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Pulse-chase analysis of auxin signal transduction in an Arabidopsis thaliana wildtype and an axr2-1 mutant. Wild-type and axr2-1 seedlings were labeled with 35S-methionine, and AXR2/axr2-1 protein was immunoprecipitated either immediately after the labeling period (t = 0) or following a 15-minute chase with unlabeled methionine (t = 15).
The Hodgkin–Huxley model, or conductance-based model, is a mathematical model that describes how action potentials in neurons are initiated and propagated. It is a set of nonlinear differential equations that approximates the electrical engineering characteristics of excitable cells such as neurons and muscle cells .
The graph on the right shows the impulse response of two similar systems. The green curve is the response of the system with impulse response () =, while the blue represents the system () = (). Although one response is oscillatory, both return to the original value of 0 over time.
(There are examples showing that attractivity does not imply asymptotic stability. [ 9 ] [ 10 ] [ 11 ] Such examples are easy to create using homoclinic connections .) If the Jacobian of the dynamical system at an equilibrium happens to be a stability matrix (i.e., if the real part of each eigenvalue is strictly negative), then the equilibrium ...
Based on Tasaki's work, Konrad Kaufman proposed sound waves as a physical basis for nerve pulse propagation in an unpublished manuscript. [11] The basic idea at the core of the soliton model is the balancing of intrinsic dispersion of the two dimensional sound waves in the membrane by nonlinear elastic properties near a phase transition.
Another may be a conductance-based neuron model that views neurons as points and describes the membrane voltage dynamics as a function of trans-membrane currents. A mathematically simpler "integrate-and-fire" model significantly simplifies the description of ion channel and membrane potential dynamics (initially studied by Lapique in 1907).
The impulse can be modeled as a Dirac delta function for continuous-time systems, or as the discrete unit sample function for discrete-time systems. The Dirac delta represents the limiting case of a pulse made very short in time while maintaining its area or integral (thus giving an infinitely high peak).
The impulse response of a system is the change in an evolving variable in response to a change in the value of a shock term k periods earlier, as a function of k. Since the AR model is a special case of the vector autoregressive model, the computation of the impulse response in vector autoregression#impulse response applies here.