This is justified by the observation that typical diffusivities are extremely small (of the order of 10-10 cm2/second), and that movement of surface EGF receptors is restricted by the cytoskeletal network [19]. Manage cookies/Do not sell my data we use in the preference centre. Journal of Cell Science. Although the amplitudes of the virtual Erk activation level were altered, the prediction of comparable or higher activation levels in the low calcium, relative to the physiological calcium simulations continued to hold true in every case (results not shown). figure 9b), than in physiological calcium environments. 10.1083/jcb.200403043, Lee J, Leonard M, Oliver T, Ishihara A, Jacobson K: Traction forces generated by locomoting keratocytes. Below are the links to the authors original submitted files for images. 10.1002/(SICI)1097-0290(19980305)57:5<571::AID-BIT9>3.0.CO;2-D.

In these conditions, space constraints limit cell migration and the opportunity for cells to form transient contacts, and the Erk-PP profiles are similar in both low and physiological calcium environments. Juxtacrine signalling has been demonstrated to be a powerful new mechanism whereby discrete networks of cells can communicate and develop complex patterns such as those required for organismal development. Techniques such as Western Blotting inherently make the assumption that variations between individual cells are not significant. Springer Nature. AB Each cell will have n sets of equations 15, each associated with an existing intercellular contact i.e. Juxtocrine signaling is a type of intercellular communication that is transmitted by oligosaccharide, lipid or protein components of a cell membrane. FEBS Letters. This information can now be found on Gateway to Research (GtR) Biochemistry. 10.1083/jcb.200510087, van Leeuwen I, Byrne H, Jensen O, King J: Elucidating the interactions between the adhesive and transcriptional functions of beta-catenin in normal and cancerous cells.

We have observed that even in low calcium environments, cells can form E-cadherin-mediated adherens junctions in medium to high density cultures/simulations, although these are substantially less common than in physiological calcium (figures 7, 8, [20] and additional files 3 and 4). It has several distinct binding sites and their interaction with appropriate molecules result in proper alignment of cells with extracellular matrix. This multi-scale, multi-paradigm approach has enabled us to simulate Extracellular signal-regulated kinase (Erk) activation in a population of cells and to examine the consequences of interpretation at a single cell or population-based level using virtual assays. This approach ignores the fact that even within a genetically-homogeneous population, local conditions may influence cell signalling and result in phenotypic heterogeneity. Macromolecules form a region of noncellular material in the regions between cells. It has been demonstrated that intercellular contacts form in cultures of normal human urothelial (NHU) cells at a critical calcium concentration 1 mM [20]. DeWitt A, Dong J, Wiley H, Lauffenburger D: Quantitative analysis of the EGF receptor autocrine system reveals cryptic regulation of cell response by ligand capture. 2006, Singh A, Harris R: Autocrine, paracrine and juxtacrine signaling by EGFR ligands.

Unlike conventional modelling of intracellular signalling pathways, agent modelling allows the response of signalling to be interpreted at the cellular level. 10.1074/jbc.274.42.30169, Schoeberl B, Eichler-Jonsson C, Gilles ED, Mller G: Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors. We have also ignored the presence of soluble autocrine or exogenous ligands in the medium, which might provide some level of pathway activation independently of any juxtacrine effect (as demonstrated by immunofluorescence in figure 6, where exogenous EGF was present in the growth medium) and other interacting intracellular cascades that may also be downstream of the EGFR (e.g. 1 frame = 30 minutes. Baumgartner W, Hinterdorfer P, Ness W, Raab A, Vestweber D, Schindler H, Drenckhahn D: Cadherin interaction probed by atomic force microscopy. PubMed volume2, Articlenumber:102 (2008) We have so far neglected possible membrane diffusion of receptors and ligands, potential targeting of newly synthesised EGFR and ligand to, or clustering at, stable E-cadherin-mediated contacts. 