1. A model of the electrophysiological properties of single thalamocortical relay neurons in the rodent and cat dorsal lateral geniculate nucleus was constructed, based in part on teh voltae dependence and kinetics of ionic currents detailed with voltage-calmp techniques. The model made the simplifying assumption of a single uniform compartment an incorported a fast and transient Na+ current, I(Na); a presistent, depolarization-activated Na+ current, I(Nap); a low-threshold Ca2+ current, I(T); a high-threshold Ca2+ current, I(L); a Ca2+-activated K+ current, I(C); a transient and depolarization-activated K+ current, I(A); a slowly inactivating and depolarization-activated K+ current, I(K2); a hyperpolarization-activated cation current, I(h); and K+ and Na+ leak currents I(Kleak) and I(Naleak). 2. The effects of the various ionic current on the electrophyisological properties of thalamocortical relay neurons were initially investigated through examining the effect of each current individually on passive membrane responses. The two leak currents, I(Kleak) and I(Naleak), determined in large part the resting membrane potential and the apparent input resistance of the model neuron. Addition of I(A) resulted in a delaty in the response of the model cell to a depolarizing current pulse, whereas addition of I(K2), or I(L) combined with I(C), resulted in a marked and prolonged decrease in the respnse to depolarization. Addition of I(h) resulted in a deplarizing "sag" in respnse to hyperpolarization, hwereas addition of I(T) resulted in a large rebound Ca2+ spike after hyperpolarization. Finally, addition of I(Nap) resulted in enhancement of depolarization. 3. The low-threshold Ca2+ spike of rodent neurons was successfully modeled with the active currents I(T), I(L), I(A), I(C) and I(K2). The low-threshold Ca2+ current I(T) generated the low-threshold Ca2+ spike. The transient K+ current I(A) slowed the rate of rise and reduced the peak amplitude of the low-threshold Ca2+ spike, whereas the slowly inactivating K+ current I(K2) contributed greatly to the repolarization of the Ca2+ spike. Activation of I(L) during the peak of the Ca2+ spike led to activation of I(C), which also contributed to the repolarization of the Ca2+ spike. Reduction of any one of the K+ currents resulted in an increase n the other two, therby resulting in substantially smaller changes in the Ca2+ spike than would be expected on the basis of the amplitude of each ionic current alone. 4. Activation of the various K+ currents, I(A), I(K2), and I(C), also resulted in apparent rectification of the model neuron such that the response to a depolarizing current pulse was substantially smaller than the response to a hyperpolarizing current pulse. 5. Fast, Na+-dependent actionpotentials were repolarized largely by I(C) at membrane potentials positive to -60 mV, with smaller contributions by I(A) and I(K2). In contrast, I(A) and I(K2) formed a major component of the ionic currents flowing in between action potentials and therfore slowed the rate of action potential generation. 6. Addition of the hyperpolarization activated cation current I(h) resulted in adepolarizing sag on hyperpolarization and generated an apparent afterhyperpolarization after a low-threshold Ca2+ spike. During the generation of a low-threshold Ca2+ spike, I(h) deactivated, resulting in the membrane potential's fallin to a more negative level on repolarization of the Ca2+ spike. Subsequent activation of I(h) resulted in repolarization of the membrane potential and therefore the appearance of an afterhyperpolarization. 7. Rhythmic low-threshold Ca2+ spikes and burst generation were successfully modeled and depended critically on I(T), I(h), and the leak currents I(Kleak) and I(Naleak). The frequency and amplitude of rhythmic Ca2+ spike generation was strongly modulated by the amplitude of I(h), I(T), and I(Kleak). Increasing the maximal conductance of g(h) resulted in an increase in rhythmic burst generation from 0.5 to a maximum of 4 Hz. Shifting the voltage dependence of I(h) by +/- 10 mV resulted in an increase and decrease, respectively, of the frequency of thythmic Ca2+ spike generation and a decrease and increase, respectively, of the ability of the cell to maintain rhythmic oscillation. 8. The response of the model to depolarizing inputs was markedly different during rhythmic oscillation thatn during tonic depolarization. During rhythmic oscillation, depolarization of the model cell resulted in a transient burst response and disruption of rhythmic burst discharges, whereas application of the same depolarizing current pulse in the tonic firing mode resulted in a train of action potentials that displayed no spike frequency adaptation. 9. In summary, the present model of thalamocortical relay cells suggests that the various K+ currents in these neurons contribute to the repolarization of not only Na+ but also low-threshold Ca2+ spikes, control the temporal characteristics of repetitive firing, and generate an apparent rectification of the neuron at resting membrane potentials. The ionic corrents I(T) and I(h) are critically involeve in rhythmic low-threshold Ca2+ spike generation, which also depends critically on the status of the various "leak" conductance that determine the membrane potential and apparent input resistance of the cell. These finding confirm and extend previuos suggestions based on intracellular recordings of thalamocortical realy cells obtained in vivo and in vitro.