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In an excitable cell such as a muscle or neuron, the time constant of the membrane potential is = where r m is the resistance across the membrane and c m is the capacitance of the membrane. The resistance across the membrane is a function of the number of open ion channels and the capacitance is a function of the properties of the lipid bilayer .
If the time constant of the cell membrane is sufficiently long, as is the case for the cell body, then the amount of summation is increased. [6] The amplitude of one postsynaptic potential at the time point when the next one begins will algebraically summate with it, generating a larger potential than the individual potentials.
In order to quantify the behavior of electrotonic potentials there are two constants that are commonly used: the membrane time constant τ, and the membrane length constant λ. The membrane time constant measures the amount of time for an electrotonic potential to passively fall to 1/e or 37% of its maximum. A typical value for neurons can be ...
Starting from any initial state, the current flowing across either the conductance or the capacitance decays with an exponential time course, with a time constant of τ = RC, where C is the capacitance of the membrane patch, and R = 1/g net is the net resistance. For realistic situations, the time constant usually lies in the 1—100 ...
However, demyelination, which exposes internodal membrane with a higher membrane time constant than that of the original node, can also increase strength-duration time constant. [13] The strength-duration time constant of both cutaneous and motor afferents decreases with age, and this corresponds to an increase in rheobase. [7] Two possible ...
Where is the depolarization at = (point of current injection), e is the exponential constant (approximate value 2.71828) and is the voltage at a given distance x from x=0. When x = λ {\displaystyle x=\lambda } then
The typical Hodgkin–Huxley model treats each component of an excitable cell as an electrical element (as shown in the figure). The lipid bilayer is represented as a capacitance (C m). Voltage-gated ion channels are represented by electrical conductances (g n, where n is the specific ion channel) that depend on both voltage and time.
The growth constant k is the frequency (number of times per unit time) of growing by a factor e; in finance it is also called the logarithmic return, continuously compounded return, or force of interest. The e-folding time τ is the time it takes to grow by a factor e. The doubling time T is the time it takes to double.