1. To perform simulations of the various modes of action potential generation in thalamic relay neurons, we developed Hodgkin-and-Huxley style mathematical equations that describe the voltage dependence and kinetics of activation and inactivation of four different currents, including the transient, low-voltage-activated Ca2+ current (IT), the rapidly inactivating transient K+ current (IA), the slowly inactivating K+ current (IK2), and the hyperpolarization-activated, mixed cationic current (Ih). The modeled currents were derived either from acutely dissociated rat thalamic relay neurons (IT, IA, IK2), or from guinea pig thalamic relay cells maintained in slices in vitro (Ih). 2. The voltage dependence of steady-state activation and inactivation of IT, IA, and IK2 and the activation of Ih could be modeled with Boltzmann-style equations. Modeling of the behavior of IT to depolarizing steps in voltage clamp required the use of the constant field equation to relate permeability to T-current amplitude. The time constant of activation of IT was described by a continuous bell-shaped function with a maximum near 15 ms at threshold for activation (-75 mV) and 23 degrees C. Mathematical description of the kinetics of inactivation and removal of inactivation of this current required two separate functions. 3. The rapidly activating and inactivating K+ current IA was modeled by assuming two components with different time constants of inactivation. The kinetics of activation was described as a continuous function of voltage with the slowest time constant, near 2.5 ms, at threshold for activation (-60 mV) and 23 degrees C. In contrast, the kinetics of inactivation of both components were described as voltage independent, consistent with experimental data. The rate or removal of inactivation of both components of IA was described as continuously increasing with the degree of hyperpolarization. 4. The slowly inactivating K+ current IK2 was also modeled by assuming two components with different rates of inactivation. The kinetics of activation were described by a bell-shaped function with a maximum time constant near 80 ms at -40 mV and 23 degrees C, whereas threshold for activation was approximately -60 mV. Inactivation of both components was modeled as relatively independent of voltage, whereas removal of inactivation was described as a continuous function of membrane potential. 5. The hyperpolarization-activation cationic current, Ih, was modeled by assuming that the current activates with a single exponential relation and does not inactivate.(ABSTRACT TRUNCATED AT 400 WORDS)