Current address: Centre for Molecular Processing, School of Biosciences, University of Kent, Canterbury, United Kingdom.
Current address: Institute of Agrobiotechnology, CERTH, Thessalonica, Greece.
Conceived and designed the experiments: NVV CH YU NVK GW AC. Performed the experiments: CH YU NVK. Analyzed the data: NVV CH YU NVK GW AC CA CO ST. Contributed reagents/materials/analysis tools: FON. Wrote the paper: NVV CH YU NVK AC FON.
The authors have declared that no competing interests exist.
Inflammation is characterized by altered cytokine levels produced by cell populations in a highly interdependent manner. To elucidate the mechanism of an inflammatory reaction, we have developed a mathematical model for immune cell interactions via the specific, dose-dependent cytokine production rates of cell populations. The model describes the criteria required for normal and pathological immune system responses and suggests that alterations in the cytokine production rates can lead to various stable levels which manifest themselves in different disease phenotypes. The model predicts that pairs of interacting immune cell populations can maintain homeostatic and elevated extracellular cytokine concentration levels, enabling them to operate as an immune system switch. The concept described here is developed in the context of psoriasis, an immune-mediated disease, but it can also offer mechanistic insights into other inflammatory pathologies as it explains how interactions between immune cell populations can lead to disease phenotypes.
A functional immune system requires complex interactions among diverse cell types, mediated by a variety of cytokines. These interactions include phenomena such as positive and negative feedback loops that can be experimentally characterized by dose-dependent cytokine production measurements. However, any experimental approach is not only limited with regard to the number of cell-cell interactions that can be studied at a given time, but also does not have the capacity to assess or predict the overall immune response which is the result of complex interdependent immune cell interactions. Therefore, experimental data need to be viewed from a theoretical perspective allowing the quantitative modeling of immune cell interactions. Here, we propose a strategy for a quantitative description of multiple interactions between immune cell populations based on their cytokine production profiles. The model predicts that the modified feedback loop interactions can result in the appearance of alternative steady-states causing the switch-like immune system effect that is experimentally observed in pathologic phenotypes. Overall, the quantitative description of immune cell interactions via cytokine signaling reported here offers new insights into understanding and predicting normal and pathological immune system responses.
Inflammation is an organism's protective response to injury, pathogens or irritants and represents a complex multicomponent process that mobilizes immune cells to remove pathogens and restore tissue homeostasis. Healthy inflammatory reaction only lasts for a relatively short period of time, in contrast to pathological conditions where inflammation can persist over period of months or years. Chronic inflammation can be harmful and is attributed to the loss of balanced interactions between immune cells. Such interactions occur either via relatively small soluble proteins known as cytokines and chemokines, or through direct cellular interactions between ligands and their receptors expressed on the cellular surface
Skin is a preferred system for studying inflammatory conditions, as tissue can be both easily observed and sampled. Due to its easy accessibility it can be viewed as the “window” to the human immune system. Skin is composed of mainly two layers containing different cell types: keratinocytes are the major cell type forming the outer epidermis, whereas fibroblasts are the major component of the underlying dermis. In addition, various immune cells such as dendritic cell, T cells, neutrophils or natural killer cells reside in the skin and increase in number under inflammatory conditions
A. Normal human skin contains a number of immune cells, including dendritic cells and macrophages that operate as sentinels. They are receptive to invading pathogens or other forms of physical, chemical or genetic damage. Upon activation, certain sub-populations of dendritic cells and macrophages attract and initiate numerous effector systems of the innate and adaptive immune systems. Locally activated immune system is characterised by inflamed tissue due to the increased cytokine concentrations. False activation of the immune system can lead to a number of pathologies, for example, psoriasis. B. Psoriasis is initiated by a number of factors such physical trauma, infection and drugs. The initial phase of developing psoriatic lesions is characterized by production of a large amount of IFN-γ by plasmacytoid dendritic cells (pDC). IFN-γ activates dermal myeloid dendritic cells (mDC) and initiates their migration to the local lymph node. In the lymph node mDCs induce proliferation and priming of antigen-specific T cells. mDC remaining in the dermis produce iNOS, IL-12, IL-23, and TNF-α proinflammatory cytokines. These cytokines initiate a chain of immune system reactions. The interactions between dendritic cells, lymphocytes and keratinocytes, create an area of persistent inflammation that can remain for a significant period of time. Human skin under inflammatory conditions contains increased numbers of immune cell populations and elevated levels of cytokines. The elevated concentrations of cytokines can remain for significant periods of time. While the same cells and elevated cytokine concentrations are observed in healthy skin, the major characteristic of pathology is the multifold increase of cell numbers and persistent maintenance of high cytokine concentrations. In response to inflammatory conditions keratinocytes undergo hyperproliferation and aberrant differentiation.
