A Beginner’S Guide To Simulation In Immunology
- 1. A Beginner‟s Guide to Simulation in Immunology Grazziela Figueredo (gzf@cs.nott.ac.uk) Uwe Aickelin (uxa@cs.nott.ac.uk) Peer-Olaf Siebers (pos@cs.nott.ac.uk) IMA Research Group – University of Nottingham
- 2. Outline Introduction Motivation What is Simulation? Simulation approaches The need of simulation for immunology A framework for the development of simulation for the immune system Challenges and pitfalls The potential contribution of system dynamics Conclusions and future work 2
- 3. Introduction Immune system is a set of biological structures and processes within an organism that protects it against disease by identifying and killing pathogens and eliminating danger. Immunology can benefit of simulation because: Compared with real-world experimentation, simulation is time and cost-effective. Laboratory experiments are expensive and have to be in agreement with ethical specifications. The accuracy of the results of in vitro testing relies on environmental conditions, the quality of the material collected and the appropriate procedure to 3 conduct experiments.
- 4. What is Simulation? “imitation (on a computer) of a system as it progresses through time” Purpose: understand, change, manage and control reality Better understanding of the system and/or to identify improvements to a system Focus on the main aspects of the real system Models exclude unnecessary details of the original system Predicts the performance of a system given a specific set of inputs. Experimental approach to modelling a “what-if” analysis tool 4 User determines scenarios and simulation predicts outcomes
- 5. What can I Simulate? Natural systems: systems whose origins lie in the origins of the universe atoms, molecules and galactic systems Physical systems designed by humans cars, mobile phone networks and computers Abstract systems designed by humans mathematical models Human activity systems family, schools, cities and criminal justice systems 5
- 6. Characteristics of the Simulation Approaches Static or dynamic (time representation) Stochastic or deterministic (probability) Continuous or discrete (how variables change) Top-down or bottom-up 6
- 7. Simulation Approaches …That one is easy: Mathematical (numerical) simulation • Suitable for system simulation • No need (characteristics??) for indepth understanding of mathematics Monte Carlo simulations • Some approaches allow individual System memory, spatialsimulation These are the behaviour, Dynamics approaches of our localization Discrete-event simulation • I can see what is going on over interest Agent-based simulation time 7
- 8. System Dynamics Continuous top-down approach uses stocks , flows and feedback loops as concepts to model the behaviour of complex systems Based on systems theory Initially: understand complex aggregate behaviours in industry Currently: any complex system with interdependency, mutual interaction, information feedback and circular causality Implementation: differential equations solved for a time interval Few studies apply it to immune problems 8
- 9. System Dynamics vs ODEs Ordinary differential equation models are more commonly used System Dynamics encompasses mathematical formulations and of keep info of how the elements change over time No need for an indepth understanding of mathematics to formulate a model (for many cases) The differential equations are implicit in the system‟s structure Relationships between the elements modelled can be established with experimental data 9
- 10. System Dynamics – An Example 10
- 11. Discrete-event Simulation Top-down approach Set of entities being processed and evolving over time according to the availability of resources and the triggering of events The simulator maintains an ordered queue of events Each event occurs at an instant in time and marks a change of state in the system. Process-oriented Passive entities (no proactivity) Entities individually represented and tracked over time Stochastic 11
- 12. Discrete-event Simulation – Main Loop // Initialization phase EndingCondition = FALSE; Initialize system state variables; Initialize Clock (usually starts at simulation time zero); Schedule an initial event (i.e., put some initial event into the Events List); // Main Loop while EndingCondition == FALSE do Set clock to next event time; Do next event and remove from the Events List; Update statistics; end // Output phase 12 Generate statistical report;
- 13. Discrete-event Simulation – Example 13
- 14. Agent-based Simulation: Cellular Automata Regular grid of cells cell: finite states and dimensions For each cell, a neighbourhood of other cells is defined Any automata: initial state and the subsequent states will defined by some fixed rule 14
- 15. Cellular Automata - Example Conway‟s Game of Life: No players evolution determined initial state, defined by the user. The universe: infinite 2D orthogonal grid of square cell Cell is either in the state live or dead and has eight neighbours: cells that are horizontally, vertically, or diagonally adjacent. At each step: cell with fewer than two live neighbours dies cell with two or three live neighbours lives on to the next generation cell with more than three live neighbours dies. 15 dead cell with exactly three live neighbours becomes a live
- 16. Agent-based Simulation Autonomous agents that interact with each other. The agents‟ behaviour: rules determine how they I am autonomous, self- learn, interact with each other contained, modular, and and adapt. unique Overall system behaviour arises from environment I live in an the agents‟ individual dynamics and their interactions others where I interact with I learn and adapt (EMERGENCE) I have objectives CAN I BE AN AGENT NOW??? 16
- 17. Agent-based Simulation – An example Dendritic cells (DCs) are immune cells that search for signs of danger (possible antigen) in the organism. Initially: immature state until contact with a possible antigen, where they become activated. Then DC investigates if it is a real danger or not. If yes, the dendritic cell becomes mature; otherwise, semi-mature Mature: immune response should be triggered and information about the antigen should be kept as history. Semi-mature: the foreign material should be tolerated DCs in an active state have a lifespan of days, while immature cells exist for longer For our example, we consider ten days for active cells and thirty days for immature cells 17
- 18. Agent-based Simulation – DC State Chart 18
