I picture a neuron as having multiple trees of dendrites attached to the cell body with a single axon leaving the cell body. I believe the cell body near the axon root makes the decision to fire or not fire an action potential.
If the neuron has both excitatory and inhibitory synapses in the dendrite trees, how do these communicate to the cell body?
Does something like an action potential get transmitted down the dendritic trees to the cell body?
What is the difference between the excitatory and inhibitory signals that are transmitted?
Answer
From your comment to nico's good answer, it seems that your question is really about how synaptic potentials propagate through dendrites.
Canonically, synaptic potentials travel passively along membranes and is described by cable theory. The cable equation describes how the voltage will change over time and space along a cable. The theory was originally developed for signal decay in trans-Atlantic telegraph cables, but the principle holds for a voltage-independent length of membrane like a dendrite.
A key point is that the potential change "seen" by the cell body is different from the potential change seen locally at the site of the synapse itself. In fact, the voltage decays exponentially with increasing distance from the synapse. The extent of the signal decay is governed by the axial resistance (influenced by dendritic diameter), the membrane resistance, and membrane capacitance, and the branching pattern. A common neuron modeling environment called NEURON is basically a fancy solver for the cable equation.
You'll note that a consequence of this signal decay is that synaptic location matters a lot. Given an identical synaptic potential, a very distal synapse will have much less of an effect on the soma than a more proximal dendrite. Sometimes, the synaptic strengths are scaled to compensate for this location issue (a distal synapse will have a much larger local potential change). Many inhibitory synapses capitalize on this location dependence and are located close to the soma to act as shunts for all signals coming from the dendritic tree. When activated, an inhibitory synapse will decrease the local membrane resistance thereby decreasing cell excitability.
Finally, I'll note that although we often talk about dendrites as being passive conductors, dendrites are actually quite active and have many voltage-dependent channels. The voltage-dependent phenomena in the dendrite complicates the use of pure cable theory to understand the dynamics of synaptic potentials. However, cable theory is still the essential foundation upon which our growing understanding of the active dendrite is built.
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