THE CONCEPT OF DECISION POINTS

The cost of placing a synapse at a dendritic location

When a synapse is placed at a dendritic location in a passive dendrite, its efficacy on the somatic decision point will be smaller and delayed. What is the cost, in terms of efficacy and delay, of moving a synapse from the soma to the dendrites?

1. The Net Dendritic Attenuation (NDA)

The Net Dendritic Attenuation (NDA) is the ratio between the strength of the somatic response for a dendritic input and the strength of the somatic response for a somatic input. Formally, NDA(d,s) = (d,s)/(s), where s is the somatic point and d is the dendritic location of the input. The figure shows the NDA for every point in a reconstructed cortical pyramidal cell model. The NDA from the basal dendrites and from the proximal parts of the apical tree is close to 1 (no attenuation) and it is about 0.4-0.6 for distal apical arbors. Hence, the cost, in terms of attenuation, is small, except for distal apical inputs. Parameters used: Rm = 20 kcm², Ri = 100 cm, Cm = 1 microF/cm².

2. The Net Dendritic Delay (NDD)

The Net Dendritic Delay (NDD) measures the "delay cost" that results from placing the input at point d rather than at the soma. Formally, NDD(d,s) = TD(d,s) - LD(s), where s is the somatic point and d is the location of the input. Using the Reciprocity Theorem for delays, it is easy to show that NDD(d,s) = PD(s,d).

The figure shows the NDD for every point in a reconstructed pyramidal cell model. For the basal dendrites (where most of the inputs are located) and at the proximal part of the apical dendrite, the NDD is only a few milliseconds. Such a net dendritic delay is very small, compared to the integration time-window at the soma (about , here 20ms). This means that placing the input at these points (with small NDD) does not introduce synchronization problems, or significant delays, for the somatic integration. Namely, if many inputs arrive in a time window of 20ms at various points at the basal dendrites or at the proximal part of the apical tree, they will be summed "properly" at the soma. For inputs at distal points on the apical tree, the NDD is about 10ms, which is more significant (but still less than the somatic time window). Hence, excluding distal sites on the apical dendrite, the "delay cost" for this dendritic model is small. To summarize, in many cases, removing synapses from the soma does not change significantly the time-window for input integration at the soma. Parameters used: Rm = 20 kcm², Ri = 100 cm, Cm = 1 microF/cm².

The cost of placing a synapse at the dendrites: demonstration

A "synapse" is activated at a distal basal dendritic point. The synapse is modeled by an [[alpha]]-function current injection of time-to-peak of 0.5 ms. The voltage response at the soma is shown (blue in lower left frame). In another simulation, the same input is placed directly at the soma and the voltage response at the soma is also shown in the figure (in red). It is evident that the somatic voltage responses at the soma are almost identical in both cases. Hence, the cost, in terms of efficacy and delay, of placing a synapse at the apical basal location is small (for current injection synapses).

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

Back to Contents

Hagai Agmon-Snir Home Page