Calculation of mitochondrial membrane potential from measurements with a TPP electrode

The discussion here is based on concepts contained in MiPNet 14.05, that should be consulted first. The calculation of mitochondrial Membrane Potential from measurements with an TPP Electrode is a difficult are far from settled topic that becomes even more fluent with the now ongoing extension of the technique from isolated mitochondria to permeabilized cells, tissue homogenates and permeabilized fibers. Therefore this discussion should give a more up to date, more detailed but also more fluent overview than contained MiPNet 14.05. The ongoing discussion may in some point also lead to a flat contradiction to statements in MiPNet 14.05.

Consideration of “Unspecific Binding”

The Four Compartment Model

The approach to unspecific binding chosen in MiPNEt 14.05 and in the Oroboros Spreadsheet temples is basically based on Rottenbergs 4 compartment model, developed for isolated mitochondria. As shown in the mathematical appendix to MiPNEt 14.05 this approach seems to be mathematically fundamentally equivalent to the approached by Brand and Kamo, at least for the processes inside the mitochondria. In a nutshell 4 different compartments are considered: A The liquid filled matrix of the mitochondria, containing “free, internal” TPP. B Material (membranes etc ) exposed to the typically high TPP concentration in compartment 1. In Rottenbergs original approach this is the inside face of the inner mitochondrial membrane B The liquid filled space outside the mitochondria. This comprises the entire volume of the sample chamber with the exception of compartments 1, 2, and 4. C Material (membranes etc) that are exposed to the typically low TPP concentrations outside the mitochondrial matrix. In Rottenbergs original approach this compartment comprises the outside face of the inner mitochondrial membrane and any present material for the outer mitochondrial membrane or traces ofcell material not removed during purification.

The probe ion is supposed to accumulate in compartments 2 and 3 in direct proportionally to The “size/amount” of the compartment, measured by some marker, e.g. protein content The concentration of probe molecule in the adjunct liquid phase, e.g the TPP concentration in the mitochondrial matrix A factor describing the affinity of the compartment to the probe molecule (the binding correction factor. E.g. the amount of TPP bound by the inward facing side of the inner mitochondrial membrane is Equation (A8a) in

It should be noted that a the binding correction factor (Ki’)is only useful together with a certain type of marker (Pmt) for which it was determined.

The approached by Brand and Rottenberg do not consider the outside compartments for unspecific binding. Indeed for purified isolated mitochondria the outside binding seems to have a very small effect. Therefore in all further considerations one has to discern between studies of purified isolated mitochondria and other studies with other sample types.

(Purified) Isolated Mitochondria and Unspecific Binding inside the mitochondria Due to the small amount of material exposed to the outside concentrations and the low outside concentrations only the inside binding is significant. The absolute values for delta Psi will depend on the chosen binding correction factors

The absolute difference between membrane potentials (either between different states or different samples) will NOT depend on the chosen inside binding correction factor see MiPNEt 14.05 Mathematical Appendix. Therefore it should be possible to obtain absolute delta delta Psi’s for this sample type. Only a few binding correction factors for inside binding have been published, based on rat liver mitochondria or membrane models under very different conditions (temperatures, mitochondrial membrane potential,…) While different mathematical approaches were sued to describe the binding an attempt to convert these factors between different mathematical values shows quite similar values for the probe TPMP, the probe for which most values are available. This may indicate a certain soundness to the approach. Conclusion: For purified isolated mitochondria

absolute delta deltaPsi values can be obtained

Precise absolute delta psi values can not be obtained without actually measuring the binding correction factor for the studied system. Literature values will usually not be available for the desired system. Permeabilized cells, homogenates, permeabilized fibers. In these sample types there is a large amount of materials outside the mitochondrial matrix present. But potential even more difficult than the absolute amount of material is the variety of materials. Inside the mitochondrial matrix the mitochondrial membrane is the only type of material taking up the probe and can therefore be accurately described by a single binding correction factor. Outside the mitochondria there may be membranes, proteins, other lipid compartments and even components of the medium to consider. It is reasonable to expect that all of them show a different affinity to TPP or other probes.

