Phenomenological modeling of diverse and heterogeneous synaptic dynamics at natural density

TL;DR

This chapter sheds light on the synaptic organization of the brain from the perspective of computational neuroscience by providing an introductory overview on how to account for empirical data in mathematical models, implement such models in software, and perform simulations reflecting experiments.

Abstract

This chapter sheds light on the synaptic organization of the brain from the perspective of computational neuroscience. It provides an introductory overview on how to account for empirical data in mathematical models, implement such models in software, and perform simulations reflecting experiments. This path is demonstrated with respect to four key aspects of synaptic signaling: the connectivity of brain networks, synaptic transmission, synaptic plasticity, and the heterogeneity across synapses. Each step and aspect of the modeling and simulation workflow comes with its own challenges and pitfalls, which are highlighted and addressed.

Figures (5)

• Figure 1: Cycle of modeling and simulation. The empirical data from the brain structure under study (the "system of interest") is first mathematically modeled and then implemented in software. Closing the loop, simulation results can be compared to experimental recordings. Reproduced with permission from Fig. 1 in 10.3389/fninf.2018.00081.
• Figure 2: Substructures of the cortex on different scales. The neurons in the cortex are organized into areas on the macroscale (middle). In each area, neurons are organized into layers with distinct connectivity (here, shown as a microcircuit under $1~\textrm{mm}^{2}$ of cortical surface) and into populations of neurons with similar properties within each layer (upper left). Blue triangles and red circles represent excitatory and inhibitory neurons, respectively. Long-range projections connect the areas (lower left). Moreover, on an intermediate scale of millimeters, both intra-area and inter-area excitatory connections cluster into "patches" (right, only outgoing connections for one neuron shown). Adapted with permission from Fig. 1 in schmidt2018multi under license https://creativecommons.org/licenses/by/4.0/ originally from Fig. 1 in potjans2014cell and Fig. 1 in kunkel2009simulating.
• Figure 3: Fitting a model of connectivity to observed data.A--F Layer-resolved axonal tracing data from V1 of New World monkeys Sincich4416. Images show staining of cortical layers after an injection of biocytin into layer 3, anterogradely staining axons. G Fit of a 2D symmetric exponential function $f(r)=a e^{-\lambda/r}+b$ (red) to the axonal density distribution (blue) of layer 5. The model does not fully capture the connectivity profile for layers 2, 3, and 4B (A, B, C), which display patchy connectivity.
• Figure 4: Spike-timing-dependent plasticity (STDP).A Weight change expressed as a function of relative pre- and postsynaptic spike timing for an example of STDP with an anti-symmetric (and slightly asymmetric), Hebbian learning window. Markers correspond to empirical data from bi1998synaptic. Solid lines show exponential approximations used in the model (red indicates depression and blue indicates potentiation in all panels). An anti-Hebbian window would look similar but mirrored about the vertical axis. B-D Three nearest-neighbor spike pairing rule variants for STDP. BSymmetric: each presynaptic spike is paired with the last postsynaptic spike, and each postsynaptic spike is paired with the last presynaptic spike. CPresynaptic centered: each presynaptic spike is paired with the last postsynaptic spike and the next postsynaptic spike. DReduced symmetric: as in panel C, but only for closest pairs. Adapted from Fig. 7 in morrison2008phenomenological.
• Figure 5: Specific and unspecific heterogeneity in synaptic connectivity.A Sketch of a neuronal network comprising three populations of neurons of type $X$, $Y$, and $Z$ (boxes). The properties of the different projections (arrows), such as the number of synapses, the synaptic weights, synaptic time constants, or synaptic delays, depend on the types of pre- and postsynaptic neurons. We refer to the resulting synapse-type specific diversity as specific heterogeneity. B For each type of projection $\{PQ\}$ from population $Q$ to population $P$ ($P,Q\in\{X,Y,Z\}$), the synaptic parameters are distributed (illustrated here with bell-shaped curves). We refer to this form of variability as unspecific heterogeneity. The parameters characterizing each distribution, such as the mean (horizontal position of each curve) or the variance, are usually synapse-type specific.