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Difference between revisions of "Iconic symbols"

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{{MitoPedia
{{MitoPedia
|abbr=
|abbr=
|description='''Iconic symbols''' are used in [[ergodynamics]] to indicate more explicitely ā€” compared to standard SI or IUPAC symbols ā€” the quantity represented. This is particularly the case in normalized quantities (ratios of quantities). Iconic (or canonical) symbols help to clarify the meaning, are based on SI and IUPAC symbols as far as possible, and may be translated into more commonly used, practical symbols. Several ambiguities in SI and IUPAC symbols are eliminated by the systematic structure of iconic symbols, but it may be impossible to avoid all ambiguities, particulary when long (canonical) symbols are abbreviated in a particular context. Clarity is improved always by showing the unit of a quantity together with the symbol of the quantity. Iconic symbols cannot be identical with IUPAC symbols when a different definition is used ā€” this would add to the confusion. For example, the IUPAC symbols ''n''<sub>B</sub> [mol] and ''V''<sub>B</sub> [m<sup>3</sup>] denote amount and volume of B. Consequently, it should be expected, that the symbol ''Q''<sub>B</sub> indicates charge of B [C]. However, the IUPAC symbol ''Q''<sub>B</sub> is used for particle charge per ion B [CĀ·x<sup>-1</sup>]. This prohibits a consistent definition of ''Q''<sub>B</sub> as a potential iconic symbol for charge carried by a given quantity of ions B with unit [C], instead of particle charge per ion B with unit [CĀ·x<sup>-1</sup>]. Hence, the conventional ambigous system forces compatible iconic symbols to be more complicated, using ''Q''<sub>elB</sub> [C] and ''Q''<sub>''<u>U</u>''B</sub> [CĀ·x<sup>-1</sup>] to distinguish charge of B from charge per elementary B. ''Q''<sub>''<u>n</u>''B</sub> [CĀ·mol<sup>-1</sup>] is charge per molar amount of B.
|description='''Iconic symbols''' are used in [[ergodynamics]] to indicate more explicitely ā€” compared to standard SI or IUPAC symbols ā€” the quantity represented and some boundary conditions. This is particularly the case in normalized quantities (ratios of quantities). Iconic (or canonical) symbols help to clarify the meaning, are based on SI and IUPAC symbols as far as possible, and may be translated into more commonly used, practical symbols. Several ambiguities in SI and IUPAC symbols are eliminated by the systematic structure of iconic symbols, but it may be impossible to avoid all ambiguities, particulary when long (canonical) symbols are abbreviated in a particular context. Clarity is improved always by showing the unit of a quantity together with the symbol of the quantity. Iconic symbols cannot be identical with IUPAC symbols when a different definition is used ā€” this would add to the confusion. For example, the IUPAC symbols ''n''<sub>B</sub> [mol] and ''V''<sub>B</sub> [m<sup>3</sup>] denote amount and volume of B. Consequently, it should be expected, that the symbol ''Q''<sub>B</sub> indicates charge of B [C]. However, the IUPAC symbol ''Q''<sub>B</sub> is used for particle charge per ion B [CĀ·x<sup>-1</sup>]. This prohibits a consistent definition of ''Q''<sub>B</sub> as a potential iconic symbol for charge carried by a given quantity of ions B with unit [C], instead of particle charge per ion B with unit [CĀ·x<sup>-1</sup>]. Hence, the conventional ambigous system forces compatible iconic symbols to be more complicated, using ''Q''<sub>elB</sub> [C] and ''Q''<sub>''<u>N</u>''B</sub> [CĀ·x<sup>-1</sup>] to distinguish charge of B from charge per elementary B. ''Q''<sub>''<u>n</u>''B</sub> [CĀ·mol<sup>-1</sup>] is charge per molar amount of B.
|info=[[Gnaiger 2020 MitoPathways]]
|info=[[Gnaiger 2020 BEC MitoPathways]]
}}
}}
__TOC__
__TOC__
Ā  Communicated by [[Gnaiger E]] 2020-11-30
Ā  Communicated by [[Gnaiger E]] (2020-11-30) last update 2022-10-19
:::: The use of SI and IUPAC symbols and units is recommended for clarity and consistency of presenting concepts and reporting data, as far as consistency and disambiguation are implemented in these international conventions.
:::: The use of SI and IUPAC symbols and units is recommended for clarity and consistency of presenting concepts and reporting data, as far as consistency and disambiguation are implemented in these international conventions.