2004, 167 (6): 1183-1194. Model flow. At this stage we do not know which other intercellular mechanisms are involved in positive and negative growth modulation, but one candidate is -catenin, which is a nuclear transcription factor inactivated by E-cadherin sequestration. Large datasets are available through Proceedings B's partnership with Dryad, Plastic Surgery - Principles and Practice, Micro- and Nanoengineering of the Cell Surface, Proceedings of the National Academy of Sciences, 2007 4th Symposium on Computational Intelligence in Bioinformatics and Computational Biology, Clinical Experimental Allergy, Progress in Biophysics and Molecular Biology, Mathematical Models for Biological Pattern Formation, Skin Structure and Function, Wound Healing and Scarring, An invitro model demonstrates the potential of neoplastic human germ cells to influence the tumour microenvironment, International Union of Basic and Clinical Pharmacology. They allow for direct electrical communication between cells, 2.) The reason for selecting a relatively large perturbation factor was that the kinetic parameters for the upstream pathway model were derived from radio-labelling studies utilising the soluble form of an EGFR binding ligand (e.g. We consider the dynamics of this system following a localised disturbance, such as would be provided by a source of ligand or by the generation of a free edge via wounding. Results of intracellular signalling model. In this paradigm, factors that modulate the random nature of the cell contact may have a major role in influencing the behaviour or phenotype of emergent subpopulations. Fibronectin is a large glycoprotein dimer synthesized by numerous cell types. the P13K-Akt pathway [30]). Journal of Cell Biology. Finally, numerical simulations will determine the effect of irregular two dimensional networks, in particular how robust patterns on regular arrays are to geometric perturbations. cell cycle stage, location, shape) according to a number of pre-programmed rules representing biological behaviour, such as proliferation, intercellular adhesion, migration and apoptosis. Cells are considered to be oblate hemi-spheroids (as shown in figure 2). There exists four different notch receptors in mammals: NOTCH1, NOTCH2, NOTCH3, and NOTCH4. 1990, 29 (14): 3563-3569. This page was last edited on 28 July 2019, at 20:45. 2) A receptor on one cell binds to its ligand on the extracellular matrix given off by another cell. The durations of the signals were relatively insensitive to the model parameters. Cardiac valve homeostasis along with other repercussions in disorders involving the cardiovascular system, 3.) In order to assume a functional conformation, E-cadherin requires the presence of extracellular calcium ions. Proc Nat Acad Sci USA. Original seeding density = 200 cells/mm2 c-d) actual immunofluorescence microscopy images of normal human urothelial cells cultured in 0.09 mM and 2.0 mM [Ca2+] conditions, c and d, respectively. , the rates of de novo receptor and ligand synthesis respectively per cell; SA denotes the total surface area of the cell; is the rate constant for E-cadherin mediated contact growth; R0, L0 and SA 0are the total receptor or ligand numbers and surface area on the cell not associated with intercellular contacts at any given time (given by equations 710 in table 2); and 10.1016/j.ccr.2008.04.020, PubMed Central When there is one homomeric connexon and one heteromeric connexon that come together or two heteromeric connexons join it is called a heterotypic gap junction. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Asthagiri A, Reinhart C, Horwitz A, Lauffenburger D: The role of transient ERK2 signals in fibronectin- and insulin-mediated DNA synthesis. Orientation restrictions are responsible for the release requirement. PubMed As described in [3], transition through this checkpoint is dependent on cell:cell bonding and cell spreading, with the underpinning rule set mimicking the phenomenon of contact inhibition of growth. EGFR is known to be a critical mediator of growth control in many cell types, including urothelium [7] and there is growing experimental evidence that EGFR ligands are biologically active prior to cleavage from the membrane [11]. These model predictions highlight the fact that experimental data obtained from populations of cells should be viewed with caution, particularly in terms of inferring behaviour on the level of the individual cell. This nearest neighbour signalling operates via the binding of proteins (ligands) displayed on a cell to receptors on adjacent cells, with binding being an intrinsically nonlinear process. We have extended our previous, simple sigmoidal relationship between extracellular calcium and E-cadherin-mediated cell contact to a more sophisticated rule set which more quantitatively reflects the observations in [21, 22]. a) Top view and b) side view of pair of cell agents sharing an elliptical intercellular contact of length xab and height zab. Modelling of intercellular contact. In order to assess the sensitivity of the results described above to the model parameters, a sensitivity analysis was carried out as follows. The biological basis for this work has been experimentally-generated observations in cultures of normal human urothelial (NHU) cells where, in the absence of exogenous growth factors, proliferation is driven through autocrine production of EGFR-binding factors [7]. 2006, 16 (12): 1171-1182. Effects of calcium-induced differentiation in cultured epithelial cells. 1999, 274: 30169-30181. 1998, 57 (5): 571-582. When two identical connexons come together to form a gap junction, it is called a homotypic gap junction., From Wikibooks, open books for an open world, 10.1158/1541-7786.MCR-07-0134. Briefly, individual cells are represented by software agents (instances of class objects in object-oriented Matlab). 2022 BioMed Central Ltd unless otherwise stated.

