Spatio-Temporal Dynamics of Pattern Formation in the Cerebral Cortex

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In this thesis I apply the tools of nonlinear dynamical systems theory to study pattern formation in the cerebral cortex on two different scales: the development of spatially complex visual maps on the level of cortical columns, and the onset dynamics of action potential generation on the level of single neurons.In the first part of this thesis, I develop a quantitatively controlled numerical method to study the dynamical processes resulting from competitive Hebbian learning in the development of orientation preference maps (OPMs). Kohonen"s self-organization feature mapping (SOFM) has been widely used to simulate the emergence and arrangement of different feature maps, but their attractor states have largely remained uncharacterized. I first identify different dynamical regimes in the Kohonen model and performs a comprehensive study for various system sizes, feature space dimensionalities and stimulus distributions. I find an essential 2D mapping close to the symmetry breaking threshold, whereas the additional n-2 feature dimensions are suppressed until the subsequent bifurcations. The transformation from initial pinwheel-rich patterns to either stripes or crystals are robust dynamical phenomena in mappings of feature spaces of different dimensionalities.In the second part of this thesis, I study the phase plot dynamics of action potential (AP) initiation in conductance based (CB) neuron models and its impact on population coding properties. I construct and characterize a new class of CB model including a fraction of cooperative sodium channels with variable strength of inter-channel cooperativity. For a low fraction of strongly cooperative channels this model reproduces the bi-phasic action potential dynamics frequently observed in neurons of the mammalian central nerves system. Strong sodium channel cooperativity is found to boost the encoding of fast varying inputs. To examine an alternative hypothesis that the rapid onset of somatic APs is due to lateral currents from the axon initial segment(AIS), I further characterize AP waveforms in multi-compartment neuron models. In models constrained to fit known physiological parameters, phase plots of somatic APs faithfully reveal the characteristics of the AP generator. Lateral currents are found to have little impact on the onset dynamics of somatic APs except in the models with large passive dendrites and an extremely high Na channel density at the AIS. Finally, the study shows a slightly weaker gain attenuation in the high frequency sensitivity with increasing of Na density at AIS than is observed in single compartment models.