A major histological feature of lesional psoriatic skin is the thickened epidermis which is due to hyperproliferation and abnormal differentiation of keratinocytes (
Histology of psoriatic plaque (B) is compared with normal skin (A). Psoriatic plaque (B) is characterized by a hyperproliferative epidermal layer that contains a fourfold larger number of epidermal cells. C. Association significance for psoriasis is shown for the key inflammatory cytokines in the whole genome-wide context. It can be observed that the major cytokines IL22, INFγ, IL1, IL17A and IL6 cytokines do not meet the significance threshold. Genome-wide association of each SNP is plotted as the −log10 (
A widely held view is that psoriasis occurs as a result of unbalanced interactions between cells of the immune system, their mediators and keratinocytes
It has been suggested that chronic inflammation occurs as a result of a modified regulation in key immune cell populations via cytokine-mediated interactions. For example, T cells are reported to be regulated by dendritic cells via feedback control mechanisms
A number of computational studies have offered insights into immune system signaling in the context of human disease. A model for a cell-cell interaction network has demonstrated that the loss of responsiveness in feedback signaling pathways is necessary and sufficient to induce leukemic transformation
These and other studies
In order to address some of the outstanding questions and increase our understanding of how immune cell interactions contribute to normal or inflamed skin phenotypes, we developed a quantitative model that captures cytokine-dependent production profiles of cytokines in immune cell populations. The model represents the immune cell interactions as coupled cytokine concentration levels in human tissue by quantifying the underlying feedback loops. The approach allows the application of general concepts in dynamic systems modeling, such as stable homeostatic solution, feedback loops, bistability or oscillations, and thereby, uncovers the causes of chronic inflammation. Moreover, the methodology has the power to differentiate inflammatory disease phenotypes according to mechanisms of immune system imbalance. In this study we consider possible scenarios of cell population interactions and we show how even small changes in cytokine production rates by a single cell population can significantly affect systems properties due to altered feedback interactions and cause immune system-mediated pathology. The model also allows for discrimination between a healthy inflammatory response and chronic inflammation. Due to shared cytokine pathways between psoriasis and other chronic inflammatory diseases, the principles introduced in this study might be applicable to a wider range of immune system disorders.
Given the importance of cytokine-mediated interactions between immune cells, cytokine genes, gene products and their receptors have been subjected to genetic and immunological analysis. Cytokines form a group of candidate susceptibility genes in psoriasis
To evaluate the genetic association approaches and altered cytokine levels observed in psoriasis, we examined the degree of genetic association in polymorphisms located in the vicinity of key psoriasis cytokines. We re-analyzed the genetic association data obtained from GWAS for psoriasis
To further assess the predictive capabilities of genome-wide screens for marker identification in inflammatory conditions, the differences in the IL-10 and IL-22 production levels between psoriatic and healthy skin samples were compared using experimental data from the literature
The above examples suggest that although GWAS and cytokine production/expression comparison allow identification of potential cytokine candidates, they may lead to conflicting conclusions and do not establish a specific cytokine function. Moreover, one can argue that even in situations when both genetic significance and cytokine production/expression differences between cases and controls are present, the mechanisms of molecular interaction between immune cell populations in normal and pathologic interactions cannot be ascertained. It is also unclear how statistically significant differences for cytokines in genotype or expression data of disease and control cases contribute to unbalanced interactions between the immune cell populations. Therefore, the need exists for the development of additional methodologies complementary to genome-wide association studies and expression level comparison that would provide further insights into how the immune system operates.
Genetic or expression level comparison studies are frequently complemented by cytokine concentration profiles, whereby the amounts of various cytokines produced by a specific cell population under normal and diseased conditions are measured by Luminex or Elisa assays. These techniques provide a closer insight into cellular interactions in disease, as individual SNPs or altered cytokine expression levels may not always translate into changes in cytokine production levels. In the previous section we showed that SNPs in cytokine genes may not always result in the modification of cytokine production profile.
