Neurosciences have a long and successful tradition of quantitative modelling, where theory and experiment have always formed a happy couple. The work of Warren Sturgis McCulloch and Walter Pitts on formal neural networks [1] gave rise to one of the best examples of cross-fertilising scientific fields, which resulted in many advances both in information technology and cognitive science. Almost as soon as digital computers became available, they were used by neuroscientists to quantitatively test their theories. One of the first numerical simulations in biology was the famous model of Alan Lloyd Hodgkin and Andrew Huxley [2], that explained the propagation of action potentials along axons – and as a by-product postulated the existence of ion channels in the membrane, before the experimental proof of their existence. Quantitatively describing a cellular behaviour emerging from the interaction between two different molecular components, a potassium and a sodium channels, the model of Hodgkin-Huxley can arguably be seen as the beginning of computational systems biology [3].
To accurately model neuronal function presents many challenges, and stretches the techniques and resources of computational biology to their limits. The molecular and cellular events mediating neuronal transmission span several spatial and temporal scales. While the signal received from a glutamatergic terminal is decoded by a 500 nanometer wide dendritic spine [4], the resulting action potential can be propagated along axons up to 1 metre long. Understanding synaptic function also means deciphering the effect of conformational transitions of ion channels, taking place on the microsecond range, onto long-term synaptic modifications lasting several weeks. Moreover, most assumptions used to simplify modelling in other fields of cell biology, such as homogenous concentrations and spatial isotropy are inappropriate. The geometry of subcellular compartments strongly affects their functions [5], as does the relative location of molecular partners and their diffusion. Finally, the morphology of neurons changes over time, and itself depends on the activity of the neurons [6,7]
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