== What do iconic symbols tell us? ==
== What do iconic symbols tell us? ==
''' Protonmotive force '''
''' How did Peter Mitchell coin Ī”p ? '''
:::: Ī”<sub>m</sub>''F''<sub>''<u>e</u>''H<sup>+</sup></sub> [V] is the iconic symbol for protonmotive force in the electrical format with unit [V = JĀ·C<sup>-1</sup>]. Starting from the proton and going clockwise, this can be read as "H+ ''<u>e</u>'' m Ī” ''F''" or "proton \ in electrical format \ motive \ difference \ force", in brief: protonmotive force ''pmF''. If you see the symbol Ī”''p'' as frequently used in bioenergetics, the only iconic aspect is the Ī” indicating a difference, whereas the entire meaning of Ī”''p'' has to be explained to any outsider. Outsiders are insiders in other fields: Ī”''p'' [Pa] is a pressure difference in respiratory medicine and cardiovascular physiology, is a death penalty for professional divers, and is generally a pressure difference in fluid dynamics and the ideal gas equation Ī”''p'' = Ī”''n''Ā·''V''<sup>-1</sup>Ā·''RT''. Why are we content with using a symbol for [[pressure]] when expressing the protonmotive [[force]]? To remove this aspect of ambiguity (= double meaning), Ī”p for the ''pmF'' should replace Ī”''p'', to read 'p' as the IUPAC symbol for the proton, instead of "''p''" for pressure. Since Peter Mitchell used a typewriter for his ''Grey Book'' (1966), italic versus upright font was not a practical option ā€” using <u>underline</u> in place of ''italic'' is tedious. Today, we should use the traditional symbol Ī”p for the ''pmF'' with reference to the proton, and Ī”''p'' for a pressure difference. Or do iconic symbols have a clear advantage in general communication?
:::: Mitchell (1966) introduced the symbol Ī”p for the [[protonmotive force]]. Peter Mitchell received the Nobel Price in Chemistry in 1987 for the underlying concept of the ''pmF''. The symbol Ī”p is unrelated to the ''symbol'' Ī”pH ā€” the symbol [[pH]] stems from the term ''potentia hydrogenii''. What is the message of Ī”p (Gnaiger 2020)?
Ā 
:::: Ī”<sub>m</sub>''F''<sub>''<u>e</u>''H<sup>+</sup></sub> [V] is the iconic symbol for protonmotive force in the electrical [[format]] with unit [V = JĀ·C<sup>-1</sup>]. Starting from the proton and going clockwise, this symbol can be read as "H<sup>+</sup> ''<u>e</u>'' m Ī” ''F''" or "hydrogen ion \ in electrical format \ motive \ difference \ force", in brief: protonmotive force ''pmF''. If you see the symbol Ī”''p'' as frequently used in bioenergetics, the only iconic aspect is the Ī” indicating a difference, whereas the entire meaning of Ī”''p'' has to be explained to any outsider. Outsiders are insiders in other fields: Ī”''p'' [Pa] is a pressure difference in respiratory medicine and cardiovascular physiology, is a death penalty for professional and other high-risk divers, and is generally a pressure difference in fluid dynamics and the ideal gas equation Ī”''p'' = Ī”''n''Ā·''V''<sup>-1</sup>Ā·''RT''. Why are we content with using a symbol for [[pressure]] when expressing the protonmotive [[force]]? To remove this aspect of ambiguity (= double meaning), Michtell's classical Ī”p for the ''pmF'' should be maintained instead of the italicized Ī”''p'', to read 'p' as the IUPAC symbol for the proton, instead of "''p''" for pressure. When Peter Mitchell used a typewriter for his ''Grey Book'' (1966), italic versus upright font was not a practical option ā€” using <u>underline</u> in place of ''italic'' is tedious. Today, we should use the traditional symbol Ī”p for the ''pmF'' with reference to the proton, and Ī”''p'' for a pressure difference. Or do iconic symbols have a clear advantage in general communication?


