Simulation

3. Simulation

We are developing tools that will allow exploration of the functional consequences of variation in dendritic structure and composition on signaling in dendrites at a finer scale. Over time, we will systematically upscale these models as we learn how to simplify the realistic domain structures appropriately and allow incorporation of those features that significantly impact dendritic signaling into more realistic whole neuronal models.

We are creating models based on the cable equation

and the Poisson-Nernst-Planck equations.

for use on models at the scale of realistic domains as shown in the pipeline.
We will examine the effects that various spine parameters (neck width, neck length, base-to-tip length, etc) have on the results of our simulations.
We will also model electrical field effects which is an important feature in many brain regions, including the hippocampus. These effects include synchronous bursting behavior which is known to correlate with epileptic seizures.

EPSP modeling with high fidelity geometric model
We have performed a series of experiments to determine the effect reduction of geometric features to simplified models has on neurological simulations. The image above shows EPSP propagation in several dendrite models under the oblique dendrite boundary condition. a A model dendrite was attached to a thick multi-compartment cable representing the main apical dendrite. An EPSP was initiated on the oblique dendrite at the branch point, and several cases were compared: the oblique, reduced model dendrite with spines intact (red synapse, left); the oblique, reduced model dendrite with all spines removed (blue synapse, middle); and a constant diameter dendrite with no spines in which the diameter is set to the average diameter of the reduced model (black synapse, right). b Plot of the decay in EPSP amplitude with distance from the branch point under four conditions. The spine-cut, varying diameter dendrite model is split into two cases. In one, the spines are merely removed without any corresponding compensation to the membrane conductance and capacitance for the missing membrane (blue line and triangles). In the other, the missing membrane is compensated (blue squares). The averaged constant diameter dendrite is also compensated for missing spines. c Plot of the time to EPSP peak from EPSP initiation with distance from the branch point.
EPSP modeling with high fidelity geometric model
Using multiple reduced models to simulate ephaptic coupling between dendritic and axonal processes. a Depiction of two neighboring, spatially realistic dendrites and eight surrounding axons from which reduced models were constructed. b NEURON representation of the configuration (dendrites black, axons colored). Extending cables were attached to both ends of all axons and dendrites (extended process boundary condition) but are not shown here for clarity. c Schematic depicts a non-ephaptic model of extracellular recording in NEURON. In the non-ephaptic model, the net extracellular potential at the indicated location is measured by summing up contributions arising from the transmembrane currents of all six compartments (three from each process). Red lines indicate the evaluated transfer resistances, linking each compartment node to the recording site. Arrows indicate the directionality from measured transmembrane current to resulting extracellular potential via this transfer resistance. d In the ephaptic version, the compartment nodes themselves are linked to one another. The extracellular voltage at the location of compartment 1_1 is computed by summing contributions from the transmembrane currents of 2_1, 2_2, and 2_3 and so forth for each of the other compartments in turn. Recording in the extracellular space is still allowed as in the non-ephaptic model but is not shown in the diagram for clarity. e The two simulated dendrites, labeled A and B, are shown in the absence of the axons. Arrowheads indicate four of the five spines on which EPSPs were simultaneously initiated in Dendrite A for the simulation results shown in Fig. 9. The fifth spine projects behind Dendrite A and so is not visible in this figure. f Dendrites A and B are shown from another angle. The spine indicated by an asterisk in Dendrite A corresponds to the same spine so indicated in e and is utilized in Fig. 9e. Three particular spines in Dendrite B are also utilized in Fig. 9 and are labeled as spines 1, 2, and 3. For clarity, all of the other spines in Dendrite B have been removed from the image
EPSP modeling with high fidelity geometric model
Simulating ephaptic effects. a A single action potential is initiated simultaneously in each of the eight axons depicted in Figs. 8a,b. The resulting extracellular potential is plotted as a function of time (left) for an extracellular location corresponding to a point approximately midway between the two dendrites (marked by the black circle and arrow, right). b Five EPSPs are simultaneously initiated, one on each of five different spine heads, on Dendrite A (Fig. 8e). The extracellular potential is plotted at the same location midway between Dendrites A and B as in a. c The membrane potential of Dendrite A is plotted at three locations (the center and each end of the dendrite shaft) under the stimulation of the five summed EPSPs (left). The correspondingly colored arrows attached to Dendrite A indicate the locations of membrane potential recording (right). d The membrane potential of Dendrite B in response to the stimulation of Dendrite A is plotted at three locations (near the center and each end of the dendrite shaft, as indicated by the colored arrows attached to Dendrite B). Note the change in scale between c and d. e The membrane potential (left) at the synaptic location on the spine of Dendrite A that is indicated by an asterisk (right) is shown. f The membrane potential at three locations within Spine 1 of Dendrite B. Again, the recording locations are indicated by the colored arrows attached to Spine 1 in e, right. Note the change in scale between e and f. g The membrane potential at three locations within Spine 2 of Dendrite B. h The membrane potential at three locations within Spine 3 of Dendrite B.