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The thalamic reticular nucleus (TRN) is a shell of GABAergic neurons that surrounds the dorsal thalamus. Previous work has shown that TRN neurons send GABAergic projections to thalamocortical (TC) cells to form reciprocal, closed-loop circuits. This has led to the hypothesis that the TRN is responsible for oscillatory phenomena, such as sleep spindles and absence seizures. However, there is emerging evidence that open-loop circuits are also found between TRN and TC cells. The implications of open-loop configurations are not yet known, particularly when they include time-dependent nonlinearities in TC cells such as low-threshold bursting. We hypothesized that low-threshold bursting in an open-loop circuit could be a mechanism by which the TRN could paradoxically enhance TC activation, and that enhancement would depend on the relative timing of TRN vs. TC cell stimulation. To test this, we modeled small circuits containing TC neurons, TRN neurons, and layer 4 thalamorecipient cells in both open- and closed-loop configurations. We found that open-loop TRN stimulation, rather than universally depressing TC activation, increased cortical output across a broad parameter space, modified the filter properties of TC neurons, and altered the mutual information between input and output in a frequency-dependent and T-type calcium channel-dependent manner. Therefore, an open-loop model of TRN-TC interactions, rather than suppressing transmission through the thalamus, creates a tunable filter whose properties may be modified by outside influences onto the TRN. These simulations make experimentally testable predictions about the potential role for the TRN for flexible enhancement of cortical activation.