''' Molar mass and molar volume'''
''' Molar mass and molar volume'''
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:::: Subscript B in ''V''<sub>B</sub> does not imply the meaning 'molar volume' [m<sup>3</sup>Ā·mol<sup>-1</sup>] (comparable to molar mass ''M''<sub>B</sub> [kgĀ·mol<sup>-1</sup>]), but ''V''<sub>B</sub> [m<sup>3</sup>] is the volume of a given quantity of entities B (comparable with ''n''<sub>B</sub>). Therefore, IUPAC uses the ''ad hoc''-symbol ''V''<sub>m,B</sub> [m<sup>3</sup>Ā·mol<sup>-1</sup>] for molar volume of entity B (but not ''M''<sub>m,B</sub> for molar mass).
:::: Subscript B in ''V''<sub>B</sub> does not imply the meaning 'molar volume' [m<sup>3</sup>Ā·mol<sup>-1</sup>] (comparable to molar mass ''M''<sub>B</sub> [kgĀ·mol<sup>-1</sup>]), but ''V''<sub>B</sub> [m<sup>3</sup>] is the volume of a given quantity of entities B (comparable with ''n''<sub>B</sub>). Therefore, IUPAC uses the ''ad hoc''-symbol ''V''<sub>m,B</sub> [m<sup>3</sup>Ā·mol<sup>-1</sup>] for molar volume of entity B (but not ''M''<sub>m,B</sub> for molar mass).


:::: Due to the ambiguity of elements in these symbols and an inconsistent system of symbols, we are forced to memorize these IUPAC symbols like complex Chinese characters. In contrast, iconic symbols are composed of readable letters that carry consistent and visible ā€” iconic ā€” meaning. Iconic symbols follow a visible structure, as far as possible. Once you learn the 'iconic alphabet', you can read a variety of symbols instead of having to learn and memorize each complex symbol separately. The following table illustrates the systematic principle of iconic compared to IUPAC symbols:
:::: Due to the ambiguity of elements in these symbols and an inconsistent system of symbols, we are forced to memorize these IUPAC symbols like complex Chinese characters. In contrast, iconic symbols are composed of readable letters that carry consistent and visible ā€” iconic ā€” meaning. Iconic symbols follow a visible structure, as far as possible. Once you learn the 'iconic alphabet', you can read a variety of symbols like words composed of letters, instead of having to learn and memorize each complex symbol separately. Did Chinese culture exert such an impact on IUPAC, and even more so on all scientists using non-iconic symbols? (This does not imply, that the ~50 000 characters in a standard national Chinese dictionary lack any iconic traces.) The following table illustrates the systematic principle of iconic compared to IUPAC symbols:


