Background
Stem cell research has been arguably the biggest growth area of medical science in recent years. However, experiments are very limited because it is not possible to track stem cells in the adult human body. Even if you remove cells from the human body and look at them in the laboratory you can only tell if you had some stem cells in your original sample some weeks later when you see what the cells have actually done. However, we do know what stem cells do at the system level. They maintain the population of the various functional cells in our bodies, they can maintain there own number, and can also recover populations of stem and functional cells after disease, injury or radiation theory.
So we know what the system of stem cells does functionalily but we do not have much idea of what happens at the level of individual cells and this gives us a clear reason as to why we might want to model and simulate systems of stem cells. Specifically we are interested in relating the behaviour of the system (macro) to what happens at the local cell (micro).
Untill quite recently it seems that many researchers that stem cell fate was essentially pre-determined and that it was simply a matter of time before a stem cell did what it was pre-programmed to do. However, it is now reasonbly clear that stem cell fate is a function of the local interaction with its environment. If we take this view then the most obvious computational metahpor we have is the "agent" metaphor.
Computational agents are software systems that are situated within an environment that they can perceive and act in. The action will change the state of the environment (and so may in turn affect the perception of that environment subsequently) and may also change the internal state of the agent. Agents have another advantage over other mathematical/computational methods in that they are biologically intuitive. One of the key features of any model of stem cells is that it is significant and useful for researchers working in the laboratories. Either they make predictions that can be tested in the laboratory or they challenge the conceptual models, or way researchers think about stem cells in general, and thus enable new modes of thinking.
Of course we must remain pretty humble with our models and simulations. The level of complexity and sophistiction of the elements within a simulation pales in comparison to the sophistication and subtlety of living biological systems. However, modelling has a history of working in the other sciences and there is no reason why it shouldn't help to give us a handle on how biologcial systems work. It is our belief that simple theoretical models of the kind will become key to understanding fundamental properties of complex biological systems.Aims
- To build an agent-based modelling framewok in which current and new theories of stem cell behaviour can be modelled.
- To develop an associated computational environment where the models of stem cells can br simulated.
- To demonstrate the generality of our approach by incorporating existing models of stem cell behaviour into our framework and simulation.
- To include a visualisation tool that allows us to perceive the simulation in different ways depending on purpose and biological expertise.
- To investigate how the behaviour of a system of stem cells is related to the local cell-cell and cell-environment interactions.
- To challenge current modes of conceptualising stem cell behaviour.
- To predict properties of systems of stem cells that can be tested experimental that will provide insights into what behaviour is happening at the cellular level,
The Z Specification Language
We use the Z specification language to build the mathematical model our agent framework and all the related systems for the following reasons.
- Z is a mathematical language that can be understood comparatively easily. This is especially important when we are working in an interdisciplinary context.
- Z models can be related strongly to simulations of the model.
- We have considerable experience of using Z to specify agent systems and that always helps.
- Z is the most expressive language I know. You can use it to produce a consistent and unified account of a system, the state of the system, and the operation of the system.
- We have a principled methdology (or practice) for modelling in Z in general based on years of experience
Simulations
So far we have developed a number of simulations as Java applets. The applets can be viewed by following the links below. We also have Z specifications of these simulations.
Simulations Based on Previous Work by Other Researchers
- Z.
Agur, Y. Daniel and Y. Ginosar. The universal properties of stem cells
as pinpointed by a simple discrete model. Jour. Math. Biol. 2002;
44(1):79-86.
- Agur et al a cellular automata model of stem cell niche maintenance.
- Agent-Based Agur a biologically intuitive agent version of the original model with cell division
- Multiway Agent-Based Agur this is exactly the same as the agent version but allows up to 4-way cell division. It is included because it has the same behaviour as the original CA Model.
- I.
Roeder and M. Loeffler. A novel dynamic model of hematopoietic stem
cell organization based on the concept of within-tissue plasticity Exp.
Hematol. 30(8):853-61
- Roeder & Loeffler one of the most sophisticated models we have seen to date, we need to talk to the author to fine tune this model.
- 3D Roeder & Loeffler this is the same model as the one above but with a more sophisticated visualisation of the simulation. If you do not have Java installed on your machine then you may want to download a movie of this applet in action. sprite_roeder.avi (~24Mb)
- Agent-Based Roeder & Loeffler we have taken away probability functions (that require global information) by including chemical secretion (from stromal cells and stem cells), which can attract and repel various types of cell.
