| Contents |
| I will discuss methods for spatio-temporal modelling in cell biology. Three classes of models will be considered:
\begin{itemize}
\item[(i)] microscopic (molecular-based) models which are based on the simulation of trajectories of molecules
and their localized interactions (for example, reactions);
\item[(ii)] mesoscopic (lattice-based) models which divide the computational domain into a finite number of compartments
and simulate the time evolution of the numbers of molecules in each compartment; and
\item[(iii)] macroscopic (deterministic) models which are written in terms of mean-field reaction-diffusion-advection partial
differential equations (PDEs) for spatially varying concentrations.
\end{itemize}
In the first part of my talk, I will discuss connections between the modelling frameworks (i)-(iii). I will consider chemical
reactions both at a surface and in the bulk. In the second part of my talk, I will present hybrid (multiscale) algorithms
which usemodels with a different level of detail in different parts of the computational domain. The main goal of this
multiscale methodology is to use a detailed modelling approach in localized regions of particular interest (in which
accuracy and microscopic detail is important) and a less detailed model in other regions in which accuracy may be
traded for simulation efficiency. |
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