In this section we demonstrate that up- or down-regulation of cytokine production levels in disease is due to the interactions between immune cells. Experimental measurements of cytokine production profiles in individual cell populations are usually performed in a physiological “cocktail” of other cytokines. Here we demonstrate that a random choice of the cytokine concentrations in such a physiological cocktail creates grounds for misconceiving the role of a particular cytokine in disease, as illustrated below.
Measurement of a particular cytokine concentration largely depends on the levels of other cytokines also present in the medium. We consider the dose-response curve for IL-17 production in bone marrow derived macrophages as a function of IL-23 concentration shown on
Cytokine production rates by immune cell populations are measured at physiological, but often random background cytokine concentrations. This example illustrates that arbitrary choice of the background cytokine cocktail conditions (in this case IL-23) may lead to different IL-17 production results. A. IL-17 production by bone-derived marrow fibroblasts depends on IL-23 concentration, both important pro-inflammatory cytokines (concentration profiles adopted from
It is essential to note that the overall cytokine production dependence in tissue combines both the cytokine production by a specific cell population as well as other cytokine-dependent effects, such as proliferation and apoptosis. Regulation through proliferation and apoptosis changes the number of cells in skin and therefore also modulates the dose-response profiles. For example,
Cytokine production in a cell population is complemented by a number of mechanisms that counterbalance cytokine production in tissues. Extracellular concentrations of cytokines are affected by diffusion, cleavage by metalloproteases and cytokine binding followed by uptake. The dose-dependence of cytokine B on cytokine A concentration represents a dose-dependent curve of homeostatic balance. It is mediated by immune cell populations and balanced by the cytokine removal mechanisms described above. According to the dose-response curve, any given extracellular concentration of cytokine A in tissue translates to a specific extracellular concentration of cytokine B, under conditions of equilibrium. However, it is also possible that additional cytokine A or B production by other cell populations can also occur in tissue, resulting in cytokine A and B concentrations that do not fit the line of homeostatic equilibrium for the immune cell population considered (
A. Cytokine B production by a cell population as a function of cytokine A concentration defines a continuous line of “homeostasis” for a given immune cell population, where for each concentration of cytokine A corresponds concentration of cytokine B produced by the specified cells. However, other immune cells in the tissue can also produce either or both cytokines A and B so that the combination of the A and B cytokine concentrations in tissue is no longer on the “homeostasis” line. Under normal conditions, the system has to return to a point of homeostasis on the “homeostatic” line. The point of homeostasis can be unambiguously defined by the superimposition of two interacting cell populations: one population produces cytokine B and has receptors to cytokine A (B) and another produces cytokine B in cytokine A-dependent manner (C). Simultaneous consideration of two interdependent cell populations (D) with the superimposition of the cytokine-cytokine dose-dependent curves (E) shows that the point of crossing is the only point where the homeostasis is achieved both “opposite” cell populations.
Owing to the infinite combination of cytokine A and B concentrations in homeostasis mentioned above (
Physiologically relevant consideration of two cell populations jointly (
In order to model the performance of the immune system under normal homeostatic conditions, we analyzed dynamic system responses shown in
A. Phase diagram shows simulated lines (red and blue) of homeostasis for two cell populations. The intersection of the cytokine dose-dependent curves defines the stable steady-state solution that represents the homeostatic concentrations for cytokines A and B as indicated by the violet dotted lines. The green lines describe the trajectories of A and B cytokine alterations from any non-homeostatic combinations of A and B concentrations. Arrowheads indicate the directions of the cytokine concentration alterations towards the homeostatic point of equilibrium from any nonequilibrium combination of cytokine concentrations, as predicted by the systems model. B. When an immune system in homeostasis is exposed to external or internal temporal cytokine application, it responds by generating a cytokine impulse. The response of interdependent cell population to small external perturbation can be introduced by other immune cells. The green lines show the trajectories of cytokine concentration divergence from homeostasis in response to small and transient external cytokine A impulses. Trajectories 1 and 3 occur in response to smallest and largest cytokine A applications, respectively. C. The largest external perturbation leading to trajectory 3 on (B). D. The immune sub-system cytokine A and B spikes, generated in response to the external cytokine A spike on (C). The comparison of the impulse applied and the response generated shows clearly that a relatively small application of cytokine A can generate an impulse nearly two orders of magnitude larger compare to the applied spike. Such model prediction suggests that (i) an immune system can amplify inflammatory signals and (ii) even a healthy system can experience a significant, but transitory, elevation of cytokine concentrations above homeostatic levels.