Intracellular signalling pathway model derived from [15] and [14] and b) receptor trafficking and c) ligand trafficking on the cell surface. stabilization of arterial endothelial fate and angiogenesis (the growth of new blood vessels from pre-existing vessels). EGFR-MAPK pathway model. Nevertheless, the example used to illustrate our novel approach to modelling heterogeneity within populations is biologically-relevant, and this single example of extrinsic heterogeneity could be extended to examine other nutrients, growth factors or cytokines in the environment. We have used this simple rule-based model to simulate monolayer growth [3] and wound healing [4] in normal human urothelial cell cultures and have adapted it to explore stratification and differentiation in normal and transformed keratinocytes [5]. The Extracellular Matrix as a Source of Critical Developmental Signals. Privacy The multi-agent simulations inherently include inter-agent microenvironment heterogeneity, as this reflects variation in the nature of intercellular contacts experienced by individual cell agents as a result of their position within the population. Results of sensitivity analysis. The extracellular matrix consists of macromolecules secreted by cells into their immediate environment. Case 2 shows the same initial formation pattern, but in this case there is an instantaneous break of contact after 4 hours when it has reached 16 m length. The proposed research will further our understanding of pattern formation in discrete nonlinear mathematical models, and of the developmental potential of juxtacrine signalling mechanisms. Biosystems. a) Mean number of E-cadherin mediated contacts per cell predicted by the agent model for a starting cell density of 200 agents/mm and b) mean total perimeter length of each agent associated with E-Cadherin mediated contacts. These results suggest that the inclusion of rate constants that have been derived from interaction of soluble ligands with cell surface receptors in a model of juxtacrine signalling is not likely to be the largest cause of error and uncertainty in the model, and irrespective of the exact values of these constants, the temporal pattern of Erk activation is likely to depend on the nature of intercellular contacts. and height z A qualitative, second level sensitivity analysis was conducted for a starting cell density of 200 cells/mm2. Systems Biology. Developmental Biology. Google Scholar, Walker DC, Sun T, Macneil S, Smallwood RH: Modeling the effect of exogenous calcium on keratinocyte and HaCat cell proliferation and differentiation using an agent-based computational paradigm. These could represent weak interactions mediated by inter-membrane surface tension, as implied by immunofluorescence microscopy (see [20], and additional files 1 and 2). This demonstrates that even after the simulated cell cultures reach confluence, E-cadherin-mediated contacts are significantly more common and more stable in physiological calcium conditions.

Our approach of using an individual-based paradigm naturally lends itself to examining heterogeneity, either by varying the internal parameters (memory state) of each agent, or by observing the emergent behaviour of agents in differing micro-environments. The binding of integrins to the extracellular matrix can stimulate RTK-Ras pathway. Recent biological discoveries include evidence that juxtacrine ligands may also exist as diffusible molecules. Diffusion of EGFR and ligands in and out of the contact area is ignored. 4.) (AVI 17 MB). It is known that activated Erk (Erk-PP) translocates to the nucleus where it can activate transcription of key cell cycle regulators, such as cyclin D1. In order to focus on modelling cellular interaction, and in particular, biochemical signalling processes that might be influenced by direct cellular contact, it was necessary to increase the complexity of rule sets governing migratory and adhesive behaviour. 2000, 97 (8): 4005-4010. FEBS Letters. This prediction was supported by immunolabelling of an epithelial cell population grown in vitro, which confirmed heterogeneity of Erk activation. 2006, 173 (3): 431-441. Google Scholar, Wojtusciszyn A, Armanet M, Morel P, Berney T, Bosco D: Insulin secretion from human beta cells is heterogeneous and dependent on cell-to-cell contacts. A key component of this work will be to determine the dependence of pattern wavelengths on parameters, which represents a considerable mathematical challenge. Disease involving Notch signalling include: T-ALL (T-cell acute lymphoblastic leukemia), CADASIL (Celebral Autosomal Dominant Arteriopathy with Sub-cortical Infarcts and Leukoencephalophy), Multiple Sclerosis (MS), Tetralogy of Fallot, Alagile syndrome as well as other disease. int = 1 if the contact is defined to be expanding in size, and = 0 otherwise. Ensure that molecules and currents passing through gap junction do not leak into the intracellular space. The data passed between the models on a per contact and per agent basis is summarised in figure 3. Gemma Hill produced the time lapse movie in additional file 2. Case 3 shows the signal arising from an 'instantaneously' formed 12 m contact. A positive relationship between cell contact and proliferation has also been observed in endothelial and smooth muscle cells [26] and in kidney epithelial cells [27]. Oehrtman G, Wiley H, Lauffenburger D: Escape of autocrine ligands into extracellular