ANALYSIS OF AN EXCITABLE DENDRITIC SPINE WITH AN ACTIVITY-DEPENDENT STEM CONDUCTANCE

Dendritic spines are the major target for excitatory synaptic inputs i n the vertebrate brain. They are tiny evaginations of the dendritic su rface consisting of a bulbous head and a tenuous stem. Spines are cons idered to be an important locus for plastic changes underlying memory and learning processes. The findings that synaptic morphology may be a ctivity-dependent and that spine head membrane may be endowed with vol tage-dependent (excitable) channels is the motivation for this study. We first explore the dynamics, when an excitable, yet morphologically fixed spine receives a constant current input. Two parameter Andronov- Hopf bifurcation diagrams are constructed showing stability boundaries between oscillations and steady-states. We show how these boundaries can change as a function of both the spine stem conductance and the co nductance load of the attached dendrite. Building on this reference ca se an idealized model for an activity-dependent spine is formulated an d analyzed. Specifically we examine the possibility that the spine ste m resistance, the tunable ''synaptic weight'' parameter identified by Rall and Rinzel, is activity-dependent. In the model the spine stern c onductance depends (slowly) on the local electrical interactions betwe en the spine head and the dendritic cable; parameter regimes are found for bursting, steady states, continuous spiking, and more complex osc illatory behavior. We find that conductance load of the dendrite stron gly influences the burst pattern as well as other dynamics. When the s pine head membrane potential exhibits relaxation oscillations a simple model is formulated that captures the dynamical features of the full model.