Bioinformatics Advance Access originally published online on July 19, 2005
Bioinformatics 2005 21(17):3541-3547; doi:10.1093/bioinformatics/bti585
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A multicellular systems biology model predicts epidermal morphology, kinetics and Ca2+ flow
1Center for Bioinformatics, University Hamburg Bundesstrasse 43, 20146 Hamburg, Germany
2Department of Dermatology, University Hospital Hamburg-Eppendorf Martinistrasse 52, 20246 Hamburg, Germany
*To whom correspondence should be addressed.
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Abstract |
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 TOP Abstract 1 INTRODUCTION2 SYSTEMS AND METHODS3 ALGORITHMS4 RESULTS AND DISCUSSION5 CONCLUSIONREFERENCES |
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Motivation: Systems biology is currently focused on integrating intracellular networks, although clinically, diseases are largely defined by their histological features. For example, no computational model can simulate today the formation of a horizontally layered epidermis. Since the epidermis is the most complex structured epithelial tissue, systems biology models could yield important insights in epithelial tissue, in which most of all human cancers arise.
Results: We describe the algorithms of a system, capable of simulating the tissue homeostasis in human epidermis leading to a horizontally layered tissue with cells of different differentiation stages. The system predicts epidermal morphology, tissue kinetics and 2D flow of Ca2+ ions. Predicted properties of an epidermis with a healthy and a disturbed barrier are compared with the literature. The system closely mimics the respecting physiological situations.
Availability: Additional information and films of the simulation are available at the website. Source code is available on request. http://www.zbh.uni-hamburg.de/research/ESB/index.php
Contact: grabe{at}zbh.uni-hamburg.de
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1 INTRODUCTION |
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TOPAbstract1 INTRODUCTION2 SYSTEMS AND METHODS3 ALGORITHMS4 RESULTS AND DISCUSSION5 CONCLUSIONREFERENCES |
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In recent systems biology publications, the modeled dynamic systems are nearly exclusively focused on intracellular networks, following the historical molecular roots of bioinformatics. Setting this situation into contrast with the clinical reality where tissue samples are judged by their microscopic morphology, it is instantly clear that systems biology has to become the bridge between the histological and the molecular level.
The outer part of the skin, the epidermis is an ideally suited example for modeling tissue homeostasis. It is an epithelial tissue with a stratified squamous architecture and a cornified surface. Epithelia are found throughout the body; e.g. the alveoli of the lungs are of the simple squamous type whereas the bladder is formed by the transitional type, resembling the epidermis. The main functions of epidermis include protection against physical damage, defense against biological invasion, the regulation of the inward and outward passage of materials and the receipt and transmission of signals to other organisms. It consists mainly of one cell type: the keratinocyte, but additional cells are also present; melanocytes producing the skin coloring pigment, immunocompetent Langerhans cells and neuroendocrine Merkel cells. Keratinocytes move progressively from attachment to the epidermal basement membrane toward the skin surface, forming several well-defined layers during their transit: the stratum basale, stratum spinosum, stratum granulosum and stratum corneum. Although the basal layer is attached to a strongly undulating basal membrane, the epidermis is mainly flat from the stratum granulosum upward. In interaction with the stratum granulosum, the stratum corneum builds the sealing barrier against the outer environment. According to the brick-and-mortar model (Elias, 2004) the barrier is built by using the cell envelopes of dead keratinocytes (corneocytes) as the bricks and the lipid-mixture of lamellar or Odland bodies (Odland and Holbrook, 1981) as the mortar.
