In recent years there has been an increasing amount of interest in the style of synthesis implemented by Don Buchla in his instrument designs from the early 1960s until the present. A key part of the Buchla synthesizer and its characteristic quality is the ’lowpass gate’ filter and the acoustic-like plucked sounds that it provides. In this work we examine the circuit of the low-pass gate, both its audio and control portions. We propose a number of digital models of these circuits, as well as a model of the photoresistive optoisolator or ’vactrol’ used within them. In the case of the audio path of the device, we pay particular attention to maintaining desirable behavior under time-variation of its parameters. The resulting digital model retains much of the interesting character of the analog system, and is computationally cheap enough to use within a standard computer-music setup.