:::::: '''Table: Mass and volume ā€” molar mass and molar volume''': Iconic symbols show the quantity, the format ''<u>n</u>'' of the normalization in the subscript, and the entity type B in the subscript. The normalized quantities are '''per''' B. In the quantities ''m''<sub>B</sub>, ''n''<sub>B</sub>, and ''V''<sub>B</sub>, the subscript B without attachment to a format indicates the quantity '''of''' B. Molar count [xĀ·mol<sup>-1</sup>] and molar charge [CĀ·mol<sup>-1</sup>] can be added to the list. The corresponding iconic symbols (''N''<sub><u>''n''</u>B</sub> = ''N''<sub>B</sub>/''n''<sub>B</sub> and ''Q''<sub><u>''n''</u>B</sub> = ''Q''<sub>elB</sub>/''n''<sub>B</sub>) follow suit, but their counterparts of IUPAC symbols (''N''<sub>A</sub> and ''z''<sub>B</sub>Ā·''F''), are far from helping to comprehend the underlying concept.
:::::: '''Table: Mass and volume ā€” molar mass and molar volume''': Iconic symbols show the quantity, the format ''<u>n</u>'' of the normalization in the subscript, and the entity type B in the subscript. The normalized quantities are '''per''' B. In the quantities ''m''<sub>B</sub>, ''n''<sub>B</sub>, and ''V''<sub>B</sub>, the subscript B without attachment to a format indicates the quantity '''of''' B. Molar count [xĀ·mol<sup>-1</sup>] and molar charge [CĀ·mol<sup>-1</sup>] can be added to the list. The corresponding iconic symbols (''N''<sub><u>''n''</u>B</sub> = ''N''<sub>B</sub>/''n''<sub>B</sub> and ''Q''<sub><u>''n''</u>B</sub> = ''Q''<sub>elB</sub>/''n''<sub>B</sub>) follow suit, but their counterparts of IUPAC symbols (''N''<sub>A</sub> and ''z''<sub>B</sub>Ā·''F''), are far from helping to comprehend the underlying concept.
:::::: {| class="wikitable"
:::::: {| class="wikitable"
|-
|-
! Quantity !! Unit !! Normalized for quantity !! Unit !! Iconic symbol !! Unit !! IUPAC symbol !! Quantity
! Quantity !! Unit !! Normalized for amount !! Unit !! Iconic symbol !! Unit !! IUPAC symbol !! Quantity
|-
|-
| mass ''m''<sub>B</sub> || [kg] || / amount ''n''<sub>B</sub> || [mol] || = ''m''<sub><u>''n''</u>B</sub> || [kgĀ·mol<sup>-1</sup>] || ''M''<sub>B</sub> || molar mass Ā 
| mass ''m''<sub>B</sub> || [kg] || / amount ''n''<sub>B</sub> || [mol] || = ''m''<sub><u>''n''</u>B</sub> || [kgĀ·mol<sup>-1</sup>] || ''M''<sub>B</sub> || molar mass Ā 
|-
|-
| volume ''V''<sub>B</sub> || [m<sup>3</sup>] || / amount ''n''<sub>B</sub> || [mol] || = ''V''<sub><u>''n''</u>B</sub> || [m<sup>3</sup>Ā·mol<sup>-1</sup>] || ''V''<sub>m,B</sub> || molar volume
| volume ''V''<sub>B</sub> || [m<sup>3</sup>] || / amount ''n''<sub>B</sub> || [mol] || = ''V''<sub><u>''n''</u>B</sub> || [m<sup>3</sup>Ā·mol<sup>-1</sup>] || ''V''<sub>m,B</sub> || molar volume
|-
| count ''N''<sub>B</sub> || [x] || / amount ''n''<sub>B</sub> || [mol] || = ''N''<sub><u>''n''</u>B</sub> || [xĀ·mol<sup>-1</sup>] || ''N''<sub>A</sub> || molar count; Avogadro constant
|-
| charge ''Q''<sub>elB</sub> || [C] || / amount ''n''<sub>B</sub> || [mol] || = ''Q''<sub><u>''n''</u>B</sub> || [CĀ·mol<sup>-1</sup>] || ''z''<sub>B</sub>Ā·''F'' || molar charge; ''z''<sub>B</sub> Ā· Faraday constant
|}
|}
</div>
</div>
</div>
</div>




