temporally-descriptive molecular signature was produced using a novel multimethod simulation approach pioneered by our laboratory for biological research; this methodology combines hierarchical agent-based processes and continuous equation-based modeling in the same interface, all while maintaining intrinsic distributions that emulate natural biological stochasticity. The molecular signature was validated for a normal organismal aging trajectory using experimental longitudinal data from Caenorhabditis elegans and rodent studies. In addition, we have further predicted this aging molecular signature for cells impacted by the pathogenic tau protein, giving rise to distinct stress response conditions needed for cytoprotective aging. Interestingly, our simulation experiments showed that oxidative stress signaling (via daf-16 and skn-1 activities) does not substantially protect cells from all the early stressors of aging, but that it is essential in preventing a late-life degenerative cellular phenotype. Together, our simulation experiments aid in elucidating neurodegenerative triggers in the onset of AD for different genetic conditions. The long-term goal of this work is to provide more detailed diagnostic and prognostic tools for AD development and progression, and to provide more comprehensive preventative measures for this disease.

Brain aging and garbage cleaning : Modelling the role of sleep, glymphatic system, and microglia senescence in the propagation of inflammaging

Brain aging is a complex process involving many functions of our body and described by the interplay of a sleep pattern and changes in the metabolic waste concentration regulated by the microglial function and the glymphatic system. We review the existing modelling approaches to this topic and derive a novel mathematical model to describe the crosstalk between these components within the conceptual framework of inflammaging. Analysis of the model gives insight into the dynamics of garbage concentration and linked microglial senescence process resulting from a normal or disrupted sleep pattern, hence, explaining an underlying mechanism behind healthy or unhealthy brain aging. The model incorporates accumulation and elimination of garbage, induction of glial activation by garbage, and glial senescence by over-activation, as well as the production of pro-inflammatory molecules by their senescence-associated secretory phenotype (SASP). Assuming that insufficient sleep leads to the increase of garbage concentration and promotes senescence, the model predicts that if the accumulation of senescent glia overcomes an inflammaging threshold, further progression of senescence becomes unstoppable even if a normal sleep pattern is restored. Inverting this process by "rejuvenating the brain" is only possible via a reset of concentration of senescent glia below this threshold. Our model approach enables analysis of space-time dynamics of senescence, and in this way, we show that heterogeneous patterns of inflammation will accelerate the propagation of senescence profile through a network, confirming a negative effect of heterogeneity.

Mathematical modeling of septic shock based on clinical data

BACKGROUND

Mathematical models of diseases may provide a unified approach for establishing effective treatment strategies based on fundamental pathophysiology. However, models that are useful for clinical practice must overcome the massive complexity of human physiology and the diversity of patients' environmental conditions. With the aim of modeling a complex disease, we choose sepsis, which is highly complex, life-threatening systemic disease with high mortality. In particular, we focused on septic shock, a subset of sepsis in which underlying circulatory and cellular/metabolic abnormalities are profound enough to substantially increase mortality. Our model includes cardiovascular, immune, nervous system models and a pharmacological model as submodels and integrates them to create a sepsis model based on pathological facts.

RESULTS

Model validation was done in two steps. First, we established a model for a standard patient in order to confirm the validity of our approach in general aspects. For this, we checked the correspondence between the severity of infection defined in terms of pathogen growth rate and the ease of recovery defined in terms of the intensity of treatment required for recovery. The simulations for a standard patient showed good correspondence. We then applied the same simulations to a patient with heart failure as an underlying disease. The model showed that spontaneous recovery would not occur without treatment, even for a very mild infection. This is consistent with clinical experience. We next validated the model using clinical data of three sepsis patients. The model parameters were tuned for these patients based on the model for the standard patient used in the first part of the validation. In these cases, the simulations agreed well with clinical data. In fact, only a handful parameters need to be tuned for the simulations to match with the data.

