Rodney J. Douglas

Do neurons have a voltage or a current threshold for action potential initiation

The majority of neural network models consider the output of single neurons to be a continuous, positive, and saturating firing ratef(t), while a minority treat neuronal output as a series of delta pulses ∑δ (t — ti). We here argue that the issue of the proper output representation relates to the biophysics of the cells in question and, in particular, to whether initiation of somatic action potentials occurs when a certain thresholdvoltage or a thresholdcurrent is exceeded. We approach this issue using numerical simulations of the electrical behavior of a layer 5 pyramidal cell from cat visual cortex. The dendritic tree is passive while the cell body includes eight voltage- and calcium-dependent membrane conductances.We compute both the steady-state (I∞static(Vm)) and the instantaneous (Io(Vm)) I–V relationships and argue that the amplitude of the local maximum inI∞static(Vm) corresponds to the current thresholdIth for sustained inputs, while the location of the middle zero-crossing ofIo corresponds to a fixed voltage thresholdVth for rapid inputs. We confirm this using numerical simulations: for “rapid” synaptic inputs, spikes are initiated if the somatic potential exceedsVth, while for slowly varying inputIth must be exceeded. Due to the presence of the large dendritic tree, no charge thresholdQth exists for physiological input.Introducing the temporal average of the somatic membrane potential 〈(Vm)〉 while the cell is spiking repetitively, allows us to define a dynamic I-V relationship∞dynamic(〈(Vm)〉). We find an exponential relationship between 〈(Vm)〉 and the net current sunk by the somatic membrane during spiking (diode-like behavior). The slope ofI∞/dynamic(〈(Vm))〉 allows us to define a dynamic input conductance and a time constant that characterizes how rapidly the cell changes its output firing frequency in response to a change in its input.

Exploring cortical microcircuits: a combined anatomical, physiological, and computational approach

Publisher Summary This chapter discusses a simple model of neurons that can abstract the most important anatomical and physiological properties required for exploring cortical circuits. The diversity of neuron types in the visual cortex to three essential types: layer 3 small pyramidal neurons, layer 5 large pyramidal neurons, and nonspiny inhibitory neurons. These neurons are combined in a canonical microcircuit. Microcircuit modeling is a fine form of explanation and prediction. The chapter also presents the evidence derived from experimental data and computer simulations showing that the predominant communication within the cortex is among the excitatory pyramidal neurons, which form a recurrent cortical amplifier. Simulations with abstract neurons were used to examine the possibility that inhibition of the axon initial segment might provide an alternative source of strong inhibition. Inhibition functions both to control access to this amplifier and control the gain of the neurons to suprathreshold excitatory inputs. The chapter also explains the way feature selectivity operates in such a system and contrasts it with the Barlow–Levick model of directional selectivity.

The Role of Recurrent Excitation in Neocortical Circuits

John von Neumann was a pioneer of modern electronic computing. He was involved in the design and construction of the early electronic computing machines and, as part of this process, he was led to explore the analogies between automata and the brain. Consequently, he understood very clearly some essential differences in the physical mode of design and operation of the brain and digital automata.

In Search of the Canonical Microcircuits of Neocortex

“The machinery may be roughly uniform over the whole striate cortex, the difference being in the inputs. A given region of the cortex simply digests what is brought to it, and the process is the same everywhere. It may be that there is a great developmental advantage in designing such a machinery once only, and repeating it over and over monotonously, like a crystal”—Hubel and Wiesel, 1974