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I understand that when the stimulus into a neuron is greater than the threshold it triggers the action potential. Do all the contributing stimulus have to occur at the same time, or can they occur over time?

If neurons A and B connect to C, and C needs both A & B to activate to reach the threshold; can A fire first, then B - or do they both need to fire simultaneously?

If they can contribute towards the threshold over time then is there a decay that eventually returns the neuron to resting potential?

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There is temporal summation of the stimuli. This is modeled in the Hodgkin and Huxley model .

To imagine the whole process, you should know that in the dendrites of the neuron, electric impulses are propagating passively ( the strength of the stimuli is decreasing over distance and time), in the axon the electric impulse is active ( in the form of action potential(AP) ).

Let me explain your second question with the help of mathematics:

Let's assume that T is the threshold value.

Func(x, t) is a function of the stimuli, where the depolarizing effect is decreasing with time and distance:

Func(A, t) > Func(A, t+1)

So after your assumption:

Func(A, 0) + Func(B, 0) = T

If we don't take into account temporal summation, in other words, if we are looking at only just one phase of the time, and A and B stimuli are not simultaneous, and in t=0, then there will be no AP.

Func(A, t1) + Func(B, t2) < T , where t1 != t2

But with temporal summation we can add previous stimuli into the equation. For example:

From the previous asyncronous stimuli, we got our two decreasing depolarizing factors, and over time we got one more stimulus from A, then with temporal summation they CAN produce an AP.

Func(A, t1) + Func(B, t2) + Func(A, 0) >= T, if Func(A, t1) + Func(B, t2) >= Func(B, 0)

So after a depolarizing effect, the neuron enters into a hyperpolarized state and most of the sodium channels are inactive. This is called the refractory period. This is when, even A and B is applied simultaneously there will be no AP. And after the membrane potential gets back to his resting potential, then the whole process (including the temporospatial summation) starts from the beginning.

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