Design Challenge 2

Background

For several years we have been working on an interdisciplinary project investigating stem cells. Here are a selection of the goals of this project. We wish to

1. design and build a conceptual framework (using mathematics) for modeling stem cells;

2. build simulations of these models;

3. design visualizations of the simulations and;

4. have an impact on the practice of experimental stem cell biology.

The Interdisciplinary Problem.

Many Stem Cell biologists see little value in modeling, mathematics and simulation. Typical responses include “What can it do for us? We do Biology and you do maths what possible connection can there be? What possible value is there in a simulation?”

Our work must be aware of this issue. Without interplay between conceptual models and experiment investigation, the value of doing any kind of biological modeling is almost zero!

Click here to find out more on the value of simulation for stem cells.

There are several fundamental experimental limitations associated with the investigation of stem cells. Because of this we believe there is fundamental role for using computer simulation to investigate the complex behaviour of stem cells.

Given these experimental limitations and issues there is a clear need for new conceptual models that can be simulated (run on a computer) to investigate possible mechanisms that fit with current experimental observation. Conceptual models can provide clear, precise definitions of various terms and concepts that can help catalyse a common conceptual framework amongst experimentalist, and also between experimentalists and modelers.

Simulation can investigate the wholeness of a living system. As we have stated above, experiment cannot. Moreover, lots of experiments can be run very easily where we can investigate potentiality versus actuality. It is possible to explore the relationship between the behaviour of the individual stem cells and of the system of stem cells. In fact simulation is the only way to investigate the bahaviour of our models as this system is so massively complex. Manipulation of the mathematics is simply unteneable. The key value in simulation is if it makes predictions that can be tested in the laboratory.

Visualisation is about making elements of the simulation perceivable. This is typically a visual interpretation on a computer screen. From our experiences so far, we see visualisations almost as a Trojan horse for conceptual modeling in Stem Cell Biology.

There has been work on using CA to model stem cells. The best way to think of a CA model is to imagine a fixed grid, like a chess-board. Each grid is in a “state”. At each tick of the clock the “state” is updated depending on the its own state and the state of its neighbours.

Before reading on you might want to see what the visualisation looks like here.

http://users.wmin.ac.uk/~dinverm/cell/simulations/agur/index.html

In this model white grid locations are stem cells, red cells are determined cells (which we can think of as blood cells, or liver cells), and black grid locations are empty spaces.

If you want to find out more details of the model then click here.

Problems with the CA approach suggesting a MAS approach.
 
The key value of this model is that it relates the behaviour of individual cells to the system behaviour. In all simulation runs of this model, there is always a constant production of determined cells and that there is a maintenance of the stem cell population. However, there are some fundamental problems with this approach.

1. “Empty cells” have counters

2. “Empty cells” can perceive what is next to them

3. However, “Empty cells” do not keep track of locations of stem cells over a history Therefore there is no explicit representation of the division of a stem cell. Stem cells appear “magically”

Empty cells” do some computational work (counter-intuitive) but not enough to model division (counter-intuitive).
We can address these issues in an agent approach that is much more biologically intuitive. We explicitly model the notion of a cell in a space, with internal state, perceptual abilities and the notion of cell division (A fundamental biological event!). This graphic provides a basic overview of the difference between CA and MAS. In fact, To get the exact behaviour of the CA requires 4-way division! Another reason why the CA doesn’t work for us!

However if we limit cell division to be 2-way as is more commonly believed, then we get a different system but still with the required system properties of self-maintenance and cell production.

You can see the agent 2-way division version here. Notice that it has a very different look but it does have much more biological intuition.

http://users.wmin.ac.uk/~dinverm/cell/simulations/agentagur/index.html

This model is based on original work of Marcus Loeffler and Ingo Roeder, discussions with Neil Theise, Jane Prophet, Rob Saunders and Mark d’Inverno.

The model starts from the basis that stem cells are a complex adapative system which is self-organising. This  model identifies mechanisms where individual stem cells can meet many of the properties that are often associated with them. These include self-maintenance, proliferation and the ability to home towards particular signalling environments and so on. The model defines two discrete signalling environments. All cells are either in one or the other of these environments. The affinity of a cell (which relates to a stem cell like property) is a measure  of how attracted a cell is to move to, or remain in, the first of these signalling environments. One signalling environment increases the affinity (reversibility), and the other decreases it. In this model, cells have a fixed cell cycle.

In addition, each cell has a counter, which determines the position in the cell cycle. A cell is defined by its place in the cell cycle, its current affinity and the current signaling environment. What the cell does next is partly based in the state of the cell and some stochastic process, which is modelled using a probability function. Essentially this determines whether cells switch between signaling environments.

We are also building a spatial and chemical environment in which to situate the stem cells. In this model cells secrete chemicals and are attracted or repelled by chemicals. Moreover, there is a physical niche which is represented by the blue chemicals. The details of this visuaslisation will be discussed in thy workshop.

http://users.wmin.ac.uk/~dinverm/cell/simulations/roeder_diffuse/index.html

This is as far as we have come with the work to date. Along with ther questions proposed in the summary the main challenege is this:

How do we design visualisations such as theseso that the experimentalists see any value in it?