[Paper Review] Immunopathogenesis in Psoriasis through a Density-type Mathematical Model

Biplab Chattopadhyay, Nirmalendu Hui|arXiv (Cornell University)|Jun 3, 2019

Psoriasis: Treatment and Pathogenesis20 references4 citations

TL;DR

This paper proposes a density-type mathematical model to simulate the immunopathogenesis of psoriasis, integrating interactions among T-cells, dendritic cells, cytokines, and keratinocytes. The model predicts self-sustaining inflammatory feedback loops and hyperproliferation of keratinocytes, consistent with clinical observations and offering testable hypotheses on disease progression and potential therapeutic targets.

ABSTRACT

Disease psoriasis occurs as chronic inflammation of skin and appears as scaly red lesions on skin surface. Advent of several immunosuppressive drugs established that the disease stems from immuno-pathogenic disorder in human blood. Cell biological as well as clinical research on the disease reveals that the helper T-cells and other Leucocytes, responsible for human immunity, may lead to psoriasis pathogenesis if produced in plenty at locations close to the dermal region. Research findings also showed that a complex, self-sustaining (cytokine and related) proteins network play important role in disease maturation by actually leading to a huge proliferation of epidermal keratinocytes. Disease pathogenesis is identified with such hyperproliferation leading to flaking of skin surface (psoriatic plaques). An excessive generation of nitric oxide by proliferated keratinocytes, through a complex chain of bio-chemical events, is causal to the scaliness of psoriatic plaques. Considering these immunopathogenic mechanisms, we propose and analyse a mathematical time differential model for the disease psoriasis. Outcomes of analysis are consistent with existing cell biological and clinical findings with some new predictions which could be tested further.

Motivation & Objective

• To develop a quantitative mathematical model capturing the complex immunological and cellular interactions driving psoriasis pathogenesis.
• To integrate experimental findings on T-cells, dendritic cells, cytokines, and keratinocyte proliferation into a dynamic system of differential equations.
• To simulate the self-sustaining nature of inflammation in psoriasis and predict disease progression under varying biological conditions.
• To provide a theoretical framework that aligns with clinical and cell biological data, enabling testable predictions.

Proposed method

• A system of nonlinear ordinary differential equations models the density dynamics of key immune and skin cells: T-cells, dendritic cells, cytokines (e.g., IL-12, TNF-α, IFN-γ), and keratinocytes.
• Cell densities are modeled as time-dependent variables with production, activation, and feedback terms based on biological evidence.
• Cytokine networks are incorporated as positive feedback loops to simulate the self-sustaining inflammatory environment in psoriatic lesions.
• The model includes nitric oxide production by hyperproliferative keratinocytes, linking cellular proliferation to clinical symptoms like scaliness.
• Parameter values are informed by existing cell biology and clinical data, ensuring biological plausibility.
• Stability analysis and numerical simulations are used to explore model behavior under different initial conditions and perturbations.

Experimental results

Research questions

• RQ1 How do interactions between T-cells, dendritic cells, and cytokines drive sustained inflammation in psoriasis?
• RQ2 What role does keratinocyte hyperproliferation play in the formation of psoriatic plaques, and how is it regulated by immune mediators?
• RQ3 Can a density-based mathematical model reproduce the self-sustaining nature of psoriatic inflammation observed clinically?
• RQ4 How does nitric oxide production by keratinocytes contribute to the scaliness of psoriatic lesions according to the model?
• RQ5 What are the key regulatory nodes in the immune-cell network that could serve as potential therapeutic targets?

Key findings

• The model successfully reproduces the self-sustaining inflammatory feedback loop involving T-cells, dendritic cells, and pro-inflammatory cytokines such as TNF-α and IFN-γ.
• Hyperproliferation of keratinocytes is predicted as a direct consequence of sustained cytokine signaling, consistent with clinical observations of psoriatic plaques.
• The model predicts that elevated nitric oxide production by keratinocytes correlates with disease severity and contributes to the scaliness of plaques.
• Numerical simulations show that perturbing key cytokines (e.g., TNF-α) can disrupt the inflammatory cycle, suggesting potential therapeutic targets.
• The model’s equilibrium states align with clinical disease states, indicating that the system can transition between homeostasis and chronic inflammation based on parameter thresholds.
• The model provides a theoretical basis for understanding how immune cell density dynamics drive disease progression, offering testable predictions for future experimental validation.