CONCLUSIONS

We have constructed a model of septic shock and have shown that it can reproduce well the time courses of treatment and disease progression. Tuning of model parameters for each patient could be easily done. This study demonstrates the feasibility of disease models, suggesting the possibility of clinical use in the prediction of disease progression, decisions on the timing of drug dosages, and the estimation of time of infection.

Mathematical Biology Models of Parkinson's Disease

Parkinsons disease (PD) is a progressive neurodegenerative disease with substantial and growing socio-economic burden. In this multifactorial disease, aging, environmental, and genetic factors contribute to neurodegeneration and dopamine (DA) deficiency in the brain. Treatments aimed at DA restoration provide symptomatic relief, however, no disease modifying treatments are available, and PD remains incurable to date. Mathematical modeling can help understand such complex multifactorial neurological diseases. We review mathematical modeling efforts in PD with a focus on mechanistic models of pathogenic processes. We consider models of α-synuclein (Asyn) aggregation, feedbacks among Asyn, DA, and mitochondria and proteolytic systems, as well as pathology propagation through the brain. We hope that critical understanding of existing literature will pave the way to the development of quantitative systems pharmacology models to aid PD drug discovery and development.

Genome-Scale Brain Metabolic Networks as Scaffolds for the Systems Biology of Neurodegenerative Diseases: Mapping Metabolic Alterations

Systems-based investigation of diseases requires integrated analysis of cellular networks and high-throughput data of gene products. The use of genome-scale metabolic networks for such integration has led to the elucidation of cellular mechanisms for several cell types from microorganisms to plants. It has become easier and cheaper to generate high-throughput data over years in the form of transcriptome, proteome and metabolome. This has tremendously improved the quality and quantity of information extracted from such data enabling the documentation of active pathways and reactions in cell metabolism. A number of omics-based datasets for several neurodegenerative diseases are now available in public repositories. This increases the potential of using genome-scale brain metabolic networks as a scaffold for this type of data to map metabolic alterations for the purpose of elucidating disease mechanisms and for the diagnosis and treatment of such disorders. This chapter first reviews omics data collected for neurodegenerative diseases to map their effect on metabolism. Later, the potential for genome-scale metabolic modeling of such data is reviewed and discussed in light of recently reconstructed brain metabolic networks at genome-scale.

A multimethod computational simulation approach for investigating mitochondrial dynamics and dysfunction in degenerative aging

Research in biogerontology has largely focused on the complex relationship between mitochondrial dysfunction and biological aging. In particular, the mitochondrial free radical theory of aging (MFRTA) has been well accepted. However, this theory has been challenged by recent studies showing minimal increases in reactive oxygen species (ROS) as not entirely deleterious in nature, and even beneficial under the appropriate cellular circumstances. To assess these significant and nonintuitive observations in the context of a functional system, we have taken an in silico approach to expand the focus of the MFRTA by including other key mitochondrial stress response pathways, as they have been observed in the nematode Caenorhabditis elegans. These include the mitochondrial unfolded protein response (UPR^mt), mitochondrial biogenesis and autophagy dynamics, the relevant DAF‐16 and SKN‐1 axes, and NAD⁺‐dependent deacetylase activities. To integrate these pathways, we have developed a multilevel hybrid‐modeling paradigm, containing agent‐based elements among stochastic system‐dynamics environments of logically derived ordinary differential equations, to simulate aging mitochondrial phenotypes within a population of energetically demanding cells. The simulation experiments resulted in accurate predictions of physiological parameters over time that accompany normal aging, such as the declines in both NAD⁺ and ATP and an increase in ROS. Additionally, the in silico system was virtually perturbed using a variety of pharmacological (e.g., rapamycin, pterostilbene, paraquat) and genetic (e.g., skn‐1, daf‐16, sod‐2) schemes to quantitate the temporal alterations of specific mechanistic targets, supporting insights into molecular determinants of aging as well as cytoprotective agents that may improve neurological or muscular healthspan.

