A minimal mechanistic model for temporal signal processing in the lateral geniculate nucleus.

The receptive fields of cells in the lateral geniculate nucleus (LGN) are shaped by their diverse set of impinging inputs: feedforward synaptic inputs stemming from retina, and feedback inputs stemming from the visual cortex and the thalamic reticular nucleus. To probe the possible roles of these feedforward and feedback inputs in shaping the temporal receptive-field structure of LGN relay cells, we here present and investigate a minimal mechanistic firing-rate model tailored to elucidate their disparate features. The model for LGN relay ON cells includes feedforward excitation and inhibition (via interneurons) from retinal ON cells and excitatory and inhibitory (via thalamic reticular nucleus cells and interneurons) feedback from cortical ON and OFF cells. From a general firing-rate model formulated in terms of Volterra integral equations, we derive a single delay differential equation with absolute delay governing the dynamics of the system. A freely available and easy-to-use GUI-based MATLAB version of this minimal mechanistic LGN circuit model is provided. We particularly investigate the LGN relay-cell impulse response and find through thorough explorations of the model's parameter space that both purely feedforward models and feedback models with feedforward excitation only, can account quantitatively for previously reported experimental results. We find, however, that the purely feedforward model predicts two impulse response measures, the time to first peak and the biphasic index (measuring the relative weight of the rebound phase) to be anticorrelated. In contrast, the models with feedback predict different correlations between these two measures. This suggests an experimental test assessing the relative importance of feedforward and feedback connections in shaping the impulse response of LGN relay cells.

Visualizing neuronal network connectivity with connectivity pattern tables.

Complex ideas are best conveyed through well-designed illustrations. Up to now, computational neuroscientists have mostly relied on box-and-arrow diagrams of even complex neuronal networks, often using ad hoc notations with conflicting use of symbols from paper to paper. This significantly impedes the communication of ideas in neuronal network modeling. We present here Connectivity Pattern Tables (CPTs) as a clutter-free visualization of connectivity in large neuronal networks containing two-dimensional populations of neurons. CPTs can be generated automatically from the same script code used to create the actual network in the NEST simulator. Through aggregation, CPTs can be viewed at different levels, providing either full detail or summary information. We also provide the open source ConnPlotter tool as a means to create connectivity pattern tables.

Rate Dynamics of Leaky Integrate-and-Fire Neurons with Strong Synapses.

Firing-rate models provide a practical tool for studying the dynamics of trial- or population-averaged neuronal signals. A wealth of theoretical and experimental studies has been dedicated to the derivation or extraction of such models by investigating the firing-rate response characteristics of ensembles of neurons. The majority of these studies assumes that neurons receive input spikes at a high rate through weak synapses (diffusion approximation). For many biological neural systems, however, this assumption cannot be justified. So far, it is unclear how time-varying presynaptic firing rates are transmitted by a population of neurons if the diffusion assumption is dropped. Here, we numerically investigate the stationary and non-stationary firing-rate response properties of leaky integrate-and-fire neurons receiving input spikes through excitatory synapses with alpha-function shaped postsynaptic currents for strong synaptic weights. Input spike trains are modeled by inhomogeneous Poisson point processes with sinusoidal rate. Average rates, modulation amplitudes, and phases of the period-averaged spike responses are measured for a broad range of stimulus, synapse, and neuron parameters. Across wide parameter regions, the resulting transfer functions can be approximated by a linear first-order low-pass filter. Below a critical synaptic weight, the cutoff frequencies are approximately constant and determined by the synaptic time constants. Only for synapses with unrealistically strong weights are the cutoff frequencies significantly increased. To account for stimuli with larger modulation depths, we combine the measured linear transfer function with the nonlinear response characteristics obtained for stationary inputs. The resulting linear-nonlinear model accurately predicts the population response for a variety of non-sinusoidal stimuli.

Towards reproducible descriptions of neuronal network models.

Progress in science depends on the effective exchange of ideas among scientists. New ideas can be assessed and criticized in a meaningful manner only if they are formulated precisely. This applies to simulation studies as well as to experiments and theories. But after more than 50 years of neuronal network simulations, we still lack a clear and common understanding of the role of computational models in neuroscience as well as established practices for describing network models in publications. This hinders the critical evaluation of network models as well as their re-use. We analyze here 14 research papers proposing neuronal network models of different complexity and find widely varying approaches to model descriptions, with regard to both the means of description and the ordering and placement of material. We further observe great variation in the graphical representation of networks and the notation used in equations. Based on our observations, we propose a good model description practice, composed of guidelines for the organization of publications, a checklist for model descriptions, templates for tables presenting model structure, and guidelines for diagrams of networks. The main purpose of this good practice is to trigger a debate about the communication of neuronal network models in a manner comprehensible to humans, as opposed to machine-readable model description languages. We believe that the good model description practice proposed here, together with a number of other recent initiatives on data-, model-, and software-sharing, may lead to a deeper and more fruitful exchange of ideas among computational neuroscientists in years to come. We further hope that work on standardized ways of describing--and thinking about--complex neuronal networks will lead the scientific community to a clearer understanding of high-level concepts in network dynamics, and will thus lead to deeper insights into the function of the brain.