It is noted that the cytokine dose-dependent relationships shown on
The quantitative representation of immune cell interactions offers a number of mechanistic insights into the immune system responses, specifically in the activation dynamics in response to external application of cytokine A, applied at the state of homeostatic equilibrium (
Inflammation-mediated skin conditions are characterized by chronically high cytokine concentrations maintained over extended periods of time. We employed our mathematical model to explore potential factors that can turn normal immune system responses into pathology.
To explore the ability of the model to predict pathologic immune responses, we varied parameter values (
Parameter | Value | Figure № | Dynamic properties of the immune system |
Stable Homeostasis | |||
Trigger switch | |||
Oscillations | |||
Stable Homeostasis | |||
Trigger switch | |||
Oscillations | |||
Stable Homeostasis | |||
Trigger switch | |||
Oscillations | |||
Stable Homeostasis | |||
Trigger switch | |||
Oscillations | |||
Stable Homeostasis | |||
Trigger switch | |||
Oscillations | |||
Internal or external factors can change the cytokine production profiles and thereby modify the immune cell interaction parameters via feedback loops. A. The nullcline diagram shows the possibility for two interacting immune cell populations to have multiple levels homeostasis as indicated by the intersections of the red and blue cytokine dose-response curves. The two filled circles represent stable solutions, whereas the hollow circle indicates the unstable solution. The green lines describe how the system converges into the stable homeostatic from any non-homeostatic combination of cytokine concentrations. B. The mathematical model predicts that an immune sub-system can switch between the states of stable low and high cytokine concentrations. The trajectory 1 shows the transition from the lower to higher homeostatic points in response to the external cytokine A impulse, whereas the transition from the higher to the lower homeostatic point occurs after the application of the external cytokine B as indicated by the trajectory 2. The time course of cytokine alterations during the transition from the low to high concentration states in response to the external cytokine A impulse (C) is shown on (D). The cytokine concentration dynamics during the switch from the higher to the lower homeostasis states in response to the external impulse of cytokine B (E) is shown on (F).
The described result implies that even minor alterations in cytokine production profiles (presumably initiated by a combination of genetic polymorphisms and environmental factors) can lead to pathological inflammation resulting from modification of feedback loop parameters. The model predicts that causative SNPs that contribute to the alteration of feedback loops via small modifications of cytokine profiles do not need to be identical across all disease phenotypes. The model relates SNPs to pathologic levels of cytokine concentration in tissue and predicts that both statistically significant and insignificant genetic polymorphisms from different immune cell populations can lead to the appearance of additional pathologic cytokine levels and describes how. This offers an explanation of why only some areas of skin can be inflamed in psoriasis while others exhibit symptomless phenotype, while all cells across the whole body carry the same genetic polymorphisms. The systems analysis indicates that genetic polymorphisms can operate in combination with external conditions and either lead to inflammation, or exhibit symptomless phenotype depending on the environmental stimulus. However, one can argue that feedback loop modifications between immune cell populations originates from genetic variants, which do not need to be the same in all disease states and can lead to the emergence of pathology with or without environmental factors.
The directed green lines on
Next, we analyzed the dynamics of cytokine alterations at the transition between the two stable homeostatic levels.
Psoriasis is characterized by a variety of clinical phenotypes. After establishing the mechanism of chronic inflammation in the form of additional stable homeostatic level as described previously, we employed the systems model for immune cell interactions to elucidate whether it can uncover the causes of variety of clinical phenotypes observed in clinical practice. Similarly to the previous case, we tested combinations of parameters within physiological limits without changing the structure of the governing equations.