== Abbreviation of iconic symbols ==
== Abbreviation of iconic symbols ==
::: Exmaple
::: Exmaple
::::* The symbol Ī”<sub>m</sub>''F''<sub>H<sup>+</sup></sub> [kJĀ·MU<sup>-1</sup>] for the ''pmF'' uses the subscript 'm' to define the partial transformations as m = d+el, accounting for the two partial transformations of chemical diffusion d and electric el. This excludes, therefore, implicitly other possible energy transformations, such as changes in temperature d''T'' or barometric pressure d''p''.
::::* On the other hand, in Ī”<sub>m</sub>''F''<sub>H<sup>+</sup></sub> the contributions of d and el are not distinguished, which requires explicit separation of the partial contributions as Ī”<sub>d</sub>''F''<sub>H<sup>+</sup></sub> (specific for H<sup>+</sup>) and Ī”<sub>el</sub>''F''<sub>p<sup>+</sup></sub> (not specific for H<sup>+</sup> but general for protons or positive charge p<sup>+</sup>). The symbols Ī”<sub>m</sub>''F''<sub>H<sup>+</sup></sub>, Ī”<sub>d</sub>''F''<sub>H<sup>+</sup></sub>, and Ī”<sub>el</sub>''F''<sub>p<sup>+</sup></sub> do not specify the motive unit [MU].
::::* The symbol Ī”<sub>m</sub>''F''<sub>''<u>n</u>''H<sup>+</sup></sub> [kJĀ·mol<sup>-1</sup>] for the ''pmF'' includes the specification of the molar format ''<u>n</u>''. If all quantities are expressed in the molar format in a particular context, then the symbol may be abbreviated as Ī”<sub>m</sub>''F''<sub>H<sup>+</sup></sub> [kJĀ·mol<sup>-1</sup>]. This opens up an ambiguity, since in another context the same abbreviated symbol Ī”<sub>m</sub>''F''<sub>H<sup>+</sup></sub> would indicate the ''pmF'' in the electrical format ''<u>e</u>'' with electrical units [V].
::::* The symbol Ī”<sub>m</sub>''F''<sub>''<u>n</u>''H<sup>+</sup></sub> [kJĀ·mol<sup>-1</sup>] for the ''pmF'' includes the specification of the molar format ''<u>n</u>''. If all quantities are expressed in the molar format in a particular context, then the symbol may be abbreviated as Ī”<sub>m</sub>''F''<sub>H<sup>+</sup></sub> [kJĀ·mol<sup>-1</sup>]. This opens up an ambiguity, since in another context the same abbreviated symbol Ī”<sub>m</sub>''F''<sub>H<sup>+</sup></sub> would indicate the ''pmF'' in the electrical format ''<u>e</u>'' with electrical units [V].
::::* Even the symbol Ī”<sub>m</sub>''F''<sub>''<u>n</u>''H<sup>+</sup></sub> is ambiguous, since the compartmental direction of the ''pmF'' is not specified. A positive or negative numerical value of Ī”<sub>m</sub>''F''<sub>''<u>n</u>''H<sup>+</sup></sub>, therefore, cannot be interpreted without further specification. This is achieved by canonical extension of the iconic symbol as Ī”<sub>m</sub>''F''<sub>''<u>n</u>''H<sup>+</sup>pos</sub>, which indicates the direction from the negative compartment (matrix) to the positive compartment across the mtIM.
::::* Even the symbol Ī”<sub>m</sub>''F''<sub>''<u>n</u>''H<sup>+</sup></sub> is ambiguous, since the compartmental direction of the ''pmF'' is not specified. A positive or negative numerical value of Ī”<sub>m</sub>''F''<sub>''<u>n</u>''H<sup>+</sup></sub>, therefore, cannot be interpreted without further specification. This is achieved by canonical extension of the iconic symbol as Ī”<sub>m</sub>''F''<sub>''<u>n</u>''H<sup>+</sup>pos</sub>, which indicates the direction from the negative compartment (mt-matrix) to the positive compartment across the mtIM.


:::: Abbreviation of iconic symbols in a well-defined context improves readability and shortens impractically long equations.
:::: Abbreviation of iconic symbols in a well-defined context improves readability and shortens impractically long equations.
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== Normalized quantities ==
== Normalized quantities ==
::: Exmaples
::: Exmaples
::::* [[protonmotive force]] Ī”<sub>m</sub>''F''<sub>''<u>e</u>''H+</sub> = ''pmF'' [V]
::::* [[protonmotive force]] Ī”<sub>m</sub>''F''<sub>''<u>e</u>''H<sup>+</sup></sub> = ''pmF'' [V]
::::* [[elementary charge |proton charge]] ''Q''<sub><u>''U''</u>H<sup>+</sup></sub> = ''e'' [CĀ·x<sup>-1</sup>]
::::* [[elementary charge |proton charge]] ''Q''<sub><u>''N''</u>H<sup>+</sup></sub> = ''e'' [CĀ·x<sup>-1</sup>]
::::* [[particle charge]] ''Q<sub><u>U</u>X</sub>'' [CĀ·x<sup>-1</sup>]
::::* [[particle charge]] ''Q<sub><u>N</u>X</sub>'' [CĀ·x<sup>-1</sup>]