Currently, there is no theory that explains how the flat surface of the epidermis is formed. For example, it is believed that ‘the flat epidermal surface might reflect the horizontal tension from pressure inside the body’ (Iizuka et al., 1996). Clearly, a simulation of the intercellular forces and movements would allow insights into these mechanisms. Several attempts have been made to build models of a spatial multicellular structure. The structurally static modeling of organs goes back to the works of Hodgkin and Huxley (1952) who predicted current flow in axons. From the 1960s Denis Noble developed models of the heart (Noble, 1962), which in the 1990s were incorporated into anatomically detailed tissue and organ models (Noble, 2004). In dermatology few works have been published. Based on the assumption of a simple, vertically segmented organization of the epidermis, simple models of cell stacks have been simulated (Honda et al., 1979; Honda and Oshibe, 1984). Structurally dynamic models of cell heaps and cell cultures have been shown recently (Walker et al., 2004; Galle et al., 2005). In general, tissue forming, dynamic models can be separated into lattice-free and lattice-based models. A lattice-based model without graphical representation showed evidence for a passively driven upward cell flow in epidermis (Mitrani, 1983). For modeling the kinetic homeostasis of whole tissues, it seems necessary to use a dynamic, lattice-free model. Such a model has to permit the spatial movement of cells, their proliferation, adhesion, degradation and morphological change, according to biological reality. An early attempt was made by Bartels et al. (1976) modeling a set of directed cell nuclei. The first spatial simulation of an epidermis was developed in 1996 (Rashbass, 1996) based on proliferation and differential cellular adhesion. However, the model only focuses on proliferation and the stratum granulosum of the model did not form a flat surface. The 3D movement of a set of directed cell nuclei of a pseudostratified (i.e. barrier-free) epithelial tissue, based on pathological data, was simulated 1997 (Clem et al., 1997). The lower part of epithelial tissue based on a flat surface with Voronoi-shaped cells was independently modeled in 2001 by two groups [Meineke et al. (2001) and Morel et al. (2001)]. But both approaches excluded the central barrier building process on an undulating membrane. In conclusion, none of the previous approaches described modeled a stratified epithelium ranging from the basal layer to a flat surface. Additionally, no approach has yet targeted the main characteristic of stratified epithelia. This is their layered organization, where differentiation of the cells increases gradually from the tissue-bottom to the surface.
In the present study, we show a system and algorithms for simulating the growth of a terminally differentiated, stratified squamous epithelium. The simulation reflects fundamental aspects of epithelial homeostasis and forms a layered epidermis with a flat surface.
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2 SYSTEMS AND METHODS |
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TOPAbstract1 INTRODUCTION2 SYSTEMS AND METHODS3 ALGORITHMS4 RESULTS AND DISCUSSION5 CONCLUSIONREFERENCES |
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For the simulation each cell in the tissue is modeled as an agent, with each following the same algorithms. The action of a cell depends on its inner state, which describes its differentiation level [stem cell, basal cell, transit amplifying (TA) cell, early or late stratum spinosum cell and granular cell], age, cell cycle state and concentrations of molecules in its environment. The tissue model then is defined by all of these agents. For handling the agents the Java based MASON multiagent environment (Luke et al., 2003) was used. The simulation system consists of three main components:
- The tissue borders: The basal membrane in the form of several rete ridges is a lower spatial barrier for the agents. Stem cells are seeded on it at the beginning of the simulation in a dedicated pattern.
- Mechanical flow: Proliferating cells (stem cells and amplifying cells) in the suprabasal compartment induce a granular flow. The resulting tissue morphology is dependent on the different mechanical properties of the cells, which result from their individual differentiation state.
- Molecular flow: The transported particles (ions, lamella and lipids) then lead to a vertical ion gradient inducing a vertical differentiation pattern among the cells.
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3 ALGORITHMS |
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TOPAbstract1 INTRODUCTION2 SYSTEMS AND METHODS3 ALGORITHMS4 RESULTS AND DISCUSSION5 CONCLUSIONREFERENCES |
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In the following description of the algorithms for each global user-defined parameter, its default value is given in brackets. All kinetic parameters regarding time, spatiality and function of the cells have been defined on the basis of physiological data (Castelijns et al., 1998; Heenen et al., 1998; Bauer et al., 2001; Hoath and Leahy, 2003). The system is propagated in time units of 30 min, in which for each agent the algorithms bounce and waterflow are executed which are described in the following.