- 19. And what now? Which one should I pick? The choice of a modelling technique for a problem is driven by the resources available such as experimental data, understanding of the mechanisms involved, the hypothesis to be tested and the level of abstraction needed to test the hypothesis 19
- 20. 20
- 21. Time for a break 21
- 22. The Need for Simulation of the Immune System 22
- 23. Is Mathematics Enough? Most work is based on math equations Mathematical models have enabled biologists and immunologists to improve their comprehension of models and methods Over 200 models developed Mostly ODEs However: limits the modelling effort to simple dynamics involving few immune elements such as cells or molecules Only allows analysis at an aggregate level Determine outputs given inputs (I cant see what is going on) Not trivial to model problems involving individual localisation, memory and emerging properties Simulation overcomes these limitations! 23
- 24. What about Reductionism? in reductionism “the dynamics of a system is understood from studying the properties of its parts. Once one knows the parts, the dynamics of the whole can be derived” The problem is: in immunology its not always possible to know the parts … and reductionism does not represent 24 emergence
- 25. OK, Simulation! But how do I start? 1. Define the Objectives: validate a theory (based on experimental data or an intuition of what might happen in reality) current models do not match realworld experimentation further investigation New hypothesis and research questions defined with immunologists as simulation goals. The objectives come from real-world observation (previously performed by immunologists) 25
- 26. OK, Simulation! But how do I start? 2. Describe the system: Documents (immunology books, articles, interview with experts, etc.) on how immune elements work and interact The description is generally based on knowledge acquired by theoretical work, real-world observation and laboratory experimentation Due to the complexity of the elements knowledge is mostly scarce. The immune system is far from being fully knowable, and the descriptions found in literature are only partial representations and assumptions of what occurs in reality …and that’s when the problems for computer scientists 26 begin
- 27. And? 3. Investigate existing theories and established models Mostly mathematical models describing the phenomenon Verified using experimental data Existing models their hypothesis, objectives, validation process and limitations. new model: improvement of what has already been done 4. Use experimental data Most simulation models are built based on real-world experimentation Cases where no data is available: based on theoretical assumptions to provide more insights about the real world No data: lack of understanding of a process, difficulty/impossibility to collect information with current technology. A hypothesis is first formulated and it needs experimental 27 data to confirm it.
- 28. Next step... 5. Build conceptual model abstraction intended to contain the principal aspects observed in the real world, considering the necessary level of details Challenges: Keep it simple Work with information available Hierarchical charadteristics of the Immune System Field constantly gathering information needs frequent 28 updates
- 29. Now the Simulation 6. Identify elements, parameters, aggregates, etc. already established in theory and real-world data 7. Decide the appropriate simulation approach 8. Represent elements, parameters, etc. using the appropriate simulation approach 9. Build the simulation model 10. Verify the model (Do I model the thing right?) 11. Validate the model with existing theories and, if available, real-world data. (Do I model do the right thing?) Bear in mind that: For immunology models are not 100% accurate for a number of reasons: (1) there is no real world data to compare against, (2) there is little data, (3) real-world data is inaccurate, (4) even if the data is accurate, the real world data is only a 29 sample, which in itself creates inaccuracy.
- 30. 30
- 31. Building a Simulation Let us build a simulation from scratch and see What do we have to do to define simulation a problem? 31
- 32. Building a Model from Scratch Objective: understand peripheral naive T cell repertoire dynamics over time. 32
- 33. Building a Model from Scratch Describe the System: There is a type of white blood cell, naive T cell, which plays an important role in the immune system by responding to new infections. Before the age of 20, the set of naive T cells is sustained primarily from thymic output. In middle age there is a change in the source of naive T cells: as the thymus involutes, there is a considerable shrinkage in its T cell output, which means that new T cells are mostly produced by peripheral expansion. There is also a belief that some memory T cells have their phenotype reverted back to the naive proliferation cells type Furthermore, memory cells are originated from active 33 T cells.
- 34. Building a Model from Scratch Investigate existing theories and models: Immunologists found out that thymic contribution in an individual are quantified by the level of a biological marker called „T cell receptors excision circle‟ (TREC). TREC is circular DNA originated during the formation of the T-cell receptor. The percentage of T cells possessing TRECs decays with shrinkage of thymic output, activation and reproduction of naive T cells This means that naive T cells originating from the thymus have a greater percentage of TREC than those originating through other proliferation. 34
- 35. Building a Model from Scratch Experimental data: There is TREC data collected by immunologists (Murray et al., 2003), which also develops a mathematical model for the dynamics of peripheral naive Tcells. Furthermore, the authors provided us with data on active cells and total naive T cells in individuals with age ranging from 1 to 55 years. Assuming that this data has been validated, we can use it to continue our simulation 35
- 36. Building a Model from Scratch Conceptual model: can you help me with this one? 36
- 37. Building a Model from Scratch Best simulation approach and parameters? 37
- 39. System Dynamics - Results 39
- 40. Conclusions Summary of simulation and its main approaches The importance of simulation for immunology Framework to help with the development of simulations for immunology We demonstrated the importance of SD in immunological research Working now on the conversion between approaches (Future talk) 40
- 41. Questions? 41