Will the neuron pictured in the center here go to action potential? Well, in order to decide, it must interpret all of the incoming information. And this may be difficult because there may be 10,000 synaptic knobs from other neurons which contact its dendrites and soma.
The neuron depicted in the center, the postsynaptic neuron, must perform spatial summation. It must... add together the cumulative effects of all of these presynaptic neurons.
Now some of these presynaptic neurons are releasing neurotransmitters which depolarize the postsynaptic neuron. In other words, their effects are causing excitatory postsynaptic potentials or EPSPs. In contrast, some of the neurotransmitters secreted by these presynaptic neurons are are inhibiting the postsynaptic neuron and making it less likely to go to action potential.
They are causing IPSPs, or inhibitory postsynaptic potentials. There is only one section of the postsynaptic neuron, however, which can generate an action potential. That is an area at the base of the axon known as the axon hillock, also known as the trigger zone.
The only time that the postsynaptic neuron generates an action potential is when this axon hillock depolarizes to threshold. Depolarization in other parts of the cell, such as the dendrites, do affect the membrane potential but do not cause an action potential. Only the axon hillock is capable of generating an action potential.
And so therefore, if the cumulative effect of all of these other neurons added together all of their EPSPs and IPSPs, depolarize the axon hillock to threshold voltage, then the postsynaptic cell will generate an action potential. Now, not all of these presynaptic neurons have an equal effect on the axon hillock. Some are closer, and so therefore, synaptic knobs which are closer to the axon hillock have a greater effect on whether or not an an action potential is generated, while synaptic knobs, which are far from the axon hillock, terminating in dendrites, for example, these synaptic knobs have a lesser effect on whether the postsynaptic cell goes to action potential. This is spatial summation, the adding together of the cumulative effects of many synaptic knobs, and position matters.
The closer a synaptic knob is to the axon hillock, the greater its overall effect.