Modelling the molecular mechanisms of aging

The aging process is driven at the cellular level by random molecular damage that slowly accumulates with age. Although cells possess mechanisms to repair or remove damage, they are not 100% efficient and their efficiency declines with age. There are many molecular mechanisms involved and exogenous factors such as stress also contribute to the aging process. The complexity of the aging process has stimulated the use of computational modelling in order to increase our understanding of the system, test hypotheses and make testable predictions. As many different mechanisms are involved, a wide range of models have been developed. This paper gives an overview of the types of models that have been developed, the range of tools used, modelling standards and discusses many specific examples of models that have been grouped according to the main mechanisms that they address. We conclude by discussing the opportunities and challenges for future modelling in this field.

The Impact of Mathematical Modeling in Understanding the Mechanisms Underlying Neurodegeneration: Evolving Dimensions and Future Directions

Neurodegenerative diseases are a heterogeneous group of disorders that are characterized by the progressive dysfunction and loss of neurons. Here, we distil and discuss the current state of modeling in the area of neurodegeneration, and objectively compare the gaps between existing clinical knowledge and the mechanistic understanding of the major pathological processes implicated in neurodegenerative disorders. We also discuss new directions in the field of neurodegeneration that hold potential for furthering therapeutic interventions and strategies.

Aging and computational systems biology

Aging research is undergoing a paradigm shift, which has led to new and innovative methods of exploring this complex phenomenon. The systems biology approach endeavors to understand biological systems in a holistic manner, by taking account of intrinsic interactions, while also attempting to account for the impact of external inputs, such as diet. A key technique employed in systems biology is computational modeling, which involves mathematically describing and simulating the dynamics of biological systems. Although a large number of computational models have been developed in recent years, these models have focused on various discrete components of the aging process, and to date no model has succeeded in completely representing the full scope of aging. Combining existing models or developing new models may help to address this need and in so doing could help achieve an improved understanding of the intrinsic mechanisms which underpin aging.

A constraint-based modelling approach to metabolic dysfunction in Parkinson's disease

One of the hallmarks of sporadic Parkinson's disease is degeneration of dopaminergic neurons in the pars compacta of the substantia nigra. The aetiopathogenesis of this degeneration is still not fully understood, with dysfunction of many biochemical pathways in different subsystems suggested to be involved. Recent advances in constraint-based modelling approaches hold great potential to systematically examine the relative contribution of dysfunction in disparate pathways to dopaminergic neuronal degeneration, but few studies have employed these methods in Parkinson's disease research. Therefore, this review outlines a framework for future constraint-based modelling of dopaminergic neuronal metabolism to decipher the multi-factorial mechanisms underlying the neuronal pathology of Parkinson's disease.

Metabolomics and in-silico analysis reveal critical energy deregulations in animal models of Parkinson's disease

Parkinson's disease (PD) is a multifactorial disease known to result from a variety of factors. Although age is the principal risk factor, other etiological mechanisms have been identified, including gene mutations and exposure to toxins. Deregulation of energy metabolism, mostly through the loss of complex I efficiency, is involved in disease progression in both the genetic and sporadic forms of the disease. In this study, we investigated energy deregulation in the cerebral tissue of animal models (genetic and toxin induced) of PD using an approach that combines metabolomics and mathematical modelling. In a first step, quantitative measurements of energy-related metabolites in mouse brain slices revealed most affected pathways. A genetic model of PD, the Park2 knockout, was compared to the effect of CCCP, a mitochondrial uncoupler [corrected]. Model simulated and experimental results revealed a significant and sustained decrease in ATP after CCCP exposure, but not in the genetic mice model. In support to data analysis, a mathematical model of the relevant metabolic pathways was developed and calibrated onto experimental data. In this work, we show that a short-term stress response in nucleotide scavenging is most probably induced by the toxin exposure. In turn, the robustness of energy-related pathways in the model explains how genetic perturbations, at least in young animals, are not sufficient to induce significant changes at the metabolite level.