Previous publication suggests that multiple factors and processes, such as mitochondrial membrane potential, plasma membrane potential and efflux pump P-glycoprotein, were involved in TMRE distribution in the presence of cells. Our experimental results validated the role of these factors. So to quantitatively interpet the contribution of mitochondrial membrane potential, plasma membrane potential and efflux pump in TMRE distribution, a mathematical model was developed as showed below.
Figure 1. A schematic representation of the kinetic model of the
disposition of TMRE in pulmonary arterial endothelial cells and the
extracellular medium. The model consists three regions, medium, cytoplasm and
mitochondrial matrix. Re, Rc and Rm
are the free TMRE in the medium, cytoplasm and
mitochondrial matrix, respectively. Within the medium, TMRE participates in
nonspecific interactions with the cuvette (Be), protein binding sites (Bc, Bm). J1 and J2
are TMRE fluxes across plasma membrane and mitochondrial membrane driving by mitochondrial and plasma membrane potential, respectively; KPgp
is the constant of Pgp mediated efflux of TMRE.
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Model's Assumptions.
1. This model consists of
three regions which are the extracellular medium, cytoplasm and mitochondrial
matrix, with physical volumes Ve, Vc, and Vm,
respectively.
2. [TMREe], [TMREc] and [TMREm]
are the concentrations of free TMRE
which can diffuse across membranes freely and rapidly in extracellular medium, cytoplasm and mitochondrial matrix
respectively. The TMRE flux across plasma (J1) or inner mitochondrial membrane (J2) are
represented by modified one-dimensional Goldman–Hodgkin-Katz equations,
where P1 and P2 are TMRE membrane permeability constants
across plasma membrane and mitochondrial membrane respectively; a is a constant
dependent on the universal gas constant (R), Faraday constant (F), dye valence
(Z), and absolute temperature (T), a=ZF/RT.
3. Model allows an
equilibrating nonspecific binding-unbinding interaction between free TMRE in the
extracellular medium and cuvette binding sites (Be), which can describe by the
equation below:
k1 and k-1 are rate constants
for dye-cuvette binding and unbinding, respectively, and [Be] is the
concentration of cuvette dye binding sites.
Free TMRE in cytoplasm ([TMREc]) undergoes a rapidly equilibrating nonspecific binding-unbinding interaction with protein binding sites Bc with binding and unbinding constant k2 and k-2 which can be described by Similarily, Free TMRE in
mitochondrial matrix ([TMREm]) undergoes a rapidly equilibrating
nonspecific binding-unbinding interaction with protein binding sites Bm with
binding and unbinding constant k3 and k-3
4. Since only free TMRE
can go across membranes, to simply the model, apparent volumes instead of physical volumes are used
to represent the above rapidly interactions.
Apparent cytosol
volume V1 and apparent
mitochondrial matrix volume V2 can be described as
5. Pgp-mediated TMRE
efflux from cytoplasm to extracellular medium is assumed to follow linear
kinetics whose efflux constant is KPgp (mL-1).
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Assumptions for Inhibitors.
1. Though the assumptions for hibhitors don't affect the model itself, they are essential for the simulation of experiments.
For this method, three inhibitors were applied, which were GF120918 to inhibit P-glycoprotein , CCCP to dissipate mitochondrial membrane potential and medium containing high potassium to dissipate plasma membrane potential.
Basically, 1. in the presence of GF120918, the efflux rate of TMRE KPgp sets as zero.
2. in the presence of high potassium (138 mM) in the extracellular medium, plasma membrane potential sets as zero.
3. in the presence of CCCP, mitochondrial membrane potential sets as zero.
All of these inhibitors need some time to diffuse into the cells and affect its target. Since the second data was acquired after the cells mixed with medium for 5 minutes, which was supposed to enough for the inhibitors to affect their targets, so the onset time of inhibitors were neglected.
For this method, three inhibitors were applied, which were GF120918 to inhibit P-glycoprotein , CCCP to dissipate mitochondrial membrane potential and medium containing high potassium to dissipate plasma membrane potential.
Basically, 1. in the presence of GF120918, the efflux rate of TMRE KPgp sets as zero.
2. in the presence of high potassium (138 mM) in the extracellular medium, plasma membrane potential sets as zero.
3. in the presence of CCCP, mitochondrial membrane potential sets as zero.
All of these inhibitors need some time to diffuse into the cells and affect its target. Since the second data was acquired after the cells mixed with medium for 5 minutes, which was supposed to enough for the inhibitors to affect their targets, so the onset time of inhibitors were neglected.
Temporal Kinetic Model
Based on the properites of TMRE, cell biology as well as above assumptions, accroding to the law of mass balance and fick's law, variations in TMRE concentrations in
extracellular medium, cytosol and
mitochondrial matrix with time are described by below ordinary differential
equations:
where S1 and S2
are the surface area of plasma membrane and mitochondrial membrane
respectively.
Steady State Model
It is noticable that in the presence of both GF120918 and high potassium in extracellular medium, mitochondrial membrane potential would be the only factor affecting TMRE distribution under steady state.
In the presence of GF120918, high potassium and CCCP simutaneously, then TMRE would distribute evenly under steady state, which allows us to estimate the volume of cells.
This will make it possible to estimate mitochondrial membrane potential using a set of [TMREe] values under steady state.
While, the total mitochondrial volume was needed to estimate the contribution of mitochondrial membrane potential to TMRE distribution. In this study, the total volume of mitochondria was estimated based on the published studies, which was 2% of total volume of endothelial cells. This ratio could vary according to the type of cells.
Though theoretically it takes infinite time to reach steady state of TMRE distribution, it is possible to reach the state close enough to steady state in a limited time as showed in figure below.
In the presence of GF120918, high potassium and CCCP simutaneously, then TMRE would distribute evenly under steady state, which allows us to estimate the volume of cells.
This will make it possible to estimate mitochondrial membrane potential using a set of [TMREe] values under steady state.
While, the total mitochondrial volume was needed to estimate the contribution of mitochondrial membrane potential to TMRE distribution. In this study, the total volume of mitochondria was estimated based on the published studies, which was 2% of total volume of endothelial cells. This ratio could vary according to the type of cells.
Though theoretically it takes infinite time to reach steady state of TMRE distribution, it is possible to reach the state close enough to steady state in a limited time as showed in figure below.
Mitochondrial membrane potential could be estimated by the equation below: .
a: constant, a=ZF/RT=0.0374 /mV
b: ratio between total mitochondrial volume and total cell volume. For endothelial cells, b=0.02 Rs0: Extracellular TMRE concentration under steady state in the absence of cells (the value in the top red circle) Rs1: Extracelllular TMRE concentration under steady state in the presence of cells, GF120918, CCCP and high potassium ( the value in the middle red circle) Rs2: Extracellular TMRE concentration under steady state in the presence of cells, GF120918 and high potassium. ( the value in the bottom red circle) |
Related Publication:
Quantifying mitochondrial and plasma membrane potentials in intact pulmonary arterial endothelial cells based on extracellular disposition of rhodamine dyes
Gan Z, Audi SH, Bongard RD, Gauthier KM, Merker MP.
Am J Physiol Lung Cell Mol Physiol. 2011 May;300(5):L762-72
Quantifying mitochondrial and plasma membrane potentials in intact pulmonary arterial endothelial cells based on extracellular disposition of rhodamine dyes
Gan Z, Audi SH, Bongard RD, Gauthier KM, Merker MP.
Am J Physiol Lung Cell Mol Physiol. 2011 May;300(5):L762-72