Under certain combination of parameters (
Internal or external factors can alter the cytokine production profiles and thereby modify the immune cell interaction parameters via feedback loops. Such modification can lead not only to the shift or appearance of new levels of homeostasis, but also to the loss of homeostatic stability with the appearance of limit cycles. A. The nullcline diagram shows the multiple homeostasis solutions as indicated by the intersections of the red and blue cytokine dose-response curves. The filled circle represents a stable solution, whereas the hollow circles demonstrate unstable solutions. One of the unstable solutions forms a limit cycle which represents the possibility for cytokine concentrations to oscillate. The green lines show how the system converges either into the stable homeostatic point or stable oscillations from any other combination of non-homeostatic cytokine concentrations. B. The nullcline diagram describes the case of one unstable solution that forms a limit cycle. C. External perturbations of variable amplitude can shift the system from the stable low cytokine concentration state into the mode of stable oscillations in the higher concentration range, as indicated by trajectory 1. Interestingly, higher amplitude perturbations, applied externally, cause the interdependent cell populations generate large spikes and followed by return to the homeostasis point bypassing the oscillatory mode (trajectory 2). D. An external impulse of small magnitude applied during the oscillatory regime is able to return the system into the basal level of homeostasis.
Variation of cytokine oscillation-driven pathology is shown on
In order to analyze the dynamic properties of immune cell interactions in relation to the type of pathology (
Variable magnitude impulses of cytokine A (A) and (D) applied to the interacting cell populations can shift the cells from the basal homeostasis point into the mode of stable oscillations (B) and (C) or generate a large spike and return into the homeostasis (E) and (F). The larger perturbation (D) causes the immune cell population system to generate a single impulse instead of undergoing stable oscillations. In both cases the magnitude of the perturbation is significantly smaller compare to the response generated by the interacting immune cells.
Small external impulses of cytokines A (A) and cytokine B (D) applied for a temporal period of time can switch the immune system from generating stable oscillations back into the level of homeostasis. The dynamics of cytokine concentrations during the transition from the oscillatory mode back into homeostasis after the cytokine A and cytokine B perturbations are shown on (B–C) and (E–F), respectively.
We propose a new systems biology model that captures crucial properties of immune cell interactions and predicts the conditions under which normal and pathological inflammatory responses are elicited. The model integrates individual characteristics of immune cell populations and allows the definition of homeostasis as specific cytokine concentrations estimated by the intersection of the immune cell population cytokine dose-response curves. The model predictions provide novel insights into the mechanism of elevated levels of inflammatory cytokines in disease
This study suggests that cytokine concentrations can deviate from homeostatic levels even in the absence of any pathology, as long as such deviations are temporal and always return to homeostatic level in equilibrium. Normal immune response initiates temporal increase of key cytokines concentrations for a time span sufficient to execute the effector system and eliminate the cause of inflammatory reaction. Pathology occurs if the inflammatory response is not temporal and cytokine concentrations fail to return to the original levels. According to the model predictions, homeostatic cytokine concentrations can only be estimated from the interactions of interdependent cell populations. Homeostasis is therefore a systems effect and occurs at the crossing of the dose-dependent cytokine productions curves from at least two immune cell populations (
Alterations in the feedback loop parameters
The quantitative model for immune cell interactions in this study offers a mechanistic distinction between healthy inflammatory reaction and pathological inflammation. Internal and environmental factors can alter cellular interactions in the form of modified cytokine production curves. In order to investigate how such alterations can translate into various pathologies, the derived model was subjected to exhaustive evaluation of the underlying parameters of cytokine production and degradation rates without any modifications in the model structure. Such an assumption reflects the physiological situation where the interacting immune cell population pairs remain the same, but the parameters of the interactions can vary due to genetic mutations. The model predicts that the autoimmune mediated pathology occurs in those cases where the modified feedback interactions between immune cells lead to the appearance of additional levels of homeostasis (
The healthy homeostatic and pathologic model predictions have been obtained through exhaustive screening of possible parameter values. The summary of representative sets of parameters chosen approximately in the middle range of the corresponding dynamic behavior is found in
The combinations of parameter values are closely related to the model application on actual cytokines and, as noted earlier, two potential candidates for the proposed model are IL-17 and IL-23. Other cytokines that have been shown to be essential in skin inflammation include IL-22, oncostatin M, TNF-α, IL-1α
(A) Under normal conditions the homeostasis (defined by the dose-dependent cytokine production curve intersection) is reached at one steady-state point at low cytokine concentration levels. Combinations of SNPs and modified cytokine expression levels observed in disease can cause more than one stable (B) or unstable (C) homeostasis. In case of additional stable cytokine level (B), the interacting immune cell populations represent a trigger that can switch and remain in the state of either low or high cytokine concentration levels. When the combination of genetic alterations causes an additional homeostasis point which is unstable with a limit cycle, the cytokine levels can oscillate both locally and spatiotemporally. In such case, the inflammatory cytokines are more likely to be distributed more unevenly across the site of inflammation causing a skin inflammation phenotype of heterogeneous nature (C).