Ā 
:::: Iconic symbols show the quantity, the format of the normalization in the subscript (''<u>N</u>'', ''<u>n</u>'', ''<u>e</u>''), and the entity specified in the subscript (''X''). The normalized quantities are '''per''' ''X''. In the quantities ''Q''<sub>el''X''</sub>, ''N<sub>X</sub>'', ''n<sub>X</sub>'', ''V<sub>X</sub>'', ''m<sub>X</sub>'', the subscript ''X'' without attachment to a format indicates the quantity '''of''' ''X''.
:::: Iconic symbols show the quantity, the format of the normalization in the subscript (''<u>U</u>'', ''<u>n</u>'', ''<u>e</u>''), and the entity specified in the subscript (''X''). The normalized quantities are '''per''' ''X''. In the quantities ''Q''<sub>el''X''</sub>, ''N<sub>X</sub>'', ''n<sub>X</sub>'', ''V<sub>X</sub>'', ''m<sub>X</sub>'', the subscript ''X'' without attachment to a format indicates the quantity '''of''' ''X''.
{{Template:Keywords: Charge}}
{{Template:Keywords: Charge}}




== References ==
== References ==
::::# Gnaiger E (2020) Mitochondrial pathways and respiratory control. An introduction to OXPHOS analysis. 5th ed. Bioenerg Commun 2020.2. - [[Gnaiger 2020 MitoPathways |Ā»Bioblast linkĀ«]]
:::# Bureau International des Poids et Mesures (2019) The International System of Units (SI). 9th edition:117-216 ISBN 978-92-822-2272-0. - [[Bureau International des Poids et Mesures 2019 The International System of Units (SI) |Ā»Bioblast linkĀ«]]
::::# Gnaiger Erich (2020) Canonical reviewer's comments on: Bureau International des Poids et Mesures (2019) The International System of Units (SI) 9th ed. MitoFit Preprint Arch 2020.4 [[doi:10.26124/mitofit:200004]]. Ā 
:::# Cohen ER, Cvitas T, Frey JG, Holmstrƶm B, Kuchitsu K, Marquardt R, Mills I, Pavese F, Quack M, Stohner J, Strauss HL, Takami M, Thor HL (2008) Quantities, Units and Symbols in Physical Chemistry. IUPAC Green Book 3rd Edition, 2nd Printing, IUPAC & RSC Publishing, Cambridge. - [[Cohen 2008 IUPAC Green BookĀ  |Ā»Bioblast linkĀ«]]
::::# Grosholz Emily R (2007) Representation and productive ambiguity in mathematics and the sciences. Oxford Univ Press 312 pp. - [[Grosholz 2007 Oxford Univ Press |Ā»Bioblast linkĀ«]]
:::# Gnaiger E (2020) Mitochondrial pathways and respiratory control. An introduction to OXPHOS analysis. 5th ed. Bioenerg Commun 2020.2. - [[Gnaiger 2020 BEC MitoPathways |Ā»Bioblast linkĀ«]]
:::# Gnaiger E (2021) The elementary unit ā€” canonical reviewer's comments on: Bureau International des Poids et Mesures (2019) The International System of Units (SI) 9th ed. MitoFit Preprints 2020.4.v2. https://doi.org/10.26124/mitofit:200004.v2. Ā 
:::# Grosholz ER (2007) Representation and productive ambiguity in mathematics and the sciences. Oxford Univ Press:312 pp. - [[Grosholz 2007 Oxford Univ Press |Ā»Bioblast linkĀ«]]
:::# Mitchell P (1966) Chemiosmotic coupling in oxidative and photosynthetic phosphorylation. Biochim Biophys Acta Bioenergetics 1807 (2011):1507-38. - [[Mitchell 2011 Biochim Biophys Acta |Ā»Bioblast linkĀ«]] ā€“ ''The Grey Book''
Ā 





