| Abstract: |
| Keratins are a family of proteins involved in several cellular processes. They are a crucial element of the cytoskeleton, and they contribute to many of the mechanical properties of the cell. In the experiments, we cannot observe all the aspects of the keratin dynamics. In turn, we use a mathematical model, adjusted using experimental data, to study the mechanisms underlying the keratin structure.
We present a one-dimensional reaction-diffusion model for the dynamics of keratin. We derive the model from first principles and from assumptions based on the current knowledge in biology.
We use a Bayesian approach to perform the parameter identification. In order to prescribe sensible priors, we incorporate the assumptions provided by biologists. Several parameters depend on the spatial position within the cell, and therefore we define the priors on functional spaces. We use a parallel Metropolis-Hastings sampler to obtain numerical approximations of the posterior distributions.
The posterior distribution for the parameters reveals the underlying mechanisms of the keratin dynamics. The location of the keratin assembly and disassembly regions in the cell matches results obtained independently using image processing techniques. The results also show the existence of a limiting assembly and disassembly reaction rate. |
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