Skin Disease Modeling from a Mathematical Perspective

In Silico Elucidation of Key Drivers of Staphyloccocus aureus-Staphyloccocus epidermidis-Induced Skin Damage in Atopic Dermatitis Lesions

Staphylococcus aureus (SA) colonizes and can damage skin in atopic dermatitis lesions, despite being commonly found with Staphylococcus epidermidis (SE), a commensal that can inhibit SA's virulence and kill SA. In this study, we developed an in silico model, termed a virtual skin site, describing the dynamic interplay between SA, SE, and the skin barrier in atopic dermatitis lesions to investigate the mechanisms driving skin damage by SA and SE. We generated 106 virtual skin sites by varying model parameters to represent different skin physiologies and bacterial properties. In silico analysis revealed that virtual skin sites with no skin damage in the model were characterized by parameters representing stronger SA and SE growth attenuation than those with skin damage. This inspired an in silico treatment strategy combining SA-killing with an enhanced SA-SE growth attenuation, which was found through simulations to recover many more damaged virtual skin sites to a non-damaged state, compared with SA-killing alone. This study demonstrates that in silico modelling can help elucidate the key factors driving skin damage caused by SA-SE colonization in atopic dermatitis lesions and help propose strategies to control it, which we envision will contribute to the design of promising treatments for clinical studies.

Mathematical model and stability analysis on the transmission dynamics of skin sores

In this study, a non-linear deterministic model for the transmission dynamics of skin sores (impetigo) disease is developed and analysed by the help of stability of differential equations. Some basic properties of the model including existence and positivity as well as boundedness of the solutions of the model are investigated. The disease-free and endemic equilibrium were investigated, as well as the basic reproduction number, R₀, also calculated using the next-generation matrix approach. When R₀ < 1, the model's stability analysis reveals that the system is asymptotically stable at disease-free critical point globally as well as locally. If R₀ > 1, the system is asymptotically stable at disease-endemic equilibrium both locally and globally. The long-term behaviour of the skin sores model's steady-state solution in a population is investigated using numerical simulations of the model.

Role of subnetworks mediated by [Formula: see text], IL-23/IL-17 and IL-15 in a network involved in the pathogenesis of psoriasis

Psoriasis is a chronic inflammatory skin disease clinically characterized by the appearance of red colored, well-demarcated plaques with thickened skin and with silvery scales. Recent studies have established the involvement of a complex signalling network of interactions between cytokines, immune cells and skin cells called keratinocytes. Keratinocytes form the cells of the outermost layer of the skin (epidermis). Visible plaques in psoriasis are developed due to the fast proliferation and unusual differentiation of keratinocyte cells. Despite that, the exact mechanism of the appearance of these plaques in the cytokine-immune cell network is not clear. A mathematical model embodying interactions between key immune cells believed to be involved in psoriasis, keratinocytes and relevant cytokines has been developed. The complex network formed of these interactions poses several challenges. Here, we choose to study subnetworks of this complex network and initially focus on interactions involving [Formula: see text], IL-23/IL-17, and IL-15. These are chosen based on known evidence of their therapeutic efficacy. In addition, we explore the role of IL-15 in the pathogenesis of psoriasis and its potential as a future drug target for a novel treatment option. We perform steady state analyses for these subnetworks and demonstrate that the interactions between cells, driven by cytokines could cause the emergence of a psoriasis state (hyper-proliferation of keratinocytes) when levels of [Formula: see text], IL-23/IL-17 or IL-15 are increased. The model results explain and support the clinical potentiality of anti-cytokine treatments. Interestingly, our results suggest different dynamic scenarios underpin the pathogenesis of psoriasis, depending upon the dominant cytokines of subnetworks. We observed that the increase in the level of IL-23/IL-17 and IL-15 could lead to psoriasis via a bistable route, whereas an increase in the level of [Formula: see text] would lead to a monotonic and gradual disease progression. Further, we demonstrate how this insight, bistability, could be exploited to improve the current therapies and develop novel treatment strategies for psoriasis.

Sensitivity analysis methods in the biomedical sciences

Sensitivity analysis is an important part of a mathematical modeller's toolbox for model analysis. In this review paper, we describe the most frequently used sensitivity techniques, discussing their advantages and limitations, before applying each method to a simple model. Also included is a summary of current software packages, as well as a modeller's guide for carrying out sensitivity analyses. Finally, we apply the popular Morris and Sobol methods to two models with biomedical applications, with the intention of providing a deeper understanding behind both the principles of these methods and the presentation of their results.