- Agent-Based Roeder & Loeffler with Small Niche this is the same agent model as above except this simulation has a smaller niche. Using this type of simulation it should be possible to explore the effects of niche morphologies on stem cell system behaviour.
- Agent-Based Roeder & Loeffler with Linear Niche this is the same agent model as above except this simulation has a linear niche, like a channel. If you don't have Java installed on your machine you may want to download a movie of this applet in action. agent_roeder_linear_niche.avi (~10Mb)
- Agent-Based Roeder & Loeffler with Foreign Cells This is the same agent model as above except that this simulation supports the introduction of foreign stem cells into the system. Using this type of simulation it should be possible to explore the possible behaviour of foreign stem cells when they are engrafted into a stem cell system.
- M. Kirkland. A phase space model of hemopoiesis and the concept of stem cell renewal. Exp. Hematol., 32:511-519, 2004.
- Kirkland another probability based model, which we have tuned after discussion with the author.
Simulations Using Our New Multi-Agent Framework
- N. D. Theise and D. Krause. Toward a new paradigm of cell plasticity. Leukemia 2002; 16:542-548.
- N. D. Theise. New principles of cell plasticity. C R Biologies 2003; 325:1039-1043.
- Simuation of Model from the CELL Project based on original work described in papers.
- Lineage Tree Viewer
Test Simulations
- Conway's Game-of-Life probably the most famous CA around
- Double Heatbugs nice and emergent!
Recommended papers
By Us
- M. dInverno and M. Luck, Understanding Agent Systems, Second Edition, 242 pp, Springer, 2004.
- M. Luck and M. dInverno. A Conceptual Framework for Agent Definition and Development, The Computer Journal, 44(1), 1-20, 2001.
- N. D. Theise. Now you See it Now you Don't, Nature, 2005.
- N. D. Theise and M. dInverno. Understanding cell lineages as complex adaptive systems. Blood, Cells, Molecules and Diseases, 32:17-20, 2003.
- J. Prophet and M. dInverno. Transdisciplinary research in CELL. In Paul Fishwick, editor, Aesthetic Computing. MIT Press, 2006.
- M. dInverno, N. D. Theise, and
J. Prophet. Mathematical modelling of stem cells: a complexity primer
for the stem cell biologist. In Christopher Potten, Jim Watson, Robert
Clarke, and Andrew Renehan, editors, Tissue Stem Cells: Biology and
Applications, To
Appear, 2006. - Mark dInverno and Jane Prophet. Biology, Computer Science and Bioinformatics: Multidisciplinary Models, Metaphors and Tools, chapter Multidisciplinary Investigation into Adult Stem Cell Behaviour. LNCS Transactions on Computational System Biology. Springer, Emanuela Merelli, Pablo Gonzalez and Andrea Omicini (editors), LNAI, To appear 2006.
- Mark dInverno and Rob Saunders,
Agent-based modelling of Stem Cell organisation in a Niche, Engineering
Self-Organising Systems: Methodologies and Applications, LNAI, Sven A.
Brueckner, Giovanna Di Marzo, Serugendo, Anthony Karageorgos and
Radhika
Nagpal (Editors), LNAI, Springer, 2005.
By Others
We work closely with Dr Ingo Roeder's group in Leipzig who have done some of the most important work on understanding mechanisinms for the dynamic and responsive self-organisation of stem cell populations. We suggest you check out their work if you are interested in our project. Visit their website..
M. Loeffler and I. Roeder. Tissue stem cells: definition, plasticity, heterogeneity, self-organization Cells Tissues Organs, 171:8-26, 2002.
S. Viswanathan and P. Zandstra. Toward predictive models of stem cell fate. Cryotechnology Review, 41(2):1-31, 2004.
The CELL Project
The background for this work is through an interdisciplinary project called "Cell" originally funded by the Wellcome Trust. The idea was simply to bring people together from different backgrounds in order to look at new experimental findings in stem cell research. The collaborators were the artist Jane Prophet, the modeller and agents systems specialist Mark d'Inverno the liver pathologist and stem cell researcher Neil Theise, the Artificial Life specialist Rob Saunders and the curator and producer Peter Ride. We hope that a web site for this project will be available soon and Ill let you know about it when its ready to go live.