Characterization of Membrane Potential Dependency of Mitochondrial Ca 2+ Uptake by an Improved Biophysical Model of Mitochondrial Ca 2+ Uniporter Ranjan K. Pradhan, Feng Qi, Daniel A. Beard, Ranjan K. Dash* Biotechnology and Bioengineering Center and Department of Physiology, Medical College of Wisconsin, Milwaukee, Wisconsin Abstract Mitochondrial Ca 2+ uniporter is the primary influx pathway for Ca 2+ into respiring mitochondria, and hence plays a key role in mitochondrial Ca 2+ homeostasis. Though the mechanism of extra-matrix Ca 2+ dependency of mitochondrial Ca 2+ uptake has been well characterized both experimentally and mathematically, the mechanism of membrane potential (DY) dependency of mitochondrial Ca 2+ uptake has not been completely characterized. In this paper, we perform a quantitative reevaluation of a previous biophysical model of mitochondrial Ca 2+ uniporter that characterized the possible mechanism of DY dependency of mitochondrial Ca 2+ uptake. Based on a model simulation analysis, we show that model predictions with a variant assumption (Case 2: external and internal Ca 2+ binding constants for the uniporter are distinct), that provides the best possible description of the DY dependency, are highly sensitive to variation in matrix [Ca 2+ ], indicating limitations in the variant assumption (Case 2) in providing physiologically plausible description of the observed DY dependency. This sensitivity is attributed to negative estimate of a biophysical parameter that characterizes binding of internal Ca 2+ 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 Ca 2+ binding constants for the uniporter may be equal (Case 1). The model predictions in this case are insensitive to variation in matrix [Ca 2+ ] but do not match the DY dependent data in the domain DY#120 mV. To effectively characterize this DY dependency, we reformulate the DY dependencies of the rate constants of Ca 2+ translocation via the uniporter by exclusively redefining the biophysical parameters associated with the free-energy barrier of Ca 2+ 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 Ca 2+ and DY dependencies of mitochondrial Ca 2+ uptake. In addition, the model is insensitive to variation in matrix [Ca 2+ ], predicting relatively stable physiological operation. The model is critical in developing mechanistic, integrated models of mitochondrial bioenergetics and Ca 2+ handling. Citation: Pradhan RK, Qi F, Beard DA, Dash RK (2010) Characterization of Membrane Potential Dependency of Mitochondrial Ca 2+ Uptake by an Improved Biophysical Model of Mitochondrial Ca 2+ Uniporter. PLoS ONE 5(10): e13278. doi:10.1371/journal.pone.0013278 Editor: Jo ¨ rg Langowski, German Cancer Research Center, Germany Received June 28, 2010; Accepted September 13, 2010; Published October 8, 2010 Copyright: ß 2010 Pradhan et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Funding: This work was supported by National Institutes of Health grants R01-HL072011 (DAB) and R01-HL095122 (RKD) and American Heart Association grant SDG-0735093N (RKD). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. * E-mail: rdash@mcw.edu Introduction Mitochondrial Ca 2+ uniporter is the primary influx pathway for Ca 2+ into respiring mitochondria, and hence is a key regulator of mitochondrial Ca 2+ . Mitochondrial Ca 2+ homeostasis is critical for metabolic regulation, mitochondrial function/dysfunction, and cell physiology/pathophysiology [1–9]. Therefore, a mechanistic characterization of mitochondrial Ca 2+ uptake via the uniporter is essential for developing mechanistic, integrated models of mitochondrial bioenergetics and Ca 2+ handling that can be helpful in understanding the mechanisms by which Ca 2+ plays a role in mediating signaling pathways between cytosol and mitochondria and modulating mitochondrial energy metabolism in health and disease [10,11]. The kinetics of mitochondrial Ca 2+ uptake depends on the catalytic properties of the uniporter and also on the electrochem- ical gradient of Ca 2+ across the inner mitochondrial membrane (IMM), which has been extensively studied both experimentally [12–18] and with the help of mathematical models [10,11,19–21]. Though the mechanism of extra-matrix Ca 2+ dependency of mitochondrial Ca 2+ uptake has been well characterized, the mechanism of membrane potential (DY) dependency of mito- chondrial Ca 2+ uptake has not been completely characterized. In a recent paper [11], we introduced a mechanistic mathe- matical model of mitochondrial Ca 2+ uniporter (presented briefly in Materials S1) that satisfactorily describes the available experi- mental data on the kinetics of mitochondrial Ca 2+ uptake, measured in suspensions of respiring mitochondria isolated from rat hearts and rat livers under various experimental conditions [12,13,16]. This model is developed based on a multi-state catalytic binding and interconversion mechanism (Michaelis-Menten kinetics) for carrier- mediated facilitated transport [22,23], and Eyring’s free-energy barrier theory for interconversion and electrodiffusion [22,24–26]. The model also accounts for possible allosteric, cooperative binding of Ca 2+ to the uniporter, as seen experimentally [12,13]. Therefore, the biophysical formulation, thermodynamic feasibility, and ability PLoS ONE | www.plosone.org 1 October 2010 | Volume 5 | Issue 10 | e13278