Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

Using Simulation and Statistical Techniques toExplore Lymphoid Tissue Organogenesis

University of Birmingham, 7th March 2013

Dr Kieran Alden1

1. School of Biosciences, University of Birmingham

k.j.alden@bham.ac.uk

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

Lecture Objectives

In this lecture, we will:

Look at a case study of simulation being used to further ourunderstanding of a biological system

Examine statistical techniques that can be used to analysesimulation results

See how these techniques can provide some insight into thesystem being modelled

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

Setting the Context: A Quick Recap

Complex Systems Modelling: What’s the point?

What techniques have been used?

Any examples of their use?

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

Advancing Biological Understanding Through Modelling

Use of models in advancing biological understanding commonplace for generations

Computational modelling is a continuation of the approach

Current understanding of a biological system is captured as amodel, that may then be instantiated as a simulation

The goal is to move the field from a reductionist, descriptivestate to one that is predictive - away from a focus oncomponents to the higher order behaviour that emerges fromcomponents that lack the capability to do this alone

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

Advancing Biological Understanding Through Modelling

Use of models in advancing biological understanding commonplace for generations

Computational modelling is a continuation of the approach

Current understanding of a biological system is captured as amodel, that may then be instantiated as a simulation

The goal is to move the field from a reductionist, descriptivestate to one that is predictive - away from a focus oncomponents to the higher order behaviour that emerges fromcomponents that lack the capability to do this alone

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

A Case Study: Secondary Lymphoid Tissue

Specialised tissues of the immune system; include lymphnodes, tonsils, spleen, and Peyer’s Patches

Initiate adaptive immune responses to infection

Though lab experimentation has generated a basic model oftissue formation, it has not yet been possible to fullyunderstand the process of tissue development

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

Peyer’s Patches: Overview

Lymphoid tissue in the intestine which has a key role ininduction of antibody responses

Forms during embryonic development or chronic infection

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

Peyer’s Patches: Overview

Adapted from van de Pavert & Mebius, 2010

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

Laboratory Work

Adapted from Patel et al, Science Signalling, 2012

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

Agent-Based Modelling

Each biological entity (i.e. a cell) is represented explicitly

Agent behaviour determined by a set of rules that determinethe state a cell may exist in and the event that must occur forstate to change

Time and space can be explicitly represented

Shown in some applications (such as HIV) to produce a moreaccurate result than ODE counterparts

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

Our Model in a Nutshell

Three cell types represented as agents, each having its ownindividual state and characteristics

Chemoattractant expression modelled using an inversesigmoidal curve

Linear function to capture espression of surface adhesionmarker

Incorporates measures that we’ve taken from the lab andliterature

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

Time and Space: Environmental Modelling

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

Simulator

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

Results: Cell Behaviour

We have found there to be no statistical difference betweencell behaviour observed ex vivo and that observed in silico

Patel et al, Science Signalling, 2012

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

Controls

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

So what can we do with our model?

Can we work out the influence of each biological factor?

Can we determine when a factor becomes influential?

Can we determine how robust the simulation is to a change inparameter values

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

SPARTAN

No comprehensive toolkit exists to analyse simulation results

Thus, we have compiled a number of statistical techniquesand released this as the SPARTAN toolkit (SimulationParameter Analysis R Toolkit ApplicatioN)

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

SPARTAN

No comprehensive toolkit exists to analyse simulation results

Thus, we have compiled a number of statistical techniquesand released this as the SPARTAN toolkit (SimulationParameter Analysis R Toolkit ApplicatioN)

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

Simulation Parameter Analysis R Toolkit Application

Package of statistical techniques designed to understand therelationship between a simulation and the real world system

Helps identify which results can be attributed to the dynamicsof the modelled system, rather than simulation stochasticity.

Can help reveal the influence that pathways and componentshave on simulation behaviour

Spartan is open source, implemented within the R statisticalenvironment, and freely available

Manuals, comprehensive tutorials, and example simulationdata are also available.

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

Simulation Parameter Analysis R Toolkit Application

Package of statistical techniques designed to understand therelationship between a simulation and the real world system

Helps identify which results can be attributed to the dynamicsof the modelled system, rather than simulation stochasticity.

Can help reveal the influence that pathways and componentshave on simulation behaviour

Spartan is open source, implemented within the R statisticalenvironment, and freely available

Manuals, comprehensive tutorials, and example simulationdata are also available.

