Dynamical Systems in Neuroscience:

20 Introductionwith coupled neurons. There we show how the details of spike-generation mechanismof neurons affect their collective properties, such as synchronization.1.2.5 Building models (revisited)To have a good model of a neuron, it is not enough to put the right kind of currents togetherand tune the parameters so that the model can fire spikes. It is not even enoughto reproduce the right input resistance, rheobase, and firing frequencies. The modelhas to reproduce all the neuro-computational features of the neuron, starting withthe co-existence of resting and spiking states, spike latencies, subthreshold oscillations,rebound spikes, etc.A good way to start is to determine what kind of bifurcations the neuron underconsideration undergoes and how the bifurcations depend on neuromodulators andpharmacological blockers. Instead of or in addition to measuring neuronal responsesto get the kinetic parameters, we need to measure them to get the right bifurcationbehavior. Only in this case we can be sure that the behavior of the model is equivalentto that of the neuron, even if we omitted a current or guessed some of the parametersincorrectly.Implementation of this research program is still a pipe dream. The people whounderstand the mathematical aspects of neuron dynamics, those who see beyond conductancesand currents, those people do not usually have the opportunity to do experiments.Conversely, those who study neurons in vitro or in vivo on a daily basis,those who see spiking, bursting, oscillations, those who can manipulate the experimentalsetup to test practically any aspect of neuronal activity, those people do notusually see the value of studying phase portraits, bifurcations, and nonlinear dynamicsin general. One of the goals of this book is to change this state and bring these twogroups of people closer together.