Modelling calcium-dependent proteins in the spine - challenges and solutions
Melanie I. Stefan (California Institute of Technology, Biology Division), Shirley Pepke (California Institute of Technology, Biology Division), Stefan Mihalas (California Institute of Technology, Biology Division), Thomas Bartol (Salk Institute), Terrence Sejnowki (Salk Institute), Mary B. Kennedy (California Institute of Technology, Biology Division)
Three features of this signalling system pose a challenge to computational modellers: First, the absolute number of molecules in a dendritic spine is small, which makes reactions stochastic and affects competition between proteins. Second, the constrained geometry within the dendritic spine affects diffusion and creates distinct, dynamic signalling microdomains. Third, the large number of possible modifications on signalling proteins such as CaMKII increases combinatorial complexity and requires modelling strategies that can work with large numbers of possible states.
To manage all three of these challenges, we are using the spatial stochastic simulator MCell [Kerr et al. SIAM J Sci Comput, 2008]. MCell is an agent-based Monte-Carlo simulator that allows stochastic modelling in arbitrarily complex geometries. It is therefore ideally suited to model systems with small molecule numbers and spatial constraints. A realistic reconstruction of a portion of a dendrite has recently been used for modelling calcium transients within CA1 neurons using MCell [Keller et al. submitted]. We are currently combining this technology with an earlier kinetic model of calmodulin activation by calcium [Pepke et al. PLoS Comput Biol, 2010] to explore the relationship between calcium signalling, calmodulin activation and the regulation of calmodulin targets in the spine.
As an agent-based simulator, MCell allows for simulation of multistate signalling systems which are so complex as to be intractable using ODE/PDE or the Gillespie algorithm. This allows us to use MCell to construct a detailed model of CaMKII activation that includes all the complexities of calmodulin binding [Stefan et al. PLoS ONE, 2012], phosphorylation [Miller and Kennedy. Cell, 1986], conformational change and intramolecular regulation [Chao et al. Nat Struct Mol Biol, 2010].