3.1 Modeling of the basal membrane
The epidermis is situated on top of the lower dermis. The surface between both parts of the skin is characterized by strong undulations increasing the surface area, thereby stabilizing the mechanical adhesion between both parts and improving the exchange of molecules. The epidermal parts reaching into the dermis are termed rete ridges. Dermis and epidermis are separated through the basal membrane. Thus the basal membrane of the epidermis naturally forms the spatial lower barrier for the simulation and can be used to describe the form of the rete ridges. According to the undulating interface between dermis and epidermis, the basal membrane is modeled by Gaussian type like splines. These splines can be modified during the runtime of the implemented model. For two-dimensions the function bm(x) describes the basal membrane [Equation (1)].
 | (1) |
Basal cells, including the stem cells, are attached to the basal membrane by hemidesmosomes. Therefore, a change in the form of the basal membrane, which could be caused by an elongation of the rete ridges, also implies an automatic adjustment of the position of all basal cells.
3.2 Modeling of the granular flow induced by proliferating cells
Proliferation is implemented for stem cells and TA cells. After a constant period of time StemCycle (62 h), a stem cell spawns a TA cell which proliferates in the period of TAcycle (62 h). All cells except stem cells have a limited life span defined as maxage (1000 h). TA cells spawn committed cells in a first fraction of their lifetime called TACellBirthPeriod (10%), after which they become a differentiated cell. Both cell-types, TA and stem cells, give birth to other cells only when every preceding birth has been fully completed. Proliferation of cells leads to a temporary spatial overlap of cells (collision). Collisions induce an incremental displacement of both collision partners. This displacement partially restores the optimal distance between a cell and its collision partner [Equation (2)].
 | (2) |
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The cell movement is implemented using the approximative Algorithm 1 (bounce). Similar to Algorithm 2 (waterflow) defined in section 3.3, which organizes the particle flow in the simulation, bounce is periodically called by the function main.
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When a cell c has to calculate its movement, it first checks which requirements for movement (stored in the vector (rx[c], ry[c])) it has summed from the other cells, since it last moved. From this sum an updated new position (xc,yc) is calculated, where the maximal displacement is limited by a constant µ(0.06 µm). It is then determined with which cells it collides at this potential position. From the potential collisions with other cells, a displacement vector (dx, dy) is summed for correcting the position of c. At the same time, the calculated displacements are added to the requirements vector (rx[o], ry[o]) of each colliding cell. The length of vector (dx, dy) is restricted to the length of the initial vector: |(rx[c], ry[c])| to avoid overcorrection. If the newly calculated position (xc, yc) is free of collisions, the new position is accepted. A collision is only allowed in the case of a mitotic process, in which a cell may overlap with its child cell. The algorithm requires an existing function neighbors() which returns all neighbors in user-defined distance, and a function setlength() which adjusts the length of a vector to a given length. In the multiagent simulation environment MASON these are provided. External global parameters are underlined.
3.3 Modeling of the flow of Ca2+ ions
There is direct evidence that acute and sustained fluctuations in epidermal calcium regulate expression of differentiation-specific proteins in vivo. Modulations in epidermal calcium coordinately regulate events late in epidermal differentiation that together form the barrier (Elias et al., 2002b). Therefore, the flow of Ca2+ ions is of central importance for an epidermal model. Intact and healthy epidermis displays a vertical calcium ion gradient with low calcium levels in the lower, basal and spinous layers, whereas calcium levels subsequently increase toward the granular layer and sharply decrease in the stratum corneum (Elias et al., 2002b). This calcium gradient disappears after disruption of the epidermal barrier and is restored after wound closure. Decreased calcium levels in the outer epidermis lead to an instant secretion of lamellar bodies preformed in deeper layers of the epidermis. In this way an automatic repair system is achieved. Whether the calcium gradient is formed by active (i.e. ion pumping) or passive mechanisms is still a matter of debate. As a potential passive mechanism, the transepidermal water flux has been identified. Disruption of the epidermal barrier results in an increased flow of water which causes a sudden loss of ionic concentrations in the cells' microenvironments (Grubauer et al., 1989; Elias et al., 2002a). The water flux, therefore, acts as a central repair signal. Besides controlling barrier formation, the calcium gradient controls the vertical keratinocyte differentiation (Elias et al., 2002b).
The water flux is modeled in the simulation by the introduction of a local particle environment for each cell termed cac for the Ca2+ concentration, lamc for the lamella concentration and lipc for lipid concentration around cell c. The transcutaneous water flux then transports the particles between neighboring cells toward the surface. Algorithm 2 achieves this by increasing each cell's particle concentration with those of neighboring, spatially sublocated cells.
