Stretch-activated ion channels (SAC) affect volume regulation, motility, and cellular growth and division. In myocytes, these channels modulate electrical signaling and contractility. Recently researchers identified the canonical transient receptor potential type 1 (TRPC1) as a component of the vertebrate mechanosensitive cation channel that is activated by pressure and modulated by voltage. We setout to formulate and parameterize a Markov model of TRPC1 channel kinetics to reconstruct the recent data measured in voltage clamp studies. To reproduce the data, we proposed three aggregated Markov models whose transition rates are functions of both pressure and voltage. Although several methods for parameterizing Markov models have been suggested previously, these methods are not designed for Markov models with time dependent rates. Therefore, we derived a novel optimization method whereby we constrained a subset of parameters in each model to fit distinct features in the data. Our results showed that only one of the proposed models, Model 2, reproduced the data and, consequently, the model suggests a mechanism for the fast and slow kinetics observed in TRPC1 data. We further demonstrated how a similarity transformation applied to Model 2 created a different model that is indistinguishable from Model 2 in simulations despite their different topologies. Mathematically both models produce identical statistics, so either can be used in simulations. Biophysically, however, the models suggest that the fast and slow kinetics could be decoupled and, therefore, we explained how future experiments can aid in identifying a unique model. This work also provides a quantitative means to explore the role of TRPC1 in various physiological processes.