Modelling calcium-dependent proteins in the spine - challenges and solutions

Synaptic plasticity is mediated by calcium signalling in the postsynaptic spine. One hypothesis suggests that the direction of plasticity is determined by the relative activation of two Ca2+-/calmodulin dependent proteins, CaMKII and calcineurin [Lisman. PNAS, 1989], and the subsequent activation of tightly regulated signalling pathways in the spine. Computational modelling allows us to gain an insight into how proteins within this complex signalling pathway may be regulated and in turn regulate each other. It can also improve understanding of its complex and often non-intuitive behaviour under varying conditions.

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].