According to the proposed model, pathology occurs as a result of one or a combination of SNPs in cytokine or any other genes with the net effect of altered type of homeostatic level via the modification of parameters in the feedback loop interactions between immune cells. The description of the homeostatic mechanism from the systems perspective explains why SNPs in some cytokines (e.g. in IL-22), can have very low statistical association with psoriasis, but can contribute to pathology in a number of cases (
The proposed quantitative model for immune system explains how normal and pathologic inflammatory immune reactions can be mediated by the same immune cell populations. Current research in immuno-genetics mainly focuses on the search of polymorphisms highlighting candidate genes responsible for pathological inflammation. This work proposes that the altered feedback loop parameters (potentially arising from genetic polymorphisms) in the interactions between immune cell populations participate in the maintenance of inflamed lesions. The system model predictions for the possible coexistence of multiple homeostatic levels explains how inflammatory disease affected individuals can simultaneously have both non-inflamed and inflamed areas of skin while carrying the same genotype with disease-associated SNPs. The proposed approach, therefore, offers a mechanistic explanation for why “causative” SNPs mediate inflammatory lesions at some regions of skin while they do not do so at others.
The systems model described in this work is relatively generic and applicable to analysis of a range of inflammatory conditions. The mathematical model allows the prediction of mechanisms in inflammatory disease and the formulation of requirements for therapeutic interventions. The model-guided screening of therapeutic agents can be performed on the bases of eliminating the second possible level of stable or unstable homeostasis or lowering existing cytokine concentrations.
The model describes different pathology phenotypes which are due to the appearance of additional stable or unstable levels of homeostasis, the loss of stability of the basal level of homeostasis or due to the shift of homeostasis to the levels of higher cytokine concentrations. The last case is probably the most frequent and “simple” scenario of inflammatory pathology that occurs when the cytokine production curves intersect at higher cytokine concentration levels. For example, different homeostatic concentrations of a cytokine A shown on
The systems model for cytokine-mediated immune cell population interactions offers new strategies for development of pharmaceutical interventions. A. The altered cytokine production profiles lead to the modification of feedback parameters between immune cell populations. Modified feedback changes the level of steady-state homeostatic for individual cytokines. The lower and higher homeostatic concentrations for the cytokine A, indicated by violet and green circles, take place for two dose-dependent cytokine profiles from normal and pathologic immune cell populations. In this case, potential therapeutic strategies may focus on identification such compounds that will rescue the original cytokine production profile. B. The interdependence of cytokines via cell populations suggests new strategies for indirect therapeutic interventions by cytokine injections. In this example, injections of cytokine B are likely to decrease the levels of cytokine A. C. The graph, adopted from
The proposed mathematical approach offers new exciting therapeutic opportunities for various inflammatory conditions. One interesting example where the ideas proposed in this study have already been utilized in a similar fashion is the type II diabetes. There are two ways of estimating insulin resistance in diabetes: the glucose clamp test
The majority of currently available pharmacological agents allow temporal elimination of inflammatory symptoms. In the context of the proposed systems model, this effect can be considered as a switch from the inflamed to perilesional steady-state (A). While such compounds or antibodies offer temporal relieve from inflammatory symptoms, they do not represent effective means of cure. The new pharmacological agents can be developed and selected on the action that leads to the disappearance of the additional inflammatory level (B).
Systems modeling of inflammatory responses initiated by interdependent immune cell populations can offer new avenues for inflammatory disease-associated data interpretation. In a vast number of cases, the comparison between cytokine production or expression levels is performed statically, by calculating the medians between readouts obtained from cases and controls (
A. The comparison of cytokine production levels between may not provide statistically significant differences between health and pathology. More importantly, the widely used approach does not offer insights into the mechanism of the observed differences. B. The representation of an immune system as a system of interdependent cells interconnected by the cytokine production and degradation mechanisms provides new possibilities of data interpretation. Experimentally observed readout variability can be interpreted as time course points during an immune response. C. The time course perspective shows the possibility of oscillatory cytokine dynamics.
