A fundamental concern in biology is the origins of, and the mechanisms responsible for the structures
and patterns observed within, organisms [1]. Turing patterns and the Turing mechanism may explain the
processes behind biological pattern formation. Theoretical studies of the Turing mechanism show that it
is highly sensitive to fluctuations and variations in kinetic parameters. Various experiments have shown
that biochemical processes in living cells are inherently noisy systems, they are subjected to a diverse
range of fluctuations. This ‘robustness problem’ raises the question of how such a seemingly sensitive
mechanism could produce robust patterns amidst noise [2]. Recent computational advances allow for
large-scale explorations of the design space of regulatory networks underpinning pattern production. Such
explorations generate insights into the Turing mechanism’s robustness and sensitivity. Part 1 of the thesis
performs a large-scale exploration within a discrete modelling framework, identifying the same pattern
producing network types identified within previous studies. The equivalence we find across modelling
frameworks suggests that a deeper underlying principle of these Turing mechanisms exist. In contrast
to the continuous case , networks appear to be more robust in the discrete framework we explore here,
suggesting that these networks might be more robust than previously thought. Part 2 of the thesis focuses
on Turing patterns as a inverse problem: is it possible to infer the parameters that most likely produced
a given pattern? Here, we distill the information of a pattern into a one-dimensional representation based
on resistance distances, a concept from electrical networks [3]. We shown this representation to be robust
against fluctuations in the pattern stemming from random initial conditions, or stochasticity of the model,
and therefore permits the application of machine learning methods such as neural networks and support
vector regression for parameter inference. We apply this method to infer one and three parameters for
both deterministic and stochastic models of the Gierer-Meinhardt system. We show that the ’resistance
distance histogram’ method is more robust to noise, and performs better for limited number of data
samples than a vanilla convolutional neural network approach. Robustness of parameter inference with
respect to noise and limited data samples is of particular importance when considering real experimental
data. Overall, this thesis advances our understanding on the design principles of pattern formation, and
provides insight into possible methods for inferring details of regulatory networks behind experimental
evidence of Turing patterns.Open Acces