Mathematical modelling of contact dermatitis from nickel and chromium

Dermal exposure to metal allergens can lead to irritant and allergic contact dermatitis (ACD). In this paper we present a mathematical model of the absorption of metal ions, hexavalent chromium and nickel, into the viable epidermis and compare the localised irritant and T-lymphocyte (T-cell) mediated immune responses. The model accounts for the spatial-temporal variation of skin health, extra and intracellular allergen concentrations, innate immune cells, T-cells, cytokine signalling and lymph node activity up to about 6 days after contact with these metals; repair processes associated with withdrawal of exposure to both metals is not considered in the current model, being assumed secondary during the initial phases of exposure. Simulations of the resulting system of PDEs are studied in one-dimension, i.e. across skin depth, and three-dimensional scenarios with the aim of comparing the responses to the two ions in the cases of first contact (no T-cells initially present) and second contact (T-cells initially present). The results show that on continuous contact, chromium ions elicit stronger skin inflammation, but for nickel, subsequent re-exposure stimulates stronger responses due to an accumulation of cytotoxic T-cell mediated responses which characterise ACD. Furthermore, the surface area of contact to these metals has little effect on the speed of response, whilst sensitivity is predicted to increase with the thickness of skin. The modelling approach is generic and should be applicable to describe contact dermatitis from a wide range of allergens.

Multidisciplinary insight into clonal expansion of HTLV-1-infected cells in adult T-cell leukemia via modeling by deterministic finite automata coupled with high-throughput sequencing

Background

Clonal expansion of leukemic cells leads to onset of adult T-cell leukemia (ATL), an aggressive lymphoid malignancy with a very poor prognosis. Infection with human T-cell leukemia virus type-1 (HTLV-1) is the direct cause of ATL onset, and integration of HTLV-1 into the human genome is essential for clonal expansion of leukemic cells. Therefore, monitoring clonal expansion of HTLV-1–infected cells via isolation of integration sites assists in analyzing infected individuals from early infection to the final stage of ATL development. However, because of the complex nature of clonal expansion, the underlying mechanisms have yet to be clarified. Combining computational/mathematical modeling with experimental and clinical data of integration site–based clonality analysis derived from next generation sequencing technologies provides an appropriate strategy to achieve a better understanding of ATL development.

Methods

As a comprehensively interdisciplinary project, this study combined three main aspects: wet laboratory experiments, in silico analysis and empirical modeling.

Results

We analyzed clinical samples from HTLV-1–infected individuals with a broad range of proviral loads using a high-throughput methodology that enables isolation of HTLV-1 integration sites and accurate measurement of the size of infected clones. We categorized clones into four size groups, “very small”, “small”, “big”, and “very big”, based on the patterns of clonal growth and observed clone sizes. We propose an empirical formal model based on deterministic finite state automata (DFA) analysis of real clinical samples to illustrate patterns of clonal expansion.

Conclusions

Through the developed model, we have translated biological data of clonal expansion into the formal language of mathematics and represented the observed clonality data with DFA. Our data suggest that combining experimental data (absolute size of clones) with DFA can describe the clonality status of patients. This kind of modeling provides a basic understanding as well as a unique perspective for clarifying the mechanisms of clonal expansion in ATL.

Electronic supplementary material

The online version of this article (doi:10.1186/s12920-016-0241-2) contains supplementary material, which is available to authorized users.

In silico modeling of spore inhalation reveals fungal persistence following low dose exposure

The human lung is constantly exposed to spores of the environmental mould Aspergillus fumigatus, a major opportunistic pathogen. The spectrum of resultant disease is the outcome of complex host-pathogen interactions, an integrated, quantitative understanding of which lies beyond the ethical and technical reach permitted by animal studies. Here we construct a mathematical model of spore inhalation and clearance by concerted actions of macrophages and neutrophils, and use it to derive a mechanistic understanding of pathogen clearance by the healthy, immunocompetent host. In particular, we investigated the impact of inoculum size upon outcomes of single-dose fungal exposure by simulated titrations of inoculation dose, from 10(6) to 10(2) spores. Simulated low-dose (10(2)) spore exposure, an everyday occurrence for humans, revealed a counter-intuitive prediction of fungal persistence (>3 days). The model predictions were reflected in the short-term dynamics of experimental murine exposure to fungal spores, thereby highlighting the potential of mathematical modelling for studying relevant behaviours in experimental models of fungal disease. Our model suggests that infectious outcomes can be highly dependent upon short-term dynamics of fungal exposure, which may govern occurrence of cyclic or persistent subclinical fungal colonisation of the lung following low dose spore inhalation in non-neutropenic hosts.

Controversies concerning thymus-derived regulatory T cells: fundamental issues and a new perspective

Thymus-derived regulatory T cells (Tregs) are considered to be a distinct T-cell lineage that is genetically programmed and specialised for immunosuppression. This perspective is based on the key evidence that CD25⁺ Tregs emigrate to neonatal spleen a few days later than other T cells and that thymectomy of 3-day-old mice depletes Tregs only, causing autoimmune diseases. Although widely believed, the evidence has never been reproduced as originally reported, and some studies indicate that Tregs exist in neonates. Thus we examine the consequences of the controversial evidence, revisit the fundamental issues of Tregs and thereby reveal the overlooked relationship of T-cell activation and Foxp3-mediated control of the T-cell system. Here we provide a new model of Tregs and Foxp3, a feedback control perspective, which views Tregs as a component of the system that controls T-cell activation, rather than as a distinct genetically programmed lineage. This perspective provides new insights into the roles of self-reactivity, T cell–antigen-presenting cell interaction and T-cell activation in Foxp3-mediated immune regulation.