One of the major difficulties in research of inflammatory pathologies is the lack of unambiguous definition of disease. The systems model suggests that inflammatory skin disease is unlikely to be mediated by one gene or by a specific cell population. Instead, local inflammation of the immune system in the skin arises from systems-level effects emerging from the interactions between cell populations via cytokines, chemokines and cell surface expressed ligands. Interdependent cytokine production by cell populations creates a network of immune cells with a number of emergent properties such as integration of signals across the immune system, generation of distinct outputs depending on combinations of internal and external conditions. Of particular interest is the immune system ability to form discreet steady-states and switch between them. This study analyzes the effects arising from the interaction of two cell populations only. While the mathematical model covers the range of large number of possibilities, one needs to acknowledge that more sophisticated effects can arise from larger number of interacting cell populations via cytokines. Current study does not include a specific dose-dependent or time course data for cytokine dynamics. While inflammation-associated pathologies are likely to develop according the described principles, a specific subset of cytokines and immune cell populations is needed to be identified for each specific inflammatory condition.
The high quality genotypes for 438,670 markers of the 1359 psoriasis cases and 1400 controls from the genome-wide association scan performed by the Collaborative Association Study of Psoriasis
Genome-wide association of each SNP is showed in a Manhattan plot as the −log10 (
In order to elucidate what distinguishes normal and pathological immune system performance, two cytokines interconnected via dose-dependent effects of corresponding cell populations are considered. Effects that occur in the multidimensional space of cell interactions via cytokines can be projected to two dimensions and we show below that alterations in an immune sub-system with two interacting cell immune cell populations have the potential to describe several different inflammatory phenotypes. We develop a systems model for cytokine, chemokine and surface ligand-mediated immune cell interactions that can unravel the mechanism of inflammation and provide mechanistic explanation for the inflammation in human skin. The model contains two cell populations interconnected via activatory and inhibitory cytokine production. The dose-dependent cytokine production is complemented by cytokine removal via diffusion, cleavage by metalloproteases and trapping mechanisms.
In the most general case, the speed of cytokine concentration
In order to develop the mathematical model capturing the interactions in immune cells via cytokines we defined a number of following immune cell subpopulation groups according to the classification shown on
The rate of cytokine A production by a cell population when it interacts with another population that produces inhibitory cytokine B is given by:
The rate of the cytokine B production by a cell population when it interacts with another population that produces activatory cytokine A is given by:
Cytokine production by a given cell populations can be modulated by several activatory or inhibitory cytokines. In this general case the cytokine production is given by:
Cytokine production is complemented by mechanisms of cytokine elimination. Various routes of cytokine removal from extracellular space include cleavage by metalloproteases, diffusion, cytokine trapping, binding to the cytokine receptor and uptake. Cytokine removal by diffusion and cleavage by metalloproteases are nonspecific and do not play an active role in the regulation of the extracellular cytokine concentrations, whereas the cytokine binding to the receptor followed by either release or uptake can have significant implications on the cytokine concentration dynamics. Thus, we next develop governing equations for the cytokine-cytokine receptor interactions.
Cytokine binding to the receptor initiates intracellular signaling events. Under the conditions of dynamic equilibrium, in the absence of endocytosis, the number of cytokines bound to the soluble receptors would equal to the number of cytokines released. However, due to the cytokine-cytokine receptor complexes uptake certain amount of cytokine is internalized via endocytosis mechanism and degraded. The cytokine uptake decreases the cytokine concentration in the extracellular space in the cytokine concentration-dependent manner. The rate of cytokine uptake
The total number of receptors can be divided into two fractions: receptors that are present on the surface and the subpopulation in the vesicles after the uptake event took place. In steady-state, the rate of receptor synthesis equals to the rate of receptor degradation by proteosomes; these rates are not considered in the present analysis. The conservation law applied to the two receptor populations at any given time point is given by:
The dynamics of the receptors present on the cell surface is given by:
In the steady-state, the number of receptors on the cell surface as a function of extracellular cytokine concentration is given by:
The relationship between the parameters in the normalized system of differential equations with the original description for the cytokine production and uptake rates is thus given by:
General principles of cytokine-dependent immune cell population interactions.
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Support for genotyping of samples was provided through the Genetic Association Information Network (GAIN). The dataset used for the analyses described in this manuscript were obtained from the database of Genotypes and Phenotypes (dbGaP) found at