The Spatial Processes package enables an explicit definition of a spatial
environment on top of the normal dynamic modeling SBML capabilities. The
possibility of an explicit representation of spatial dynamics increases the
representation power of SBML. In this work we used those new SBML features to
define an extensive model of colonic crypts composed of the main cellular types
(from stem cells to fully differentiated cells), alongside their spatial
dynamics.Comment: In Proceedings Wivace 2013, arXiv:1309.712

Antoniotti, Marco

Maj, Carlo

Ramazzotti, Daniele

Electronic Proceedings in Theoretical Computer Science

English

arXiv

The Spatial Processes package enables an explicit definition of a spatial environment on top of the normal dynamic modeling SBML capabilities. The possibility of an explicit representation of spatial dynamics increases the representation power of SBML. In this work we used those new SBML features to define an extensive model of colonic crypts composed of the main cellular types (from stem cells to fully differentiated cells), alongside their spatial dynamics

Carlo Maj

Marco Antoniotti

Daniele Ramazzotti

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A. Graudenzi, G. Caravagna, G. Mauri, M. Antoniotti (Eds.):Wivace 2013 - Italian Workshop onArtificial Life and Evolutionary ComputationEPTCS 130, 2013, pp. 74–78, doi:10.4204/EPTCS.130.11c© D. Ramazzotti, C. Maj & M. AntoniottiThis work is licensed under theCreative Commons Attribution License.A Model of Colonic Crypts using SBML SpatialDaniele RamazzottiDipartimento di Informatica, Sistemistica e ComunicazioneUniversità di Milano-BicoccaMilan, Italydaniele.ramazzotti@disco.unimib.itCarlo MajDipartimento di Informatica, Sistemistica e ComunicazioneUniversità di Milano-BicoccaMilan, Italycarlo.maj@disco.unimib.itMarco AntoniottiDipartimento di Informatica, Sistemistica e ComunicazioneUniversità di Milano-BicoccaMilan, Italymarco.antoniotti@disco.unimib.itColonic crypts are invaginations of the connective tissue of human intestine and are supposed to bethe site where mutations affecting the stem cells can occur leading to the emergence and progression ofColorectal Cancer (CRC)[3]. See figure 1 for a schematic representation of a colonic crypt from[7].Figure 1: Schematic representation of a colonic crypt from[7]. In the figure, on the left the cellular typespresent in the crypt are listed, while on the right the shape of the crypt is represented.Different models aimed at describing the colonic crypt behavior have been defined over the years andcan be divided in two groups: in-lattice models, [5], [8], and off-lattice, [1]. See [3] and further referencetherein for a recent review on the subject.In this work we propose a computational model that implements the most recent SBML format [4]and, in particular, the SBML Spatial Processes package. SBML is currently the most used standard forrepresenting computational models in systems biology. It is open and has widespread software supportand a community of users and developers.D. Ramazzotti, C. Maj & M. Antoniotti 75The Spatial Processes package introduces a new tag, named geometry, which enables an explicit def-inition of a spatial environment for the simulation. The possibility of an explicit representation of spatialdynamics increases the representation power of SBML. The SBML Spatial Processes package has beenproposed in 2010 and is currently still under development. At March 2013 the latest version of this pack-age is the 0.81 release of July 2012[6]. In this work, we refer to this version of SBML Spatial Processes.1Our goal is to model the dynamics and the spatial evolution of the tissue by taking into account boththe cellular differentiation and cellular migration processes in specific crypt locations. Our model con-sists of two main parts: the dynamic component, which models the cellular differentiation process, andthe spatial component, which models the positioning and the movement of cells.The basic dynamic part of the model describes 8 cellular types and 12 cellular transformations.The representation with SBML core has been done by describing the cellular types as species and thecellular transformation as reactions. In addition to these 8 species, an empty cell is considered in orderto represent the empty space in the colonic crypt.More in details, the 8 cellular types are Stem cell, Paneth cell, Ta1 (mutated cells of type 1), Ta2a(mutated cells of type 2-a), Ta2b (mutated cells of type 2-b), Goblet cell, Enteroendocrine cell and En-terocyte absorptive cell. The choice of these cellular types has been done to represent the cellular differ-entiation processes that gradually transforms the stem cell progeny into four different fully differentiatedcellular types (paneth, goblet, enteroendocrine and enterocyte). Three types of partially differentiatedcellular types are present (ta1, ta2a, ta2b) in our model.We have defined twelve reactions: seven reactions to represent the cellular differentiations, one re-action regarding the duplication of the stem cells and four reactions to represent the degradation of thefinal differentiated cell types (paneth, goblet, enteroendocrine and enterocyte). The duplication and thedegradation reactions are present in order to assure the attainment of a steady condition. More in detail,the duplication of the stem cells assures that the system does not cease to work as a consequence of thedepletion of stem cells, while the degradation of the differentiated cell prevents the unlimited formationof the terminal node of the network. In figure 2 the resulting dynamic network is shown.Once the spatial system has been defined, it is linked to and guided by the dynamic part of the systemto reflect the spatial evolution of the colonic crypts (i.e. downward displacement of the Paneth cells andupward movement of the other cells once they specify from stem cells).1In the geometry tag, five new SBML subtags are permitted:• ListOfCoordinateCompartments: in this sub-tag the spatial frame is defined. Different types of reference frames arepermitted: in our model it is a 3-dimensional Cartesian System where the x-axis represent the width, the y-axis theheight and the z-axis the depth of the geometrical shapes.