THE CONCEPT OF DECISION POINTS - CNS 95

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Hagai Agmon-Snir Tel. (301) 496-6136 Fax. (301) 402-0535

Abstract

We introduce the concept of decision points and demonstrate its use for analyzing computational processes in dendritic trees. We analyze several models of reconstructed cells (cerebellar Purkinje cells, cortical pyramidal cells and hippocampal CA1 pyramidal cells) and discuss, using the concept of decision points, the computational capabilities of these neurons. We show how to determine the dendritic region whose inputs will affect a given decision point and the effectiveness of these inputs. We also analyze synchrony requirements for typical decision points. This analysis emphasizes that the linear model of a dendritic tree has less computational capability than a tree containing local decision points that, because of local nonlinearities, modulate the information in the tree.

Summary

For analyzing the input-output relationship of the neuron, we typically emphasize the role of the soma as a site where synaptic input currents are transformed into a pattern of output action potentials. Only part of the spatio-temporal input information that arrives at the soma is expressed in the output pattern of action potentials at the axon. Hence, in the soma, a decision is made - what part of the information should be delivered to the axon.

The soma, however, is not the only decision point in the cell. Nonlinear interactions between inputs at the dendritic tree (e.g., local "veto" effect of synaptic inhibition, dendritic "hot spots", nonlinear summation of excitatory inputs at partly isolated dendritic arbors, dendro-dendritic interactions, activity dependent plastic changes, etc.) may be regarded as decision points. These decision points are triggered by a subset of the inputs that impinge on the dendrites and in many cases, the voltage response at the decision point affects other decision points.

Characterization of computation in dendrites is difficult because much of the biophysical information is still missing. Even if the data was available, the different type of data (morphology, channel density and distribution as well as input architecture) interact in a complicated way to determine the computational function of the neuron. Thus, carefully simplified and reduced models should be constructed to understand the underlying principles that govern this computation. The idea that the processing in the dendrite is done by "decisions" at "decision points" is an example of such simplification. It does not convey the entire biophysical properties of realistic neurons, but, as will be demonstrated in the presentation, it allows us to state some rules for dendritic computation.

In summary, in order to understand the rules that govern dendritic integration and its computational role, we suggest the use of simplified models of the dendritic tree. In the present work, the dendritic tree and the soma are assumed to be passive, and the inputs are modeled by current injections (rather than by conductance changes). To this passive model we add the concept of decision points. Hence, although the voltage response in the model is still calculated using the elegant methods of passive cable theory, the interpretation of the results is made from the point of view of the decision points, which are nonlinear. We believe that this "hybrid" point of view may help, at least as a reference case, to explain some of the rules of dendritic computation.

For analyzing the passive models, we use the novel framework called the method of moments(Agmon-Snir and Segev, J. Neurophysiol. 70: 2066-2085, 1993; Agmon-Snir, Biophys. J., 1995, accepted). This method provides analytic investigation of voltage attenuation, signal delay and synchronization problems in passive dendritic trees. We also utilize the morphoelectrotonic transform presentation (Zador et al., Soc. for Neur. Abst. 17: 1515, 1991; Zador et al., J. Neuroscience, 1995, in press). The combination of the method of moments, the morphoelectrotonic transform and the concept of decision points is shown to be very effective in analyzing the spatio-temporal integration in dendritic trees.

We analyze several models of reconstructed cells (cerebellar Purkinje cells, cortical pyramidal cells and hippocampal CA1 pyramidal cells) and discuss, using the concept of decision points, the computational capabilities of these neurons. A few important insights are gained, allowing us to state some general rules of thumb for dendritic integration and computation. The first general insight is the difference between the degree of synchronization required for the various computations that might be implemented in the tree. In general, computations at distal decision points require better input synchronization than computations at the somatic level. Therefore, if some nonlinear interactions occur at decision points in the tree, the timing of these interactions is very important for the "electrical message" delivered to the soma (or to another decision point in the tree). These interactions could be interactions between excitatory and inhibitory synapses, saturation effects between excitatory inputs, activating of nonlinear channels, activating plastic learning processes and activating dendro-dendritic interactions. We explain why a dendritic decision point is affected mostly by the inputs at its proximity and by inputs distal to this decision point. Hence, a dendritic decision point may be regarded as a local decision point, compared to the more global decision points which are proximal to it (closer to the soma). Therefore, the soma should be viewed as the major decision point that performs a very global computation. Generally speaking, the soma may be considered as an "integrator" while distal decision points may be considered as "coincidence detectors".

The second general insight is that, placing inputs at the passive dendrites rather than at the soma is mostly ineffective for modulating the efficacy of an input or for delaying its effect on the somatic integration. The "cost" is negligible, compared to other plausible methods for modulating synaptic efficacy and for modulating the width of the time window for input synchronization at the soma. Indeed, for passive dendrites with current injection inputs, the response at the soma to a few inputs that are triggered is a linear sum of the somatic responses to the individual inputs. We predict that in such a case, in the absence of dendritic decision points, the dendrites have a minor computational role. The computational role of dendrites must involve nonlinear interactions at the dendrites, at least by means of nonlinear interactions between synapses. We hypothesize that the main role of dendrites is to create many decision points of different computational function and with a computational hierarchy. We suggest that these local decision points are the mechanism by which the dendritic computation is executed.

An especially interesting case is the feedback mechanism from proximal decision points to distal decision points. The effect of this mechanism depends critically on the method of information transfer. If the feedback is by passive spread of current, the time window of the voltage response at the distal decision point would be long. For active propagation of an action potential backward into the dendrites (Stuart and Sakmann, 1994), the time window may be rather short.

The results of this work are also important for neural network modelers. For example, we predict that the synchrony required for learning (by plasticity changes at the synapses) does not have to be the same as the synchrony required for calculating the output of a neuron. Also, in such models, the synchronization of inputs at the soma should be of the order of the membrane time constant. The good news for point neuron modelers is that the cost of placing synapses outside the soma is small in most cases. Hence, for soma output, passive dendrites with current injections may practically be ignored. However, as explained above, the dendritic integration is not linear, because the inputs are conductance changes and because of the nonlinear decision points at the tree.

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