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

Obtaining a Robust, Representative Result

Determine the effect of simulation stochasticity on simulationresult

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A−Test Scores for 20 Dummy Parameters where Sample Size = 1

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MEASURES

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Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

Obtaining a Robust, Representative Result

Determine the effect of simulation stochasticity on simulationresult

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A−Test Scores for 20 Dummy Parameters where Sample Size = 1

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VelocityDisplacement

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large difference

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Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

Obtaining a Robust, Representative Result

Determine the effect of simulation stochasticity on simulationresult

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A−Test Scores for 20 Dummy Parameters where Sample Size = 5

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MEASURES

VelocityDisplacement

no difference

large difference

large difference

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

Obtaining a Robust, Representative Result

Determine the effect of simulation stochasticity on simulationresult

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A−Test Scores for 20 Dummy Parameters where Sample Size = 50

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MEASURES

VelocityDisplacement

no difference

large difference

large difference

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

Obtaining a Robust, Representative Result

Determine the effect of simulation stochasticity on simulationresult

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A−Test Scores for 20 Dummy Parameters where Sample Size = 100

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MEASURES

VelocityDisplacement

no difference

large difference

large difference

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

Obtaining a Robust, Representative Result

Determine the effect of simulation stochasticity on simulationresult

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A−Test Scores for 20 Dummy Parameters where Sample Size = 300

2 4 6 8 10 12 14 16 18 20

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MEASURES

VelocityDisplacement

no difference

large difference

large difference

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

Examining the Effect of Each Parameter

Value of each factor can be varied independently to determinethe effect on the cell behaviour

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

Correlations Between Factors

Varying the values of all parameters concurrently can revealany correlations between factors, while highlighting those ofstrongest influence

Parameter value selection performed using a Latin-HypercubeApproach

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

Correlations Between Factors

Run simulations for each parameter set, then for eachparameter, sort the results by parameter value

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

Determining the Quantitative Effect of Each Factor

But this doesn’t give a statistical value for that parameter,and can be affected by sampling

Another mathematical technique uses Fourier FrequencyAnalysis to choose parameter values

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

Determining the Quantitative Effect of Each Factor

Can now determine the proportion of variance accounted forby each parameter

Yet this can be computationally very expensive

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

What has our analysis told us?

At an early time-point, the simulation suggests chemokinesare not influencial

Adhesion factor expression is the major influence on cellbehaviour

What if we do the same analysis at 72 hours?

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

What has our analysis told us?

At an early time-point, the simulation suggests chemokinesare not influencial

Adhesion factor expression is the major influence on cellbehaviour

What if we do the same analysis at 72 hours?

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

A Time-Lapse Analysis

Chemokines have been shown to have an essential role in vivo

However results at 12 hours show a change in parameter valuehas no significant influence in simulation outcome

Yet changing chemokine level does have a significant effect at72 Hours

So when does this factor become influential?

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

A Time-Lapse Analysis

Chemokines have been shown to have an essential role in vivo

However results at 12 hours show a change in parameter valuehas no significant influence in simulation outcome

Yet changing chemokine level does have a significant effect at72 Hours

So when does this factor become influential?

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

When Does a Factor Become important?

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

Conclusions & Thoughts

Through use of principled approaches, we have designed arobust simulator, and results statistically similar to that seenex vivo

We have developed a set of statistical tools for the analysis ofany simulation of this kind. In this case, this suggests:

The influence adhesion factors have on behaviour of cells neara patch early in the processNo apparent role for chemokines at an early stage ofdevelopmentThe timepoint at which chemokines do begin to influence cellbehaviour

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

Conclusions & Thoughts

Through use of principled approaches, we have designed arobust simulator, and results statistically similar to that seenex vivo

We have developed a set of statistical tools for the analysis ofany simulation of this kind. In this case, this suggests:

The influence adhesion factors have on behaviour of cells neara patch early in the processNo apparent role for chemokines at an early stage ofdevelopmentThe timepoint at which chemokines do begin to influence cellbehaviour

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

Conclusions & Thoughts

We have seen that it is important to consider stochasticityinherent in a simulation

With this established, we have seen three statisticaltechniques that can be used to provide insight into the role ofeach parameter / biological factor

We have seen how results of these analyses can informbiologists, who can then test this in the lab

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

Want to Know More?

Papers on our simulation in Science Signalling & Frontiers inImmunology

Paper on Spartan in PLoS Computational Biology

Google York Computational Immunology Lab for the links andspartan tool

Spartan comes with comprehensive tutorials and examples -download them from the website and give them a go

Happy to talk about this further (k.j.alden@bham.ac.uk)

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

Want to Know More?

Papers on our simulation in Science Signalling & Frontiers inImmunology

Paper on Spartan in PLoS Computational Biology

Google York Computational Immunology Lab for the links andspartan tool

Spartan comes with comprehensive tutorials and examples -download them from the website and give them a go

Happy to talk about this further (k.j.alden@bham.ac.uk)

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

Want to Know More?

Papers on our simulation in Science Signalling & Frontiers inImmunology

Paper on Spartan in PLoS Computational Biology

Google York Computational Immunology Lab for the links andspartan tool

Spartan comes with comprehensive tutorials and examples -download them from the website and give them a go

Happy to talk about this further (k.j.alden@bham.ac.uk)

Setting the Scene Our Model Analysis Generating Hypotheses Conclusion

Acknowledgements

Centre for Immunology &Infection, University of York

Mark Coles, Patty Sachamitr,Roger Leigh, Dhananjay Desai

Institute of Molecular Medicine,University of Lisbon

Henrique Veiga-Fernandes,Amisha Patel, Manuella Ferrara

YCCSA, University of York

Jon Timmis, Paul Andrews,Mark Read