The spatial location of each cell c is stored in the vector (xc, yc); the calcium concentration of cell c is denoted (cac). Waterflux (6%) is a global scalar. It defines the fraction of particles flowing from the lower cell to the upper. The maximum concentration for Ca2+ is CaSaturation (150 mg/kg), for lipids it is LipSaturation (150 units), for lamella it is LamSaturation (150 units). Ca2+ in the amount of CaEntry (4 mg/kg/h) is taken up by those cells whose distance to the basal membrane, defined by the function describing the basal membrane bm [Equation (1)], is below a certain distance 
(5 µm).
The barrier function of the epidermis is implemented for those cells which are exposed to the air. A cell is a surface cell, when it has the outermost vertical yc location at its horizontal position xc, which can be monitored with a lookup table. Surface cells exocytose lipids. For this, lamella units, produced in the amount of LamellaProduction (10 units) are converted into lipid units by the global scalar Lamella2Lipids (50%). If enough lipids are present around the surface cells, the loss of calcium by the surface cells is reduced by the scalar BarrierReduc (3%). Otherwise, the loss is given by Waterflux. As the creation of a gradient is generally followed by a diffusion process, the system has also implemented an undirected, concentration driven diffusion simulation, which is implemented in analogy to the given transport algorithm.
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4 RESULTS AND DISCUSSION |
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TOPAbstract1 INTRODUCTION2 SYSTEMS AND METHODS3 ALGORITHMS4 RESULTS AND DISCUSSION5 CONCLUSIONREFERENCES |
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The simulation was tested for its ability to generate the general morphology of healthy and perturbed epidermis, the epidermal kinetic properties, the distribution of differentiation states and the distribution of Ca2+ in the tissue. Using the described parameter setting a healthy, horizontally layered epidermis with a flat surface can be generated (Fig. 1). An overview of the morphological and kinetic measures of the simulation indicates a realistic reproduction of the physiological conditions (Table 2). The simulation space in this model is a box of 140 µm width and 60 µm depth. In punch biopsies from normal human skin, a mean density of 73 952 nucleated cells/mm2 and a mean depth of 60 µm have been detected (Bauer et al., 2001). Assuming a spherical shape of the cells this leads to a mean radius of 5.7 µm for a single cell. Therefore, a box of the given size with the width of 1 cell should approximately contain 81 nucleated cells. The number of cells in selected differentiation states is given in Figure 2. The simulation is increasingly populated until it reaches a steady state seen in the mean age of the epidermal cells. As our simulation contains 350–400 cells this reflects 3–4 cell layers which are visible at once. This increased cellular density has two technical reasons. First, the stratum granulosum contains a substantial number of dying cells in vivo. Bauer et al. (2001) counted only living cells. In our model dying cells are counted as intact cells. Second, the higher cell density compensates the simulation's spatial restriction to two dimensions and provides a larger statistical basis for virtual experiments.
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The system also monitors tissue kinetic parameters (Fig. 3). The turnover time is the time necessary for full renewal of the tissue (Iizuka et al., 1996). It is defined as the ratio between the total number of cells in the tissue and the proliferation rate (i.e. new cells per time). A detailed discussion of the turnover time (Hoath and Leahy, 2003) reveals a time span between 28 days (672 h) and 45 days (1080 h) for the nucleated epidermis. The simulation resulted in a mean epidermal turnover time of
625 h, with extremes ranging from 500 to 750 h which is roughly in the estimated range. The cell-cycle time of the simulation of 62 h (Castelijns et al., 1998) is a user adjustable parameter and directly set. The proportion of proliferating cells in the basal layer, (growth fraction) has been determined to be not >20% of the whole cell population (Heenen et al., 1998). For estimating the growth fraction, the simulation counts the proliferating cells in a distance of 15 µm to the basal membrane. This results in a simulated growth fraction of 20%.
