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| The discussion here is based on concepts contained in [[MiPNet14.05]], which should be consulted first. The most up to date spreadsheet templates, DatLab templates, DatLab demo files, MiPNet14.05 and its mathematical appendix can be found [http://www.oroboros.at/index.php?id=protocols_tpp-membranepotential here].
| | #REDIRECT [[MiPNet15.08 TPP electrode]] |
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| 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.
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| Obviously this page will depend heavily on contributions from the community to achieve its goal.
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| '''Contributions, both in this article itself and on the corresponding discussion page are strongly encouraged!'''
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| == Sensitivity Analysis of the Method ==
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| [[File:Error_evaluation_absolute_1pc.png|thumb|300px|alt=absolute error in delta Psi by introduction of a 1 % error in c(TPP) plotted against delta Psi|absolute error in delta Psi by introduction of a 1 % error in c(TPP) plotted against delta Psi]] | |
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| The sensitivity of the method to small variations errors is strongly dependent on the membrane potential. For low membrane potential the method is inherently unsuitable. This is illustrated by introducing an artificial errors in the measured TPP concentration and plotting the resulting errors in the calculated membrane potential against the (original) membrane potential. The exact shape of the function depends on sample amount and type, binding correction and all other external factors but the general shape is usually quite constant.
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| Here this is illustrated for isolated (un purified) mitochondria, simulating the effect of a +2% and -2% error in the measured TPP concentration.
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| The used calculation template is not able to deal properly with results that would lead to a negative membrane potential, therefore error leading to a 0 or negative membrane potential are shown here as "zero".
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| == Consideration of “Unspecific Binding” ==
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| === The Four Compartment Model===
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| The approach to unspecific binding chosen in MiPNEt 14.05 and in the Oroboros Spreadsheet temples is basically based on Rottenbergs <ref name ="Rottenberg1984">Rottenberg H (1984) Membrane potential and surface potential in mitochondria: uptake and binding of lipophilic cations. J Membr Biol 81: 127-138.</ref> 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 approaches by Brand <ref name="Brand1995">Brand MD (1995) Measurement of mitochondrial protonmotive force. In Bioenergetics A Practical Approach (G.C. Brown, C.E. Cooper eds.) p. 39-62. Oxford University Press, Oxford.</ref> and Kamo <ref name="Demura1987">Demura M, Kamo N, Kobatake Y (1987) Binding of lipophilic cations to the liposomal membrane: thermodynamic analysis. Biochim Biophys Acta 903: 303-308.</ref>, at least for the processes inside the mitochondria.
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| In a nutshell, 4 different compartments are considered:
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| A The liquid filled matrix of the mitochondria, containing “free, internal” TPP.
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| B Material (membranes etc ) exposed to the typically high TPP concentration in compartment A. In Rottenbergs original approach this is the inside face of the inner mitochondrial membrane.
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| C The liquid filled space outside the mitochondria. This comprises the entire volume of the sample chamber with the exception of compartments A, B, and D.
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| D 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 of cell material not removed during purification.
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| The probe ion is supposed to accumulate in compartments B and D directly proportional to
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| *the “size/amount” of the compartment, measured by some marker, e.g. protein content
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| *the concentration of probe molecule in the adjunct liquid phase, e.g the TPP concentration in the mitochondrial matrix
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| * a factor describing the affinity of the compartment to the probe molecule (the binding correction factor.
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| E.g. the amount of TPP bound by the inward facing side of the inner mitochondrial membrane is
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| n(int,bound) = Ki' * Pmt * C(int,free)
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| (Equation A8a in the mathematical Appendix to MiPNet14.05)
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| It should be noted that a binding correction factor (e.g. Ki’)is only useful together with a certain type of marker (Pmt) for which it was determined.
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| The approaches by Brand and Kamo 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.
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| ===(Purified) Isolated Mitochondria and Unspecific Binding Inside the Mitochondria===
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| Due to the small amount of material exposed to the outside concentrations and the low outside concentrations only the inside binding is significant.
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| The absolute values for delta Psi will depend on the chosen binding correction factors
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| 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. The insensitivity against outside binging cab be shown by varying the outside binding parameter only:
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| [[File:Isolated mito Kout variation.png|500px|alt=various delta PSi values and one delta delta Psi values plotted against varying external binding parameter Kout'|various delta PSi values and one delta delta Psi values plotted against varying external binding parameter Kout']]
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| 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 used 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:
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| Brand<ref name="Brand1995"/>: 2-3.2 µl/mg (converted to Rottenbergs system)
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| Rottenberg<ref name ="Rottenberg1984"/>: 2.4 to 3.7 µl/mg
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| Kamo<ref name="Demura1987"/>: 2.7 µl/mg (converted to Rottenbergs system)
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| This may indicate a certain soundness to the approach.
