Calcium ( ) waves provide a complement to neuronal electrical signaling, forming a key part of a neuron’s second messenger system. We developed a reaction-diffusion model of an apical dendrite with diffusible inositol triphosphate ( ), diffusible , receptors ( s), endoplasmic reticulum (ER) leak, and ER pump (SERCA) on ER. is released from ER stores via s upon binding of and . This results in -induced- -release (CICR) and increases spread. At least two modes of wave spread have been suggested: a continuous mode based on presumed relative homogeneity of ER within the cell and a pseudo-saltatory model where regeneration occurs at discrete points with diffusion between them. We compared the effects of three patterns of hypothesized distribution: (1) continuous homogeneous ER, (2) hotspots with increased density ( hotspots), and (3) areas of increased ER density (ER stacks). All three modes produced waves with velocities similar to those measured in vitro (approximately 50–90 m /sec). Continuous ER showed high sensitivity to density increases, with time to onset reduced and speed increased. Increases in SERCA density resulted in opposite effects. The measures were sensitive to changes in density and spacing of hotspots and stacks. Increasing the apparent diffusion coefficient of substantially increased wave speed. An extended electrochemical model, including voltage-gated calcium channels and AMPA synapses, demonstrated that membrane priming via AMPA stimulation enhances subsequent wave amplitude and duration. Our modeling suggests that pharmacological targeting of s and SERCA could allow modulation of wave propagation in diseases where dysregulation has been implicated.

The deceptively simple laminar structure of neocortex belies the complexity of intra- and interlaminar connectivity. We developed a computational model based primarily on a unified set of brain activity mapping studies of mouse M1. The simulation consisted of 775 spiking neurons of 10 cell types with detailed population-to-population connectivity. Static analysis of connectivity with graph-theoretic tools revealed that the corticostriatal population showed strong centrality, suggesting that would provide a network hub. Subsequent dynamical analysis confirmed this observation, in addition to revealing network dynamics that cannot be readily predicted through analysis of the wiring diagram alone. Activation thresholds depended on the stimulated layer. Low stimulation produced transient activation, while stronger activation produced sustained oscillations where the threshold for sustained responses varied by layer: 13% in layer 2/3, 54% in layer 5A, 25% in layer 5B, and 17% in layer 6. The frequency and phase of the resulting oscillation also depended on stimulation layer. By demonstrating the effectiveness of combined static and dynamic analysis, our results show how static brain maps can be related to the results of brain activity mapping.

Neocortical mechanisms of learning sensorimotor control involve a complex series of interactions at multiple levels, from synaptic mechanisms to cellular dynamics to network connectomics. We developed a model of sensory and motor neocortex consisting of 704 spiking model neurons. Sensory and motor populations included excitatory cells and two types of interneurons. Neurons were interconnected with AMPA/NMDA and GABA A synapses. We trained our model using spike-timing-dependent reinforcement learning to control a two-joint virtual arm to reach to a fixed target. For each of 125 trained networks, we used 200 training sessions, each involving 15 s reaches to the target from 16 starting positions. Learning altered network dynamics, with enhancements to neuronal synchrony and behaviorally relevant information flow between neurons. After learning, networks demonstrated retention of behaviorally relevant memories by using proprioceptive information to perform reach-to-target from multiple starting positions. Networks dynamically controlled which joint rotations to use to reach a target, depending on current arm position. Learning-dependent network reorganization was evident in both sensory and motor populations: learned synaptic weights showed target-specific patterning optimized for particular reach movements. Our model embodies an integrative hypothesis of sensorimotor cortical learning that could be used to interpret future electrophysiological data recorded in vivo from sensorimotor learning experiments. We used our model to make the following predictions: learning enhances synchrony in neuronal populations and behaviorally relevant information flow across neuronal populations, enhanced sensory processing aids task-relevant motor performance and the relative ease of a particular movement in vivo depends on the amount of sensory information required to complete the movement.

The scale of large neuronal network simulations is memory limited due to the need to store connectivity information: connectivity storage grows as the square of neuron number up to anatomically relevant limits. Using the NEURON simulator as a discrete-event simulator (no integration), we explored the consequences of avoiding the space costs of connectivity through regenerating connectivity parameters when needed: just in time after a presynaptic cell fires. We explored various strategies for automated generation of one or more of the basic static connectivity parameters: delays, postsynaptic cell identities, and weights, as well as run-time connectivity state: the event queue. Comparison of the JitCon implementation to NEURON's standard NetCon connectivity method showed substantial space savings, with associated run-time penalty. Although JitCon saved space by eliminating connectivity parameters, larger simulations were still memory limited due to growth of the synaptic event queue. We therefore designed a JitEvent algorithm that added items to the queue only when required: instead of alerting multiple postsynaptic cells, a spiking presynaptic cell posted a callback event at the shortest synaptic delay time. At the time of the callback, this same presynaptic cell directly notified the first postsynaptic cell and generated another self-callback for the next delay time. The JitEvent implementation yielded substantial additional time and space savings. We conclude that just-in-time strategies are necessary for very large network simulations but that a variety of alternative strategies should be considered whose optimality will depend on the characteristics of the simulation to be run.