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A minimal model for the Mitochondrial rapid mode of Ca2+ uptake mechanism

PLoS ONE (2011) 6(6)
DOI: 10.1371/journal.pone.0021324
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Abstract

Mitochondria possess a remarkable ability to rapidly accumulate and sequester Ca2+. One of the mechanisms responsible for this ability is believed to be the rapid mode (RaM) of Ca2+ uptake. Despite the existence of many models of mitochondrial Ca2+ dynamics, very few consider RaM as a potential mechanism that regulates mitochondrial Ca2+ dynamics. To fill this gap, a novel mathematical model of the RaM mechanism is developed herein. The model is able to simulate the available experimental data of rapid Ca2+ uptake in isolated mitochondria from both chicken heart and rat liver tissues with good fidelity. The mechanism is based on Ca2+ binding to an external trigger site(s) and initiating a brief transient of high Ca2+ conductivity. It then quickly switches to an inhibited, zero-conductive state until the external Ca2+ level is dropped below a critical value (~100-150 nM). RaM's Ca2+- and time-dependent properties make it a unique Ca2+ transporter that may be an important means by which mitochondria take up Ca2+ in situ and help enable mitochondria to decode cytosolic Ca2+ signals. Integrating the developed RaM model into existing models of mitochondrial Ca2+ dynamics will help elucidate the physiological role that this unique mechanism plays in mitochondrial Ca2+-homeostasis and bioenergetics. © 2011 Bazil, Dash.

Figures

  • Table 1. 4-State RaM Model Parameters.
  • Figure 1. Simulations of the experimental data of Ca2+ uptake facilitated by RaM in heart. The corresponding pulse waveform for each experiment is shown in each panel. A) The model reproduced the measured Ca2+ uptake responses to pulses of Ca2+ at varying pulse heights and durations. The circles represent the Ca2+ uptake from a single pulse at a pulse height of 201 nM with an increasing pulse duration. The square and triangle represent the Ca2+ uptake from a 1 s duration Ca2+ pulse at a pulse height of 567 and 934 nM, respectively. The prepulse height for each pulse was 53 nM. B) The model reproduced the measured Ca2+ uptake response to a second pulse of Ca2+ following a previous pulse of the same magnitude at varying interpulse durations. The circles represent the Ca2+ uptake from a second pulse immediately after and up to 180 s after the first pulse. Both pulses were 5 s in duration at a pulse height of 209 nM with an interpulse height of 98 nM. The square represents a single, 5 s pulse at a pulse height of 181 nM with a prepulse height of 86 nM. C) The model reproduced the measured Ca2+ uptake response to a second pulse of Ca2+ following a previous pulse of the same magnitude at varying interpulse heights at a fixed interpulse duration of 60 s. Each pulse duration was 5 s. The circles represent the Ca2+ uptake from the second pulse at a pulse height of 274 nM. The square represents a single pulse at a pulse height of 273 nM for a duration of 5 s. D) The model reproduced the enhanced Ca2+ uptake response to multiple, short pulses versus a single, long pulse. The dashed line follows the trend of increasing Ca2+ uptake for in an increasing the number of pulses. All simulation results are either shown as x’s or a solid line depending on the nature of the simulation. doi:10.1371/journal.pone.0021324.g001
  • Figure 2. Simulations of the experimental data of Ca2+ uptake facilitated by RaM in liver. The corresponding pulse waveform for each experiment is shown in each panel. A) The model reproduced the measured Ca2+ uptake responses to pulses of Ca2+ at varying pulse heights and durations. The circles and squares represent the Ca2+ uptake from pulses at pulse heights of 171 and 281 nM, respectively, with an increasing pulse duration. B) The model reproduced the measured Ca2+ uptake response to a second pulse of Ca2+ following a previous pulse of the same magnitude at varying interpulse durations. The circles represent the Ca2+ uptake from a second pulse immediately after and up to 10 seconds after the first pulse. Both pulses were 5 s in duration at a pulse height of 421 nM with an interpulse height of 50 nM. C) The model reproduced the measured Ca2+ uptake response to a second pulse of Ca2+ following a previous pulse of the same magnitude at varying interpulse heights at a fixed interpulse duration of 1 second. The circles represent the Ca2+ uptake from the second pulse at a pulse height of 480 nM. Each pulse duration was 10 s. The Ca2+ uptake values were adjusted to compensate for CU activity to set the minimum uptake to be zero. D) The model reproduced the enhanced Ca2+ uptake response to multiple, short pulses versus a single, long pulse. The dashed line follows the trend of increasing Ca2+ uptake for in an increasing the number of pulses. All simulation results are either shown as x’s or a solid line depending on the nature of the simulation. In all cases, the prepulse height for each pulse was near 50 nM. doi:10.1371/journal.pone.0021324.g002
  • Figure 3. The major differences between the dynamics of the RaM model parameterized with the heart and liver parameters. The model was used to simulate the fraction of RaM in state RO and I1I2 as a function of [Ca 2+] and time to highlight the quantitative differences between heart and liver RaM as suggested by the available experimental data. Heart RaM only recovers back to the resting state when Ca2+ levels fall below 100–150 nM and sufficient time has passed (60–90 s). Liver RaM shows a very similar Ca2+-dependence; however, the time-dependence for recovery is much shorter (less than 1 s). doi:10.1371/journal.pone.0021324.g003
  • Figure 4. The steady state values for state R and time constants for the models as a function of Ca2+ is presented for heart and liver RaM. Although the steady state values for state R (A and B) are identical, the time constants (C and D) are dramatically different between heart and liver RaM. doi:10.1371/journal.pone.0021324.g004
  • Figure 5. Corroboration simulations for the RaM model. The experimental conditions outlined in [14] were simulated using the extremely simplified Ca2+ model described in the Material and Methods. A) The matrix and buffer Ca2+ dynamics were simulated for the high amplitude and frequency experiment. B) The corresponding fraction of RaM in the RO state is shown. C) The matrix and buffer Ca2+ dynamics were simulated for the low amplitude and frequency experiment. B) The corresponding fraction of RaM in the RO state is shown. doi:10.1371/journal.pone.0021324.g005
  • Figure 6. Schematic of the proposed model of the mitochondrial RaM Ca2+ uptake mechanism. The mechanism is based on that published by Starkov [13]. The model assumes that Ca2+ is required to initiate an activation cycle where the complex enters a transitory state of high Ca2+ conductance before entering an inactivated state. While the external Ca2+ remains elevated, the mechanism either stays locked in this quiescent state or triggers another conformational change eliciting the slow uptake (CU) mode. Once the external Ca2+ falls below a threshold concentration, the RaM complex dissociates and resets awaiting another trigger pulse of Ca2+. doi:10.1371/journal.pone.0021324.g006
  • Figure 7. The Ca2+ pulse waveform used in the experimental setup. The Ca2+ pulse delivery system was capable of adjusting the pre-pulse height, pulse height, pulse duration, interpulse duration, interpulse height and post-pulse height. For details concerning specific operational characteristics of the apparatus, see [72]. doi:10.1371/journal.pone.0021324.g007

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Bazil, J. N., & Dash, R. K. (2011). A minimal model for the Mitochondrial rapid mode of Ca2+ uptake mechanism. PLoS ONE, 6(6). https://doi.org/10.1371/journal.pone.0021324

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