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| Simultaneous variation of outside and inside binding parameters show
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| * the invariance of delta delta Psi
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| * that strong deviation from published Kin' values do not lead to reasonable results:
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| [[File:Isolated mito KinandKout variation.png|500px|alt=various delta Psi values and one delta delta Psi values plotted against varying external and internal binding parameter Kout'|various delta PSi values and one delta delta Psi values plotted against varying external = internal binding parameter Kout']]
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| Conclusions for purified isolated mitochondria
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| *Absolute delta delta Psi values can be obtained
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| *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. Approximate delta Psi values may be obtainable by using literature values, if variances in binding depending on samples and conditions is shown to be small.
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| ===Permeabilized Cells, Homogenates, Permeabilized Fibres and Unspecific Binding Outside the Mitochondria ===
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| 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.
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| 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).
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| From a mathematical point of few the contribution of outside binding does not cancel even for the determination of Delta Delta Psi
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| However, the first question before addressing this problems is whether outside binding is relevant at all. Brand stated that for permeabilized cells outside binding may be ignored for high mitochondrial membrane potential. Initially, 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 hundred percent caused comparable small 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 may be grossly underestimated by this approach, resulting in obviously too high membrane potentials 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.
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| [[File:Homogenate brain centrifuged Kout.png|500px|alt=various delta Psi values and one delta delta Psi values plotted against varying external binding parameter Kout'|various delta PSi values and one delta delta Psi values plotted against varying external binding parameter Kout']]
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| One problem with this approach, at least in the shown example, may be that medium membrane potential values (e.g. ADP) decrease quite strongly with increasing external binding, resulting in a very strong increase in differences (delta delta Psi values), even if the low potential states are modeled not to a psi of zero but one similar to the values observed for isolated mitochondria. More comparative values both from isolated mitochondria and from homogenate/ permeabilized fibers would be necessary to evaluate this strategy.
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| 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. This is potentially an important observation for researchers more interested in comparing just one state between different samples. It might even be argued that for very high membrane potentials an absolute delta Psi may be estimated regardless of the used binding parameters. However, this certainly needs further evaluation.
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| By increasing both the interior and external binding parameters it is again (as with isolated mitochondria)seen that strong deviation from published Kin' values do not lead to reasonable results:
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| [[File:Homogenate brain centrifuged Koutand Kin.png|500px|alt=various delta Psi values and one delta delta Psi values plotted against varying external binding parameter Kout'|various delta Psi values and one delta delta Psi values plotted against varying external binding parameter Kout']]
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| There are currently no good methods known to determine the outside binding with the possible exception of radio-tracer 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 use 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:
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| # 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.
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| # 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.
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| 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 radio-tracer 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.
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| There are two obvious ways to obtain binding correction parameters that will allow a more quantitative approach:
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| * direct determination of outside binding
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| * comparison with results obtained for isolated mitochondria under as similar as possible conditions followed by fitting the binding parameter to obtain comparable results
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| Both approaches face several theoretical and practical differences, but should be further explored.
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| ===Further Modeling options===
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| # 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.
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| # It was suggested to use the quantity "taken up TPP per mass of sample (protein content)" as a relative expression for the membrane potential for given experimental conditions. One advantage is that if the result is to be a relative number anyway, it may be easier to argue (e.g. with reviewers) to use this expression than to calculate some delta Psi and than declaring: "This is not really delta Psi, but some relative value". On the downside, the comparability between different experimental conditions is certainly worse than with some calculated "relative delta Psi, plus even for the same experimental conditions the relationship between the stated number and true membrane potential (especially the linearity of the relationship!) may be worse. This should be checked by calculations / simulations.
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| # '''Please add your suggestions!'''
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| == Correction for substance specific effects on the TPP signal ==
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| The necessity to perform a TPP chemical background experiment is explained in MiPNet 14.05. Some additional considerations:
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| ===When to apply a correction===
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| 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.
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| 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.
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| 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.
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| 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.
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| 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.
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| ===Substances===
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| Azide N3- has a very huge substance specific effect. A correction does not seem feasible.
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| The substance specific effect od ADP is comparable large and should be considered carefully.
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| ==References==
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| <references/>
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