A mathematical model of cell death in multiple sclerosis

Mathematical modeling in autoimmune diseases: from theory to clinical application

The research & development (R&D) of novel therapeutic agents for the treatment of autoimmune diseases is challenged by highly complex pathogenesis and multiple etiologies of these conditions. The number of targeted therapies available on the market is limited, whereas the prevalence of autoimmune conditions in the global population continues to rise. Mathematical modeling of biological systems is an essential tool which may be applied in support of decision-making across R&D drug programs to improve the probability of success in the development of novel medicines. Over the past decades, multiple models of autoimmune diseases have been developed. Models differ in the spectra of quantitative data used in their development and mathematical methods, as well as in the level of "mechanistic granularity" chosen to describe the underlying biology. Yet, all models strive towards the same goal: to quantitatively describe various aspects of the immune response. The aim of this review was to conduct a systematic review and analysis of mathematical models of autoimmune diseases focused on the mechanistic description of the immune system, to consolidate existing quantitative knowledge on autoimmune processes, and to outline potential directions of interest for future model-based analyses. Following a systematic literature review, 38 models describing the onset, progression, and/or the effect of treatment in 13 systemic and organ-specific autoimmune conditions were identified, most models developed for inflammatory bowel disease, multiple sclerosis, and lupus (5 models each). ≥70% of the models were developed as nonlinear systems of ordinary differential equations, others - as partial differential equations, integro-differential equations, Boolean networks, or probabilistic models. Despite covering a relatively wide range of diseases, most models described the same components of the immune system, such as T-cell response, cytokine influence, or the involvement of macrophages in autoimmune processes. All models were thoroughly analyzed with an emphasis on assumptions, limitations, and their potential applications in the development of novel medicines.

Could Mathematics be the Key to Unlocking the Mysteries of Multiple Sclerosis?

Multiple sclerosis (MS) is an autoimmune, neurodegenerative disease that is driven by immune system-mediated demyelination of nerve axons. While diseases such as cancer, HIV, malaria and even COVID have realised notable benefits from the attention of the mathematical community, MS has received significantly less attention despite the increasing disease incidence rates, lack of curative treatment, and long-term impact on patient well-being. In this review, we highlight existing, MS-specific mathematical research and discuss the outstanding challenges and open problems that remain for mathematicians. We focus on how both non-spatial and spatial deterministic models have been used to successfully further our understanding of T cell responses and treatment in MS. We also review how agent-based models and other stochastic modelling techniques have begun to shed light on the highly stochastic and oscillatory nature of this disease. Reviewing the current mathematical work in MS, alongside the biology specific to MS immunology, it is clear that mathematical research dedicated to understanding immunotherapies in cancer or the immune responses to viral infections could be readily translatable to MS and might hold the key to unlocking some of its mysteries.

Computational modeling of brain pathologies: the case of multiple sclerosis

The central nervous system is the most complex network of the human body. The existence and functionality of a large number of molecular species in human brain are still ambiguous and mostly unknown, thus posing a challenge to Science and Medicine. Neurological diseases inherit the same level of complexity, making effective treatments difficult to be found. Multiple sclerosis (MS) is a major neurological disease that causes severe inabilities and also a significant social burden on health care system: between 2 and 2.5 million people are affected by it, and the cost associated with it is significantly higher as compared with other neurological diseases because of the chronic nature of the disease and to the partial efficacy of current therapies. Despite difficulties in understanding and treating MS, many computational models have been developed to help neurologists. In the present work, we briefly review the main characteristics of MS and present a selection criteria of modeling approaches.

Relevant biological processes for tissue development with stem cells and their mechanistic modeling: A review

A potential alternative for tissue transplants is tissue engineering, in which the interaction of cells and biomaterials can be optimized. Tissue development in vitro depends on the complex interaction of several biological processes such as extracellular matrix synthesis, vascularization and cell proliferation, adhesion, migration, death, and differentiation. The complexity of an individual phenomenon or of the combination of these processes can be studied with phenomenological modeling techniques. This work reviews the main biological phenomena in tissue development and their mathematical modeling, focusing on mesenchymal stem cell growth in three-dimensional scaffolds.

Physiological Dynamics in Demyelinating Diseases: Unraveling Complex Relationships through Computer Modeling

Despite intense research, few treatments are available for most neurological disorders. Demyelinating diseases are no exception. This is perhaps not surprising considering the multifactorial nature of these diseases, which involve complex interactions between immune system cells, glia and neurons. In the case of multiple sclerosis, for example, there is no unanimity among researchers about the cause or even which system or cell type could be ground zero. This situation precludes the development and strategic application of mechanism-based therapies. We will discuss how computational modeling applied to questions at different biological levels can help link together disparate observations and decipher complex mechanisms whose solutions are not amenable to simple reductionism. By making testable predictions and revealing critical gaps in existing knowledge, such models can help direct research and will provide a rigorous framework in which to integrate new data as they are collected. Nowadays, there is no shortage of data; the challenge is to make sense of it all. In that respect, computational modeling is an invaluable tool that could, ultimately, transform how we understand, diagnose, and treat demyelinating diseases.

Systems biology as a comparative approach to understand complex gene expression in neurological diseases

Systems biology interdisciplinary approaches have become an essential analytical tool that may yield novel and powerful insights about the nature of human health and disease. Complex disorders are known to be caused by the combination of genetic, environmental, immunological or neurological factors. Thus, to understand such disorders, it becomes necessary to address the study of this complexity from a novel perspective. Here, we present a review of integrative approaches that help to understand the underlying biological processes involved in the etiopathogenesis of neurological diseases, for example, those related to autism and autism spectrum disorders (ASD) endophenotypes. Furthermore, we highlight the role of systems biology in the discovery of new biomarkers or therapeutic targets in complex disorders, a key step in the development of personalized medicine, and we demonstrate the role of systems approaches in the design of classifiers that can shorten the time for behavioral diagnosis of autism.

Biochemical Systems Theory: A Review

Biochemical systems theory (BST) is the foundation for a set of analytical andmodeling tools that facilitate the analysis of dynamic biological systems. This paper depicts major developments in BST up to the current state of the art in 2012. It discusses its rationale, describes the typical strategies and methods of designing, diagnosing, analyzing, and utilizing BST models, and reviews areas of application. The paper is intended as a guide for investigators entering the fascinating field of biological systems analysis and as a resource for practitioners and experts.

Data integration and systems biology approaches for biomarker discovery: challenges and opportunities for multiple sclerosis

New "omic" technologies and their application to systems biology approaches offer new opportunities for biomarker discovery in complex disorders, including multiple sclerosis (MS). Recent studies using massive genotyping, DNA arrays, antibody arrays, proteomics, glycomics, and metabolomics from different tissues (blood, cerebrospinal fluid, brain) have identified many molecules associated with MS, defining both susceptibility and functional targets (e.g., biomarkers). Such discoveries involve many different levels in the complex organizational hierarchy of humans (DNA, RNA, protein, etc.), and integrating these datasets into a coherent model with regard to MS pathogenesis would be a significant step forward. Given the dynamic and heterogeneous nature of MS, validating biomarkers is mandatory. To develop accurate markers of disease prognosis or therapeutic response that are clinically useful, combining molecular, clinical, and imaging data is necessary. Such an integrative approach would pave the way towards better patient care and more effective clinical trials that test new therapies, thus bringing the paradigm of personalized medicine in MS one step closer.