THE CONCEPT OF DECISION POINTS

Synchronization required for input integration at a decision point

As explained above, the local delay may serve as an estimate for the synchronization time window for integration of inputs at a decision point. The following figure demonstrates the use of the local delay in three structures.

1. Local delay in three structures

The LD is shown using the color code at right. In all models, the membrane time constant is 20 ms. In the reference case of an isopotential system (A), the input current can be discharged only through the membrane. Indeed, the local delay reflects the properties of the membrane and is exactly the membrane time constant, . In B, the LD in a case of a soma coupled to a finite cylinder is demonstrated. The LD at the soma is smaller than . At proximal points, the LD is close to . At distal points, the LD is smaller (in the case shown, it is about /2). In C, we see that in the presence of a dendritic tree, the local delay at certain dendritic locations, primarily at distal arbors, may become very small (in our case, 0.1 - 0.2 ) because the rest of the tree serves as a large current sink (large conductance load). This is demonstrated by the green colors in distal basal and apical tips of a model of a cortical pyramidal cell from layer 5 (morphological data for the cell were kindly provided by R. Douglas). The LD at the tips is about 3 ms, whereas the LD at the soma is 18 ms. As a general rule, local delay at distal dendritic arbors decreases as the complexity of the tree increases. At the head of a dendritic spine, the LD may be further reduced to 0.05 and even smaller.

2. Comparing local delays in four reconstructed structures

At upper left: pyramidal cell from layer 5 of cat visual cortex (provided by R. Douglas); at upper right: pyramidal cell from layer 2/3 in cat visual cortex (provided by R. Douglas); at lower left: cerebellar Purkinje cell from the guinea pig (provided by M. Rapp); at lower right: region CA1 hippocampal cell from the rat (provided by D. Amaral and N. Ishizuka). For all cells, default parameters were used: Rm = 20 k cm², Ri = 100 cm, Cm = 1 microF/cm² (i.e., = 20 ms). We see that for a CA1 pyramidal cell and for a layer 2/3 cortical pyramidal cell, the LD is very small at the distal tips, about 5 ms, compared to the LD at the soma (about 20 ms). For a Purkinje cell, the LD is smaller than at the tips, but it is larger than the LD at the tips of the other trees, about 10 ms. It should be noted that we used the same default electrical parameters for all the dendritic structures, to emphasize the role of the geometry on the LD. Note the fine temporal resolution required in the distal parts of the pyramidal cells, as compared to the Purkinje cell. Clearly, for a comprehensive analysis of a typical realistic model, one should use the electrical properties found experimentally for the modeled cell. The method of moments provides efficient algorithms for analyzing LD and, thus, synchronization requirements, at various decision points in various dendritic trees and various biophysical properties.

Synchronization requirements in decision points: demonstration

Two brief current inputs are injected at a tip of a basal tree. Each is modeled by an [[alpha]]-function current injection of time-to-peak of 0.5 ms. The second input is activated 4 ms after the first one (upper right frame). The voltage response at the local vicinity of the synapses is shown at the lower right frame. It is clear that no local integration of the inputs takes place. In other words, the inputs "misses" each other. The voltage response at the soma is also depicted (left frame). At the soma, inputs are integrated to build a larger response. Hence, the wide integration time window at the soma allows integration of inputs that arrive at a wide time range, while at the dendritic location, much better synchronization is required.

Parameters used: Rm = 20 kcm², Ri = 100 cm, Cm = 1 microF/cm². The simulation was made using Neuron (Hines, 1989) by M. Rapp.

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