medium: experimental test of theoretical model predictions. AB We have thus chosen to integrate and adapt existing models of this pathway [14, 15] in order to consider activation of the Erk pathway in an individual cell which occurs as a result of regions of intercellular contact with one or more neighbouring cells, through activation of EGFR by cell surface-presented cognate ligands. Article Direct Transmission of Signals through Gap Junctions. jag1 evs Journal of Biological Chemistry. The identities of cells sharing any contact are also stored. From pathway to population a multiscale model of juxtacrine EGFR-MAPK signalling, The cell culture simulation was run for a period representing 25 hours. Journal of Cell Biology. This is reasonable, given that a detailed study of high-resolution time-lapse images of urothelial cells grown in low calcium conditions (0.09 mM) suggested that most transient intercellular contacts persist between 10 and 60 minutes (e.g. Journal of Cell Biology. A Notch protein extends through the cell membrane and has an external compartment exposed to the outsides, which is where it contacts Delta, Jagged or Serrate proteins that are protruding out from an adjacent cell. From pathway to population a multiscale model of juxtacrine EGFR-MAPK signalling. However, in order to explore juxtacrine signalling, it was necessary to incorporate the concept of a finite bond length. 10.1016/j.cub.2006.04.044, Brightman F, Fell D: Differential feedback regulation of the MAPK cascade underlies the quantitative differences in EGF and NGF signalling in PC12 cells. At the end of every simulation, the updated profile of Erk-PP (equation 29) is returned to the memory of each agent. The frequency of intercellular contact in a cell population is related to cell density the greater the number of cells in a given surface area (or volume in 3D culture) the greater the likelihood of contact formation. 10.1002/1521-1878(200009)22:9<818::AID-BIES7>3.0.CO;2-6, Yamamoto T, Ebisuya M, Ashida F, Okamoto K, Yonehara S, Nishida E: Continuous ERK activation downregulates antiproliferative genes throughout G1 phase to allow cell-cycle progression. NTG carried out experimental work as a postdoctoral research fellow funded by the Engineering and Physical Sciences Research Council (EPSRC) on grant GR/S62338/01. In this case, amounts of a particular protein (active, inactive or total) averaged across a large cell population are measured and used to draw conclusions relating to expression levels in individual cells in the population. In order to investigate a possible role for contact-mediated juxtacrine signalling in epithelial cell cultures, we have utilised a mathematical ordinary differential equation (ODE) model of membrane-bound EGFR-ligand interaction, receptor dimerisation/activation and downstream signalling via the Ras-Raf-MAPK pathway. 2001, 114 (12): 2301-2313. This model was selected due to its relative simplicity compared to other more detailed descriptions, although this does not impact on its ability to predict key features of the pathway, notably the high amplitude transient peak in activated Erk, followed by a lower, but sustained activation for periods of several hours. By combining a deterministic, ODE-based model of a signalling pathway with a non-deterministic agent-based representation of a multi-cellular population, we have developed a simulation environment that can be used to compare how emergent heterogeneity in the cell population can impact on system level behaviour. However, in both images there is clear evidence of heterogeneity, with the cells indicated showing low, moderate and high levels of Erk activation, respectively, which suggests that there is a secondary mode of stimulation in these cells. 1998, 95: 15368-15373. Finally, for comparison, case 3 shows the signal arising from an 'instantaneously' formed 12 m contact (typical of those we have observed using time-lapse microscopy between migratory cells maintained in medium with a low (sub-physiological; 0.09 mM) calcium concentration). and k By using this website, you agree to our The first three terms on the right hand side of the equations (1) and (2) in table 1 represent changes in the numbers of species arising from receptor-ligand interactions. Wei J, Wunderlich M, Fox C, Alvarez S, Cigudosa J, Wilhelm J, Zheng Y, Cancelas J, Gu Y, Jansen M, Dimartino J, Mulloy J: Microenvironment determines lineage fate in a human model of MLL-AF9 leukemia. Receptors located in the region of any intercellular contact can be subject to internalisation, but with surface expression maintained by receptor recycling or de novo receptor synthesis. 10.1073/pnas.070052697, Chu Y-S, Thomas WA, Eder O, Pincet F, Perez E, Thiery JP, Dufour S: Force measurements in E-cadherin-mediated cell doublets reveal rapid adhesion strengthened by actin cytoskeleton remodeling through Rac and Cdc42. Erk-PP immunofluoresence results. The model rule implemented was that a total intercellular adhesion force less than 20 nN would result in migration of a particular cell, but for larger values the cell was not permitted to migrate. Its function is to serve as a general adhesive molecule linking cells to one another and to other substrates such as collagen and proteoglycans. Ideally, we would validate our single cell pathway model by tracking Erk activation in cells making different types of contacts under controlled conditions.

