Cellular Automaton Machines: An Overview

I recently submitted a report titled "Using a Cellular Automaton Machine to Model Chemotherapy and its Effects on Skin Cancer Tumours". The report and coded material was well-received. As it encompassed a great deal of work and contemplation on the future of technology in medical research, I have decided to share parts of the report as a way to benchmark my current understanding for future insight. The shared components will focus on how cellular automatons can be used, with reduced emphasis on skin cancer, as that aspect can be easily interchanged with any disease/treatment duo for the general principles to remain relevant.  Enjoy!

Introduction

A cellular automaton machine is a type of mathematical model that uses a universal self-replicating structure to simulate complex systems at a cell-by-cell level (Beuchat and Haenni, 2000). Automaton machines were initially formalised by John von Neumann but their application in cancer modelling was later proposed by Werner Düchting and Thomas Vogelsaenger (Düchting and Vogelsaenger, 1985). This system is established by the following characteristics:

1) All cells reside on a 1, 2 or 3-dimensional grid,

2) A cell is neighboured by other cells whose cumulative input influences the state of the environment. The extent of influence that neighbouring cells have is determined by the type of neighbourhood specified to the cellular automata. A visual representation of different types of neighbourhoods is shown in Figure 1 and Figure 2.

3) There is a finite set of predetermined states that a cell can have. The presence of these states is determined by the neighbourhood. A visual representation of this is shown in Figure 3.

Feasibility of Real-World Application 

Cellular automaton machines are an immensely useful tool through which complicated systems can be modelled. By taking known principles and using them to mathematically represent complex systems, these computer simulations present a new kind of future for skin cancer-based, chemotherapeutic drug design and development. Having said that, there are still factors that must be addressed before outright use. Firstly, automaton machines are defined by their ability to take finite states and neighbourhoods, and then model behaviour that is consistent with these defined parameters. Inherently this is not a problem as this is how cellular automatons operate, however this does complicate the extent to which they can be utilised in biological research. An example of this being a complication was demonstrated in the current model when no form of drug resistance transpired. Though drug resistance within this model can be easily implemented, this type of systems tuning demonstrates that whenever a simulation is run an overarching expectation of what is an acceptable result must be considered. This means that a general prediction of the results must be made prior to running the simulation and that adequate scientific literature must be available so that concise parameters, that accurately represent a system, are used.

Finally, cellular automaton simulations work on the basis that states and neighbourhoods that exist have always existed and will continue to exist such that subsequent behaviour can be predicated from the existing model. Like the last consideration, this is not an inherent issue, however, should be reflected upon prior to biological research use. Systems with defined parameters that have a strict set of outcomes are easily modelled in this situation, as there is no variation in the possibility of a cellular state from transpiring. An example of this is Conway’s Game of Life, a popular 2-D cellular automaton, where cells cycle through birth, survival and death (Bays, 2010). Throughout the Game of Life, though configurations may become complex, there is never a variation in what condition is required in order to change a cell’s state. A live cell will always die when surrounded by dead cells, and dead cells will always be reborn when surrounded by survival cells. In this, the relationship a cell has with being a certain state can be altered prior to running the simulation, however once running, the gathered results are only indicative of how the system operates at a particular moment in time. It may seem like the outcomes indicate a forward progression, however all that is being shown is the different configurations of cellular state change in a still universe. As any cellular automaton can be stopped, and then replayed with the exact same order of results transpiring, it is obvious that this format of simulation only provides data on how states interact in time, not across it. This is different to how real-life biological systems operate, as their ability to function is constantly changing over time. In the case of skin cancer, factors such as age and length of exposure to UV radiation can increase the propensity for a mutation to occur (Watson et al., 2016). Variables such as these alter the likelihood of a cell from switching states and presents a level of uncertainty most cellular automatons are not designed to handle. In skin cancer research, cellular automaton simulations are a great tool for understanding issues such as tumour growth and cell proliferation, however, it can be exceedingly difficult to represent principles that are defined by their constantly evolving status.


References

Bays, C. (2010). Introduction to Cellular Automata and Conway’s Game of Life. Game of Life Cellular Automata, pp.1–7

Beuchat, J.-L. and Haenni, J.O. (2000). Von Neumann’s 29-state cellular automaton: a hardware implementation. IEEE Transactions on Education, 43(3), pp.300–308

Düchting, W. and Vogelsaenger, T. (1985). Recent progress in modelling and simulation of three-dimensional tumor growth and treatment. Biosystems, 18(1), pp.79–91.

Watson, M., Holman, D.M. and Maguire-Eisen, M. (2016). Ultraviolet Radiation Exposure and Its Impact on Skin Cancer Risk. Seminars in Oncology Nursing, [online] 32(3), pp.241–254. Available at: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5036351/