Latest revision as of 09:47, 19 October 2022


high-resolution terminology - matching measurements at high-resolution


Iconic symbols

Description

Iconic symbols are used in ergodynamics to indicate more explicitely ā€” compared to standard SI or IUPAC symbols ā€” the quantity represented and some boundary conditions. This is particularly the case in normalized quantities (ratios of quantities). Iconic (or canonical) symbols help to clarify the meaning, are based on SI and IUPAC symbols as far as possible, and may be translated into more commonly used, practical symbols. Several ambiguities in SI and IUPAC symbols are eliminated by the systematic structure of iconic symbols, but it may be impossible to avoid all ambiguities, particulary when long (canonical) symbols are abbreviated in a particular context. Clarity is improved always by showing the unit of a quantity together with the symbol of the quantity. Iconic symbols cannot be identical with IUPAC symbols when a different definition is used ā€” this would add to the confusion. For example, the IUPAC symbols nB [mol] and VB [m3] denote amount and volume of B. Consequently, it should be expected, that the symbol QB indicates charge of B [C]. However, the IUPAC symbol QB is used for particle charge per ion B [CĀ·x-1]. This prohibits a consistent definition of QB as a potential iconic symbol for charge carried by a given quantity of ions B with unit [C], instead of particle charge per ion B with unit [CĀ·x-1]. Hence, the conventional ambigous system forces compatible iconic symbols to be more complicated, using QelB [C] and QNB [CĀ·x-1] to distinguish charge of B from charge per elementary B. QnB [CĀ·mol-1] is charge per molar amount of B.


Reference: Gnaiger 2020 BEC MitoPathways

Communicated by Gnaiger E (2020-11-30) last update 2022-10-19
The use of SI and IUPAC symbols and units is recommended for clarity and consistency of presenting concepts and reporting data, as far as consistency and disambiguation are implemented in these international conventions.

What do iconic symbols tell us?

How did Peter Mitchell coin Ī”p ?

Mitchell (1966) introduced the symbol Ī”p for the protonmotive force. Peter Mitchell received the Nobel Price in Chemistry in 1987 for the underlying concept of the pmF. The symbol Ī”p is unrelated to the symbol Ī”pH ā€” the symbol pH stems from the term potentia hydrogenii. What is the message of Ī”p (Gnaiger 2020)?
Ī”mFeH+ [V] is the iconic symbol for protonmotive force in the electrical format with unit [V = JĀ·C-1]. Starting from the proton and going clockwise, this symbol can be read as "H+ e m Ī” F" or "hydrogen ion \ in electrical format \ motive \ difference \ force", in brief: protonmotive force pmF. If you see the symbol Ī”p as frequently used in bioenergetics, the only iconic aspect is the Ī” indicating a difference, whereas the entire meaning of Ī”p has to be explained to any outsider. Outsiders are insiders in other fields: Ī”p [Pa] is a pressure difference in respiratory medicine and cardiovascular physiology, is a death penalty for professional and other high-risk divers, and is generally a pressure difference in fluid dynamics and the ideal gas equation Ī”p = Ī”nĀ·V-1Ā·RT. Why are we content with using a symbol for pressure when expressing the protonmotive force? To remove this aspect of ambiguity (= double meaning), Michtell's classical Ī”p for the pmF should be maintained instead of the italicized Ī”p, to read 'p' as the IUPAC symbol for the proton, instead of "p" for pressure. When Peter Mitchell used a typewriter for his Grey Book (1966), italic versus upright font was not a practical option ā€” using underline in place of italic is tedious. Today, we should use the traditional symbol Ī”p for the pmF with reference to the proton, and Ī”p for a pressure difference. Or do iconic symbols have a clear advantage in general communication?