In theory the four compartment approach can be applied to such samples. All outside material will be exposed to the low extra-mitochondrial probe concentration and can therefore be included in compartment four. Due to the different nature of the outside material it can be expected that a quite different binding correction factor will be needed than the one determined by Rottenberg for the outside binding to isolated mitochondria. Additionally, it may be discussed what would be a good marker for the amount of outside material present. It should be remembered that each binding correction factor is only valid for the use with a specific marker quantity (like protein content). From a mathematical point of few the contribution of outside binding does not cancel even for the determination of Delta Delta Psi However, the first question before addressing this problems is whether outside binding is relevant at all. Brand sted that for permeabilized cells outside binding may be ignored for high mitochondrial membrane potential. This seemed to be confirmed by our own initial sensitivity studies. Using outside binding correction factors similar to the inside ones and using protein content as marker, changing the outside binding correction factor by several 100% caused comparable changes in reasonable high membrane potentials and negligible changes in delta delta psi values for permeabilized cells. However, with growing experience it became evident that unspecific binding was grossly underestimated by this approach, resulting in obviously too high membrane potentials even and especially for states of known low potential. Modeling of the outside binding correction factor showed that the factor had to be increases by factors above 50 to model reasonable membrane potential. With such a huge contribution of outside binding also differences between states (delta delta Psi) are now very significantly influenced by the choice of the outside binding correction factor. A bit surprisingly, very high membrane potential still change only very little even when the outside binding correction factor is changed by more than a factor of 50. So the statement that outside binding may be ignored in permeabilized cells for high membrane potentials was actually verified, only with the restriction that this hold only true for the very highest membrane potentials obtainable. There are currently no good methods known to determine the outside binding with the possible exeption of raditraced experiments similar to those used to determine inside binding. Even if such experiments were done the heterogeneity and diversity of materials found in the outside compartment the results would be less transferable to other samples than the results for inside binding. An obvious way out would be to sue a known state of zero membrane potential to determine either all or at least just the outside binding correction factor. This approach faces two problems: A It is not clear how a reliable state of reliable zero membrane potential can be reached. The true membrane potential at “low potential” states like after addition of FCCP may or may not be zero. B.) As discussed above the accuracy of the entire method inherently decreases with decreasing membrane potential. At Zero membrane potential the smallest error in measured TPP Concentration will cause huge errors in delta Psi. In effect the point of lowest accuracy would be used to calibrate the entire method.

However, at least to obtain a plausibility analysis it is certainly helpful to look at this low membrane potential states. A thorough literature search for membrane potentials obtained(with a radiotracer method) e.g. after treatment with FCCP should be performed. Maybe an at least intermediate solution would be to still use literature values obtained for isolated mitochondria to model the inside binding but use a (very crude) approximation of outside binding by observation of a zero mitochondrial membrane potential state.

Further Modeling options

1.) Saturated binding The four compartment model could be extended by further parameters. One possibility would be to allow for a saturable component of binding. The amount of TPP bound would depend only on some proportionality factor and the amount of biological material present but not on the free TPP concentration in the compartment. Such a behavior could be detected by performing experiments at different TPP levels. To avoid convolution by TPP inhibition effects at higher TPP concentrations probable only the results at low membrane potentials should be compared.

Correction for substance specific effects on the TPP signal

The necessity to perform a TPP chemical background experiment is explained in MiPNet 14.05. Some additional considerations:

Substances

Azide N3- has a very huge substance specific effect. A correction does not seem feasible. The substance specific effect od ADP is comparable large and should be considered carefully.

When to apply a correction

For isolated mitochondria absolute delta delta psi seem obtainable, see above. Approximate delta psi values seem to be principally obtainable though with relying on literature data. . The strongly quantitative approach enabled thereby calls for complete quantifications including correction for unspecific effects. For permeabilized cells, homogenats and permeabilized cells, absolute values of delta or delta delta psi seem currently difficult to obtain. Currently data will have to presented as a relative value. Therefore a discussion about to do or not to do a correction for substance specific effects seems justified. Whenever changes of mitochondrial membrane potential during an experiment are of interest a correction is most definitely needed. Otherwise even the nature of the change (increase / decrease) may be misjudged. When membrane potentials obtained by different protocols but using the same parameters (binding correction factors) during calculation should be compared to each other, correction for substance specific effects has to be done, even though only relative values are compared to each other. When relative values for membrane potentials of the same state obtained via totally identical protocols are to be compared between different samples a correction may not be strictly necessary. In this case the research will have to judge on a case basis. If the correction is obviously rather difficult the danger of introducing additional errors may be greater than any benefit from getting slightly more realistic values. Even if it is decided for a particular study not to apply the correction the TPP chemical background experiments should be done non the less to detect possible problems.