Case 2 shows the same initial formation pattern, but with an instantaneous break of contact after 4 hours when it has reached 16 m length.

In our earlier agent models (e.g. 1993, 65 (5): 2021-2040. Journal of Theoretical Biology. 1994, 127: 1957-1964. the total activated receptor number is calculated on a per contact basis. However, a consistent enhancement of the in vitro growth rate in low density populations grown in physiological calcium conditions was not predicted computationally, and this divergence of in vitro and in virtuo systems led us to investigate potential mechanisms for enhanced growth mediated via intercellular contact, and in particular, juxtacrine signalling via the Epidermal Growth Factor Receptor (EGFR). When attached to one of these ligands, Notch proteins undergo a conformational change that enables it to be cut by a protease. where clen is the length of the non-specific contact length and max_r is 1.5 times the larger of the two cell radii The form of this relationship is somewhat arbitrary, but the range of contact lengths produced gives a reasonable agreement with that observed in microscopy images of growing NHU cell cultures ([20], additional file 1). JS participated in the design and coordination of the experimental study and helped to draft the manuscript. A juxtocrine signal occurs between neighboring cells that have extensive patches of closely opposed plasma membranes linked by transmembrane channels known as connexons. We develop three mathematical models for this process, involving different mathematical representations of the dynamics of membranebound ligand and free and bound receptors, within an epithelial sheet. All downstream species are then calculated on a per cell basis. Correspondence to In addition, the growth of contact areas between cells, such as that observed during E-cadherin mediated adhesion, will result in additional receptors entering the contact area. Circles represent agents (cells) and red lines represent E-cadherin mediated contacts. This is a natural extension of the model and would allow us to explore how intercellular interactions impact on intracellular molecular state and ultimately on normal and abnormal tissue growth. Distribution of fluorescently tagged Erk-PP in normal human urothelial cells maintained in low 0.09 mM (a) and physiological 2.0 mM (b) calcium. Cellular Signalling. We also present the results of a sensitivity analysis of parameters in the signalling pathway model. Virtual time lapse movies of the simulations in low (0.1 mM) and physiological (2 mM) calcium concentrations are available to view in the additional files 3 and 4 respectively. 10.1016/S0014-5793(00)02037-8, Kholodenko B, Demin O, Moehren G, Hoek J: Quantification of short term signaling by the epidermal growth factor receptor. All cells show some degree of Erk activation (indicated by the presence of nuclear Erk), which can be attributed to pathway activation by soluble EGF present in the culture medium. 2002, 20: 370-375. Waves and propagation failure in discrete space models with nonlinear coupling and feedback, A Model of Primitive Streak Initiation in the Chick Embryo, Spatiotemporal Patterning in Models of Juxtacrine Intercellular Signalling with Feedback, Gene Networks Capable of Pattern Formation: From Induction to ReactionDiffusion, Discrete model of periodic pattern formation through a combined autocrinejuxtacrine cell signaling. 2003, 373 (2): 451-463. Numbers of all intracellular molecular species (1129) are stored for every agent and surface species (15) for every contact, in order to provide the initial conditions for the next set of calculations. For instance, agents progress around the cell cycle consisting of phases representing G1, S, G2 and M, traversing a single checkpoint in G1. The intracellular pathway model shown in figure 1a was solved 'inside' every agent in direct contact with adjacent neighbours. California Privacy Statement, The various components of the model, and our methodology in integrating them are described in the Methods section and illustrated in Figure 1, 2, 3. )expansion of the hematopoietic stem cell compartment during bone development and participation in the osteoblastic lineage inferring potential therapeutic role for Notch in bone regeneration and osteoporosis. Figure 7b shows the mean length of the perimeter of each cell associated with this type of contact. cytokines generated mrna corresponding splicing alternative Cell lineage specification of the endocrine and exocrine pancreas, 4.) The basis for this component of the computational model is the prototype Epitheliome model, running on the Mathworks Matlab platform, as described in detail in [3, 4]. 10.1083/jcb.142.4.1105, Kusumi A, Sako Y, Yamamoto M: Confined lateral diffusion of membrane receptors as studied by single particle tracking (nanovid microscopy).