Computational modeling of the immune response in multiple sclerosis using epimod framework

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.

Multiple sclerosis: Exploring the limits and implications of genetic and environmental susceptibility

OBJECTIVE

To explore and describe the basis and implications of genetic and environmental susceptibility to multiple sclerosis (MS) using the Canadian population-based data.

BACKGROUND

Certain parameters of MS-epidemiology are directly observable (e.g., the recurrence-risk of MS in siblings and twins, the proportion of women among MS patients, the population-prevalence of MS, and the time-dependent changes in the sex-ratio). By contrast, other parameters can only be inferred from the observed parameters (e.g., the proportion of the population that is "genetically susceptible", the proportion of women among susceptible individuals, the probability that a susceptible individual will experience an environment "sufficient" to cause MS, and if they do, the probability that they will develop the disease).

DESIGN/METHODS

The "genetically susceptible" subset (G) of the population (Z) is defined to include everyone with any non-zero life-time chance of developing MS under some environmental conditions. The value for each observed and non-observed epidemiological parameter is assigned a "plausible" range. Using both a Cross-sectional Model and a Longitudinal Model, together with established parameter relationships, we explore, iteratively, trillions of potential parameter combinations and determine those combinations (i.e., solutions) that fall within the acceptable range for both the observed and non-observed parameters.

RESULTS

Both Models and all analyses intersect and converge to demonstrate that probability of genetic-susceptibitly, P(G), is limited to only a fraction of the population {i.e., P(G) ≤ 0.52)} and an even smaller fraction of women {i.e., P(G│F) < 0.32)}. Consequently, most individuals (particularly women) have no chance whatsoever of developing MS, regardless of their environmental exposure. However, for any susceptible individual to develop MS, requires that they also experience a "sufficient" environment. We use the Canadian data to derive, separately, the exponential response-curves for men and women that relate the increasing likelihood of developing MS to an increasing probability that a susceptible individual experiences an environment "sufficient" to cause MS. As the probability of a "sufficient" exposure increases, we define, separately, the limiting probability of developing MS in men (c) and women (d). These Canadian data strongly suggest that: (c < d ≤ 1). If so, this observation establishes both that there must be a "truly" random factor involved in MS pathogenesis and that it is this difference, rather than any difference in genetic or environmental factors, which primarily accounts for the penetrance difference between women and men.

CONCLUSIONS

The development of MS (in an individual) requires both that they have an appropriate genotype (which is uncommon in the population) and that they have an environmental exposure "sufficient" to cause MS given their genotype. Nevertheless, the two principal findings of this study are that: P(G) ≤ 0.52)} and: (c < d ≤ 1). Threfore, even when the necessary genetic and environmental factors, "sufficient" for MS pathogenesis, co-occur for an individual, they still may or may not develop MS. Consequently, disease pathogenesis, even in this circumstance, seems to involve an important element of chance. Moreover, the conclusion that the macroscopic process of disease development for MS includes a "truly" random element, if replicated (either for MS or for other complex diseases), provides empiric evidence that our universe is non-deterministic.

Holistic View on the Structure of Immune Response: Petri Net Model

The simulation of immune response is a challenging task because quantitative data are scarce. Quantitative theoretical models either focus on specific cell-cell interactions or have to make assumptions about parameters. The broad variation of, e.g., the dimensions and abundance between lymph nodes as well as between individual patients hampers conclusive quantitative modeling. No theoretical model has been established representing a consensus on the set of major cellular processes involved in the immune response. In this paper, we apply the Petri net formalism to construct a semi-quantitative mathematical model of the lymph nodes. The model covers the major cellular processes of immune response and fulfills the formal requirements of Petri net models. The intention is to develop a model taking into account the viewpoints of experienced pathologists and computer scientists in the field of systems biology. In order to verify formal requirements, we discuss invariant properties and apply the asynchronous firing rule of a place/transition net. Twenty-five transition invariants cover the model, and each is assigned to a functional mode of the immune response. In simulations, the Petri net model describes the dynamic modes of the immune response, its adaption to antigens, and its loss of memory.

Time to first treatment and risk of disability pension in relapsing-remitting multiple sclerosis

Background Initiation of disease-modifying therapy early in the disease course of relapsing-remitting multiple sclerosis (RRMS) has demonstrated beneficial effects on clinical outcomes, but socioeconomic outcomes remain largely unexplored. Objective To investigate the association between the delay from disease onset to first treatment and the hazard of disability pension. Methods We performed a population-based cohort study with data from the nationwide Danish Multiple Sclerosis Registry and Danish nationwide registries. Patients with a disease onset between 1 January 1996 to 5 April 2016 were followed until disability pension or a competing risk/censoring event. 7859 patients were assessed for eligibility of which 5208 were included in the final cohort. Key inclusion criteria were: a diagnosis of multiple sclerosis, relapsing-remitting phenotype, treatment in history, age 18-65 years and an Expanded Disability Status Scale≤4. Patients were categorised according to time from onset to first treatment: within 1 year (early), between 1 and 4 years (intermediate) and from 4 to 8 years (late). Results Of the 5208 patients, 1922 were early, 2126 were intermediate and 1160 were late. Baseline clinical and socioeconomic variables were well balanced. The hazard of receiving disability pension increased with increasing delay of treatment initiation compared with the early group. Cox regression estimates adjusted for clinical and socioeconomic confounders: intermediate (HR, 1.37; 95% CI, 1.12 to 1.68) and late (HR, 1.97; 95% CI, 1.55 to 2.51). Conclusion Early treatment initiation is associated with a reduced risk of disability pension in patients with RRMS. This finding underlines the importance of early diagnosis and treatment on a patient-centred, socioeconomic disability milestone.

Toward computational modelling on immune system function

The 3rd edition of the computational methods for the immune system function workshop has been held in San Diego, CA, in conjunction with the IEEE International Conference on Bioinformatics and Biomedicine (BIBM 2019) from November 18 to 21, 2019. The workshop has continued its growing tendency, with a total of 18 accepted papers that have been presented in a full day workshop. Among these, the best 10 papers have been selected and extended for presentation in this special issue. The covered topics range from computer-aided identification of T cell epitopes to the prediction of heart rate variability to prevent brain injuries, from In Silico modeling of Tuberculosis and generation of digital patients to machine learning applied to predict type-2 diabetes risk.