A single compartment model of pacemaking in dissasociated substantia nigra neurons: stability and energy analysis

Computational neurosciences and quantitative systems pharmacology: a powerful combination for supporting drug development in neurodegenerative diseases

Successful clinical development of new therapeutic interventions is notoriously difficult, especially in neurodegenerative diseases, where predictive biomarkers are scarce and functional improvement is often based on patient's perception, captured by structured interviews. As a consequence, mechanistic modeling of the processes relevant to therapeutic interventions in CNS disorders has been lagging behind other disease indications, probably because of the perceived complexity of the brain. However in this report, we develop the argument that a combination of Computational Neurosciences and Quantitative Systems Pharmacology (QSP) modeling of molecular pathways is a powerful simulation tool to enhance the probability of successful drug development for neurodegenerative diseases. Computational Neurosciences aims to predict action potential dynamics and neuronal circuit activation that are ultimately linked to behavioral changes and clinically relevant functional outcomes. These processes can not only be affected by the disease state, but also by common genotype variants on neurotransmitter-related proteins and the psycho-active medications often prescribed in these patient populations. Quantitative Systems Pharmacology (QSP) modeling of molecular pathways allows to simulate key pathological drivers of dementia, such as protein aggregation and neuroinflammatory responses. They often impact neurotransmitter homeostasis and voltage-gated ion-channels or lead to mitochondrial dysfunction, ultimately leading to changes in action potential dynamics and clinical readouts. Combining these two modeling approaches can lead to better actionable understanding of the many non-linear pharmacodynamic processes active in the human diseased brain. Practical applications include a rational selection of the optimal doses in combination therapies, identification of subjects more likely to respond to treatment, a more balanced stratification of treatment arms in terms of comedications, disease status and common genotype variants and re-analysis of small clinical trials to uncover a possible clinical signal. Ultimately this will lead to a higher success rate of bringing new therapeutics to the right patient populations.

Hallmarks of neurodegenerative disease: A systems pharmacology perspective

Age-related central neurodegenerative diseases, such as Alzheimer's and Parkinson's disease, are a rising public health concern and have been plagued by repeated drug development failures. The complex nature and poor mechanistic understanding of the etiology of neurodegenerative diseases has hindered the discovery and development of effective disease-modifying therapeutics. Quantitative systems pharmacology models of neurodegeneration diseases may be useful tools to enhance the understanding of pharmacological intervention strategies and to reduce drug attrition rates. Due to the similarities in pathophysiological mechanisms across neurodegenerative diseases, especially at the cellular and molecular levels, we envision the possibility of structural components that are conserved across models of neurodegenerative diseases. Conserved structural submodels can be viewed as building blocks that are pieced together alongside unique disease components to construct quantitative systems pharmacology (QSP) models of neurodegenerative diseases. Model parameterization would likely be different between the different types of neurodegenerative diseases as well as individual patients. Formulating our mechanistic understanding of neurodegenerative pathophysiology as a mathematical model could aid in the identification and prioritization of drug targets and combinatorial treatment strategies, evaluate the role of patient characteristics on disease progression and therapeutic response, and serve as a central repository of knowledge. Here, we provide a background on neurodegenerative diseases, highlight hallmarks of neurodegeneration, and summarize previous QSP models of neurodegenerative diseases.

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.

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.

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.

Implications of cellular models of dopamine neurons for disease

This review addresses the present state of single-cell models of the firing pattern of midbrain dopamine neurons and the insights that can be gained from these models into the underlying mechanisms for diseases such as Parkinson's, addiction, and schizophrenia. We will explain the analytical technique of separation of time scales and show how it can produce insights into mechanisms using simplified single-compartment models. We also use morphologically realistic multicompartmental models to address spatially heterogeneous aspects of neural signaling and neural metabolism. Separation of time scale analyses are applied to pacemaking, bursting, and depolarization block in dopamine neurons. Differences in subpopulations with respect to metabolic load are addressed using multicompartmental models.

MEIGO: an open-source software suite based on metaheuristics for global optimization in systems biology and bioinformatics

Background

Optimization is the key to solving many problems in computational biology. Global optimization methods, which provide a robust methodology, and metaheuristics in particular have proven to be the most efficient methods for many applications. Despite their utility, there is a limited availability of metaheuristic tools.

Results

We present MEIGO, an R and Matlab optimization toolbox (also available in Python via a wrapper of the R version), that implements metaheuristics capable of solving diverse problems arising in systems biology and bioinformatics. The toolbox includes the enhanced scatter search method (eSS) for continuous nonlinear programming (cNLP) and mixed-integer programming (MINLP) problems, and variable neighborhood search (VNS) for Integer Programming (IP) problems. Additionally, the R version includes BayesFit for parameter estimation by Bayesian inference. The eSS and VNS methods can be run on a single-thread or in parallel using a cooperative strategy. The code is supplied under GPLv3 and is available at http://www.iim.csic.es/~gingproc/meigo.html. Documentation and examples are included. The R package has been submitted to BioConductor. We evaluate MEIGO against optimization benchmarks, and illustrate its applicability to a series of case studies in bioinformatics and systems biology where it outperforms other state-of-the-art methods.

Conclusions

MEIGO provides a free, open-source platform for optimization that can be applied to multiple domains of systems biology and bioinformatics. It includes efficient state of the art metaheuristics, and its open and modular structure allows the addition of further methods.

Spatial Quantification of Cytosolic Ca²⁺ Accumulation in Nonexcitable Cells: An Analytical Study

Calcium ions act as messengers in a broad range of processes such as learning, apoptosis, and muscular movement. The transient profile and the temporal accumulation of calcium signals have been suggested as the two main characteristics in which calcium cues encode messages to be forwarded to downstream pathways. We address the analytical quantification of calcium temporal-accumulation in a long, thin section of a nonexcitable cell by solving a boundary value problem. In these expressions we note that the cytosolic Ca(2+) accumulation is independent of every intracellular calcium flux and depends on the Ca(2+) exchange across the membrane, cytosolic calcium diffusion, geometry of the cell, extracellular calcium perturbation, and initial concentrations. In particular, we analyse the time-integrated response of cytosolic calcium due to i) a localised initial concentration of cytosolic calcium and ii) transient extracellular perturbation of calcium. In these scenarios, we conclude that i) the range of calcium progression is confined to the vicinity of the initial concentration, thereby creating calcium microdomains; and ii) we observe a low-pass filtering effect in the response driven by extracellular Ca(2+) perturbations. Additionally, we note that our methodology can be used to analyse a broader range of stimuli and scenarios.