Regulation of ERK-MAPK signaling in human epidermis

Background

The skin is largely comprised of keratinocytes within the interfollicular epidermis. Over approximately two weeks these cells differentiate and traverse the thickness of the skin. The stage of differentiation is therefore reflected in the positions of cells within the tissue, providing a convenient axis along which to study the signaling events that occur in situ during keratinocyte terminal differentiation, over this extended two-week timescale. The canonical ERK-MAPK signaling cascade (Raf-1, MEK-1/2 and ERK-1/2) has been implicated in controlling diverse cellular behaviors, including proliferation and differentiation. While the molecular interactions involved in signal transduction through this cascade have been well characterized in cell culture experiments, our understanding of how this sequence of events unfolds to determine cell fate within a homeostatic tissue environment has not been fully characterized.

Methods

We measured the abundance of total and phosphorylated ERK-MAPK signaling proteins within interfollicular keratinocytes in transverse cross-sections of human epidermis using immunofluorescence microscopy. To investigate these data we developed a mathematical model of the signaling cascade using a normalized-Hill differential equation formalism.

Results

These data show coordinated variation in the abundance of phosphorylated ERK-MAPK components across the epidermis. Statistical analysis of these data shows that associations between phosphorylated ERK-MAPK components which correspond to canonical molecular interactions are dependent upon spatial position within the epidermis. The model demonstrates that the spatial profile of activation for ERK-MAPK signaling components across the epidermis may be maintained in a cell-autonomous fashion by an underlying spatial gradient in calcium signaling.

Conclusions

Our data demonstrate an extended phospho-protein profile of ERK-MAPK signaling cascade components across the epidermis in situ, and statistical associations in these data indicate canonical ERK-MAPK interactions underlie this spatial profile of ERK-MAPK activation. Using mathematical modelling we have demonstrated that spatially varying calcium signaling components across the epidermis may be sufficient to maintain the spatial profile of ERK-MAPK signaling cascade components in a cell-autonomous manner. These findings may have significant implications for the wide range of cancer drugs which therapeutically target ERK-MAPK signaling components.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-015-0187-6) contains supplementary material, which is available to authorized users.

Resistance to water diffusion in the stratum corneum is depth-dependent

The stratum corneum (SC) provides a permeability barrier that limits the inflow and outflow of water. The permeability barrier is continuously and dynamically formed, maintained, and degraded along the depth, from the bottom to the top, of the SC. Naturally, its functioning and structure also change dynamically in a depth-dependent manner. While transepidermal water loss is typically used to assess the function of the SC barrier, it fails to provide any information about the dynamic mechanisms that are responsible for the depth-dependent characteristics of the permeability barrier. This paper aims to quantitatively characterize the depth-dependency of the permeability barrier using in vivo non-invasive measurement data for understanding the underlying mechanisms for barrier formation, maintenance, and degradation. As a framework to combine existing experimental data, we propose a mathematical model of the SC, consisting of multiple compartments, to explicitly address and investigate the depth-dependency of the SC permeability barrier. Using this mathematical model, we derive a measure of the water permeability barrier, i.e. resistance to water diffusion in the SC, from the measurement data on transepidermal water loss and water concentration profiles measured non-invasively by Raman spectroscopy. The derived resistance profiles effectively characterize the depth-dependency of the permeability barrier, with three distinct regions corresponding to formation, maintenance, and degradation of the barrier. Quantitative characterization of the obtained resistance profiles allows us to compare and evaluate the permeability barrier of skin with different morphology and physiology (infants vs adults, different skin sites, before and after application of oils) and elucidates differences in underlying mechanisms of processing barriers. The resistance profiles were further used to predict the spatial-temporal effects of skin treatments by in silico experiments, in terms of spatial-temporal dynamics of percutaneous water penetration.

Visualisation of the T cell differentiation programme by Canonical Correspondence Analysis of transcriptomes

Background

Currently, in the era of post-genomics, immunology is facing a challenging problem to translate mutant phenotypes into gene functions based on high-throughput data, while taking into account the classifications and functions of immune cells, which requires new methods.

Results

Here we propose a novel application of a multidimensional analysis, Canonical Correspondence Analysis (CCA), to reveal the molecular characteristics of undefined cells in terms of cellular differentiation programmes by analysing two transcriptomic datasets. Using two independent datasets, whether RNA-seq or microarray data, CCA successfully visualised the cross-level relationships between genes, cells, and differentiation programmes, and thereby identified the immunological features of mutant cells (Gata3-KO T cells and Stat3-KO T cells) in a data-oriented manner. With a new concept, differentiation variable, CCA provides an automatic classification of cell samples, which had a high sensitivity and a comparable performance to other classification methods. In addition, we elaborate how CCA results can be interpreted, and reveal the features of CCA in comparison with other visualisation techniques.

Conclusions

CCA is a visualisation tool with a classification ability to reveal the cross-level relationships of genes, cells and differentiation programmes. This can be used for characterising the functional defect of cells of interest (e.g. mutant cells) in the context of cellular differentiation. The proposed approach fits with common hypothesis-oriented studies in immunology, and can be used for a wide range of molecular and genomic studies on cellular differentiation mechanisms.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2164-15-1028) contains supplementary material, which is available to authorized users.