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In vivo, healthy epidermis is characterized by a Ca2+ gradient with a low level of Ca2+ throughout the basal layer and an increasing Ca2+ concentration up to a 2-fold concentration toward the stratum granulosum (Elias et al., 2002a). Using the described algorithms this physiological Ca2+ gradient can be reproduced in silico. The system can visualize the Ca2+ concentrations in the environment of each cell while aggregating the information to an average gradient (Fig. 4a and b).
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The epidermal barrier can be disturbed by mechanical tape-stripping or by topical treatment with acetone or a detergent. This results in immediate loss of the Ca2+ gradient (Mauro et al., 1998). This experiment can be reproduced with the simulation resulting in a comparable derangement of the Ca2+ ion gradient. Therefore, the full loss of Ca2+ at the surface is allowed manually. This can be, for example, achieved by manually reducing the generation of lamella to zero which disables the secretion of lipids at the epidermal surface. The perturbation results in the instant loss of the calcium gradient. The keratinocytes of the simulated epidermis are not able differentiate any more as they have lost their Ca2+ environment (Fig. 4c and d). We conclude that the morphology, the kinetics and the ion distributions of our simulation are generally consistent with physiological conditions of human epidermis.
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5 CONCLUSION |
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TOPAbstract1 INTRODUCTION2 SYSTEMS AND METHODS3 ALGORITHMS4 RESULTS AND DISCUSSION5 CONCLUSIONREFERENCES |
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Our morphological systems biology model is capable of simulating the homeostasis of human epidermis and predicting central kinetic, morphological and Ca2+ properties which closely follow properties described in dermatological literature. As an example of a deranged epidermis, the case of acute barrier disruption was simulated resulting in the disturbed Ca2+ gradient described in literature.
From the dermatological point of view, we demonstrate for the first time the formation of a horizontally layered epidermis with a flat surface on an undulating basal membrane. Our model achieves this with two basic components. Basis is a structured proliferation–differentiation based on stem and TA (progenitor) cells including cell–cell adhesion. Second component is the trans-epidermal waterflow, which transports Ca2+ outward. These ions are trapped through the stratum granulosum, creating a gradient having its highest concentration in this layer. This high extracellular Ca2+ concentration initiates terminal differentiation and barrier building.
Cleary, our model is a simplification of the complex epidermal processes. Adhesion is only considered as an abstract parameter being, in reality, influenced by a multitude of proteins, such as integrins. Also only the passive movement of keratinocytes has been considered in the model. As a major simplification, our model is solely based on Ca2+ dynamics although different mechanisms initiating differentiation are currently discussed. But our goal was to introduce dynamic computational tissue modeling as a tool and to initiate further discussions.
For the practical experimentalist, our simulation raises new questions regarding the mechanical aspects of epidermal homeostasis. Main aspect here are the flow patterns, the spatial trajectories of individual cells, leading to epidermal homeostasis. The simulation indicates that these flow patterns are dependent on the spatial location of the stem cells. Apoptosis and terminal differentiation are natural endpoints for single cells in the simulation and can be well studied with our model.
The model also makes clear that the barrier formation requires a dedicated interplay of the physical forces originating from the stem and TA-cells, and the adhesion of all cells. Our model can be considered as a motivation to further investigate this question. Future work will also include the biochemical modeling of cell–cell communications. This will require an abstraction between the functional cellular model and the mechanical tissue representation, allowing the in silico testing of various functional cell models. This may include, for instance, cytokine signaling, which is of central importance in the epidermis. Therefore, further development of this model will lead to a better understanding of both physiological and pathological epidermal processes. We suggest that the presented approach could also become important for pharmacological research. Finally, we hope that our model contributes to a new systems biological paradigm for studying epidermal biology.
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Acknowledgments |
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We thank Dr Matthias Rarey, Dr Andrew Torda, Dr Emil Mittag and Dr Kevan Willey for critically reading the manuscript. We also thank Dr A. Schmiegel for helpful discussions and Dr Pritinder Kaur for letting us preview her recent manuscript.
Conflict of Interest: none declared.
Received on March 23, 2005; revised on May 26, 2005; accepted on July 14, 2005
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TOPAbstract1 INTRODUCTION2 SYSTEMS AND METHODS3 ALGORITHMS4 RESULTS AND DISCUSSION5 CONCLUSIONREFERENCES |
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