Mitochondrial Ca²⁺ uniporter is the primary influx pathway for Ca²⁺ into respiring mitochondria, and hence plays a key role in mitochondrial Ca²⁺ homeostasis. Though the mechanism of extra-matrix Ca²⁺ dependency of mitochondrial Ca²⁺ uptake has been well characterized both experimentally and mathematically, the mechanism of membrane potential (ΔΨ) dependency of mitochondrial Ca²⁺ uptake has not been completely characterized. In this paper, we perform a quantitative reevaluation of a previous biophysical model of mitochondrial Ca²⁺ uniporter that characterized the possible mechanism of ΔΨ dependency of mitochondrial Ca²⁺ uptake. Based on a model simulation analysis, we show that model predictions with a variant assumption (Case 2: external and internal Ca²⁺ binding constants for the uniporter are distinct), that provides the best possible description of the ΔΨ dependency, are highly sensitive to variation in matrix [Ca²⁺], indicating limitations in the variant assumption (Case 2) in providing physiologically plausible description of the observed ΔΨ dependency. This sensitivity is attributed to negative estimate of a biophysical parameter that characterizes binding of internal Ca²⁺ to the uniporter. Reparameterization of the model with additional nonnengativity constraints on the biophysical parameters showed that the two variant assumptions (Case 1 and Case 2) are indistinguishable, indicating that the external and internal Ca²⁺ binding constants for the uniporter may be equal (Case 1). The model predictions in this case are insensitive to variation in matrix [Ca²⁺] but do not match the ΔΨ dependent data in the domain ΔΨ≤120 mV. To effectively characterize this ΔΨ dependency, we reformulate the ΔΨ dependencies of the rate constants of Ca²⁺ translocation via the uniporter by exclusively redefining the biophysical parameters associated with the free-energy barrier of Ca²⁺ translocation based on a generalized, non-linear Goldman-Hodgkin-Katz formulation. This alternate uniporter model has all the characteristics of the previous uniporter model and is also able to characterize the possible mechanisms of both the extra-matrix Ca²⁺ and ΔΨ dependencies of mitochondrial Ca²⁺ uptake. In addition, the model is insensitive to variation in matrix [Ca²⁺], predicting relatively stable physiological operation. The model is critical in developing mechanistic, integrated models of mitochondrial bioenergetics and Ca²⁺ handling.