• ListOfDomainTypes: in this sub-tag, homogeneous spatial zones present in the system should be defined. Each spatialzone is intended as being anatomically and physiologically similar and the domain types defined in this tag can refer toone or multiple concrete domains (defined in the next tag). For instance, in our case the cell domain types have beendefined here, while the single concrete cells have been defined in the next tag.• ListOfDomains: the domains represent contiguous regions identified by the same domain type. For each domain aposition in the reference frame defined before is assigned. The domains defined here should match the initial conditionof the dynamic model.• ListOfAdjacentDomains: adjacent domain types can be defined here two by two. In our case we have a domain type foreach cell position in the crypt hence each domain type has multiple adjacent domains.• ListOfGeometryDefinitions: here is defined the geometrical structure of each domain type. This is an abstract structureto be assigned to the real domains linked through the domain types definition. SBML Spatial Processes offers fourpossible ways to define the geometry: in our case the AnalyticalGeometry tag has been adopted.76 A Model of Colonic Crypts using SBML SpatialFigure 2: Model Network: the resulting network generated by the model. It involves the differentiatedcell types (paneth, goblet, enteroendocrine and enterocyte) and three partially differentiated cells (ta1,ta2a, ta2b).The spatial part of the model exploits an in-lattice representation where the colonic crypt is describedwith a series of cubic cells which can be empty or filled with one of the 8 species defined in the dynamicmodel. The colonic crypt has been represented as a hollow parallelepiped placed in a 3-dimensional xyzCartesian reference frame. The width and depth of the parallelepiped are represented respectively by thex and z axis. The y-axis represents the height of the parallelepiped. The spatial dynamics of the systemconsists in upward and downward movements, hence the y-values can be within a certain range definedby the dynamic itself. See figure 3.Figure 4 shows a section of the crypt as represented in our model with a view from above.Finally, three special layers have been defined in the crypt. The first one is located in the middle-lower part of the crypt and here new stem cells are created in order to feed the system and avoid thepossibility of completly consume all the stem cells. Then two more special layers are defined at thelower and upper border of the system in order to consume the cells that are leaving the crypt.This work is a first attempt to attach the task of using SBML Spatial Processes to model coloniccrypts. The latest VCell release[2], which is the first modeling software implementing the extensionpackage, has been adopted to define and import the model.Currently, VCell is under developement and its spatial simulation capabilities will be improved inorder to allow more powerfull simulations and parameter tuning, which will be the next steps of thiswork.Ongoing simulations are aimed at defining the parameter tuning for the model parameters such, i.e.the initial conditions and the reaction rates that better represents the colonic crypt dynamics and allowsD. Ramazzotti, C. Maj & M. Antoniotti 77Figure 3: In our model the space is discretized in a finite number of cells following an in-lattice approach.Figure 4: A Section of the Colonic Crypt from above, showing the positioning of the cells and that theinterior area is empty.78 A Model of Colonic Crypts using SBML Spatialthe maintenance of a stable dynamic state, i.e. homeostasis.Besides, further simulations will be performed in order to verify the robustness and the homeostasisof the system. This will be accomplished by analysing the influence of a variation of the initial conditions,as well as perturbations of other key parameters of the model.References[1] CompuCell3D. http://www.compucell3d.org/.[2] Virtual Cell Modeling and Analysis Software. http://www.nrcam.uchc.edu/.[3] Giovanni De Matteis, Alex Graudenzi & Marco Antoniotti (2012): A review of spatial computational modelsfor multi-cellular systems, with regard to intestinal crypts and colorectal cancer development. Journal ofMathematical Biology, pp. 1–54, doi:10.1007/s00285-012-0539-4.[4] Michael Hucka, Frank T. Bergmann, Stefan Hoops, Sarah M. Keating, Sven Sahle, James C. Schaff, Lucian P.Smith & Darren J. Wilkinson (2010): The Systems Biology Markup Language (SBML): Language Specificationfor Level 3 Version 1 Core.[5] Pitt-Francis J, Pathmanathan P, Bernabeu MO, Bordas R, Cooper J, Fletcher AG, Mirams GR, Murray P, Os-borne JM, Walter A, Chapman SJ, Garny A, van Leeuwen IM, Maini PK, RodrÌguez B andWaters SL, White-ley JP, Byrne HM & Gavaghan DJ: Chaste: A test-driven approach to software development for biologicalmodelling. Computer Physics Communications 180(12), p. 2452–2471, doi:10.1016/j.cpc.2009.07.019.[6] N. Le Novere, M. Hucka, N. Anwar, G.D. Bader, E. Demir, S. Moodie & A. Sorokin (2011): Meeting reportfrom the first meetings of the Computational Modeling in Biology Network (COMBINE). Standards in genomicsciences 5(2), p. 230. doi:10.4056/sigs.2034671[7] J.P. Medema & L. Vermeulen (2011): Microenvironmental regulation of stem cells in intestinal homeostasisand cancer. Nature 474(7351), pp. 318–326. doi:10.1038/nature10212[8] Harrison NC (2012): BioCellSim 2.0. http://pcwww.liv.ac.uk/~mf0u4027/biocellsim.

A Model of Colonic Crypts using SBML Spatial

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A Model of Colonic Crypts using SBML Spatial

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