Dynamical Systems in Neuroscience:

306 Simple Models(a)74 5 6 3210(b)C 7C 6C 5C 4C 3C 2C 1C 0(c)-60 mV10 msEPSP = 4 mV(compartment C 2 )EPSP = 1 mV(soma, C 0 )synaptic inputto compartment C 2(d) C 6 +C 7 (e) C 6 +C 6 (f) C 6 +C 6 +Iall(g) soma(h) soma+IallC 7EPSP=12 mVEPSP=12 mVC 6C 5C 4C 3C 2C 120 ms50 mVsomaC 0failure to propagateforward-propagating action potentialfailure to propagateback-propagating action potentialFigure 8.22: (a) Hand drawing and (b) a 47-compartment representation of a layer5 pyramidal neuron. (c) Injection of excitatory synaptic input into the compartment2 evokes a large excitatory postsynaptic potential (EPSP) in that compartment, butmuch smaller EPSP in the somatic compartment. (d) Synaptic inputs to compartments6 and 7 result in large EPSPs there, but no dendritic spike. (e) The same synapticinputs into compartment 6 result in dendritic spike, which fails to propagate forwardto the soma. (f) The same input combined with background excitation I all = 60 pA toall compartments results in forward propagating dendritic spikes. (g) Strong synapticinput to the soma results in a spike that fails to propagate into the dendritic tree.(h) The same input combined with injection of I all = 70 pA to all compartments (tosimulate in vivo tonic background input) promotes back-propagation of spike into thedendritic tree. Each compartment is simulated by the simple model 100 ˙v = 3(v +60)(v + 50) − u + I, ˙u = 0.01{5(v + 60) − u}. Soma: if v ≥ +50, then v ← −55,u ← u + 500. Dendrites: if v ≥ +10, then v ← −35, u ← u + 1000. The conductancebetween any two adjacent compartments is 70 nS.