Molar mass and molar volume

MB is the IUPAC symbol for molar mass of entity B, which is defined for a pure substance as MB = m/nB [kgĀ·mol-1]. Subscript B is ambiguous, indicating "per mole B" in MB, but "of type B" in nB.
Subscript B in VB does not imply the meaning 'molar volume' [m3Ā·mol-1] (comparable to molar mass MB [kgĀ·mol-1]), but VB [m3] is the volume of a given quantity of entities B (comparable with nB). Therefore, IUPAC uses the ad hoc-symbol Vm,B [m3Ā·mol-1] for molar volume of entity B (but not Mm,B for molar mass).
Due to the ambiguity of elements in these symbols and an inconsistent system of symbols, we are forced to memorize these IUPAC symbols like complex Chinese characters. In contrast, iconic symbols are composed of readable letters that carry consistent and visible ā€” iconic ā€” meaning. Iconic symbols follow a visible structure, as far as possible. Once you learn the 'iconic alphabet', you can read a variety of symbols like words composed of letters, instead of having to learn and memorize each complex symbol separately. Did Chinese culture exert such an impact on IUPAC, and even more so on all scientists using non-iconic symbols? (This does not imply, that the ~50 000 characters in a standard national Chinese dictionary lack any iconic traces.) The following table illustrates the systematic principle of iconic compared to IUPAC symbols:
Table: Mass and volume ā€” molar mass and molar volume: Iconic symbols show the quantity, the format n of the normalization in the subscript, and the entity type B in the subscript. The normalized quantities are per B. In the quantities mB, nB, and VB, the subscript B without attachment to a format indicates the quantity of B. Molar count [xĀ·mol-1] and molar charge [CĀ·mol-1] can be added to the list. The corresponding iconic symbols (NnB = NB/nB and QnB = QelB/nB) follow suit, but their counterparts of IUPAC symbols (NA and zBĀ·F), are far from helping to comprehend the underlying concept.
Quantity Unit Normalized for amount Unit Iconic symbol Unit IUPAC symbol Quantity
mass mB [kg] / amount nB [mol] = mnB [kgĀ·mol-1] MB molar mass
volume VB [m3] / amount nB [mol] = VnB [m3Ā·mol-1] Vm,B molar volume
count NB [x] / amount nB [mol] = NnB [xĀ·mol-1] NA molar count; Avogadro constant
charge QelB [C] / amount nB [mol] = QnB [CĀ·mol-1] zBĀ·F molar charge; zB Ā· Faraday constant


Abbreviation of iconic symbols

Exmaple
  • The symbol Ī”mFH+ [kJĀ·MU-1] for the pmF uses the subscript 'm' to define the partial transformations as m = d+el, accounting for the two partial transformations of chemical diffusion d and electric el. This excludes, therefore, implicitly other possible energy transformations, such as changes in temperature dT or barometric pressure dp.
  • On the other hand, in Ī”mFH+ the contributions of d and el are not distinguished, which requires explicit separation of the partial contributions as Ī”dFH+ (specific for H+) and Ī”elFp+ (not specific for H+ but general for protons or positive charge p+). The symbols Ī”mFH+, Ī”dFH+, and Ī”elFp+ do not specify the motive unit [MU].
  • The symbol Ī”mFnH+ [kJĀ·mol-1] for the pmF includes the specification of the molar format n. If all quantities are expressed in the molar format in a particular context, then the symbol may be abbreviated as Ī”mFH+ [kJĀ·mol-1]. This opens up an ambiguity, since in another context the same abbreviated symbol Ī”mFH+ would indicate the pmF in the electrical format e with electrical units [V].
  • Even the symbol Ī”mFnH+ is ambiguous, since the compartmental direction of the pmF is not specified. A positive or negative numerical value of Ī”mFnH+, therefore, cannot be interpreted without further specification. This is achieved by canonical extension of the iconic symbol as Ī”mFnH+pos, which indicates the direction from the negative compartment (mt-matrix) to the positive compartment across the mtIM.
Abbreviation of iconic symbols in a well-defined context improves readability and shortens impractically long equations.


Normalized quantities

Exmaples
Iconic symbols show the quantity, the format of the normalization in the subscript (N, n, e), and the entity specified in the subscript (X). The normalized quantities are per X. In the quantities QelX, NX, nX, VX, mX, the subscript X without attachment to a format indicates the quantity of X.

Canonical comments on IUPAC definitions in the context of charge

Charge of the proton versus charge per proton

Proton charge is the elementary charge e [CĀ·x-1], which is charge per count of protons.
Qel ā‰ Qelp+ [C]
e ā‰ QNp+ = QelĀ·Np+-1  [Cāˆ™x-1]
The distinction of charge of particles versus charge per single particle is not made sufficiently clear by IUPAC, when defining "-e is the charge of an electron" ā€” it must be corrected to "-e is the charge per electron".
For comparison, the name "charge density of electrons" is used by IUPAC with symbol Ļ [CĀ·m-3]. Dividing Ļ by the count concentration of electrons [xĀ·m-3], we obtain the unit [CĀ·x-1] for the electron charge. Therefore, electron charge (or proton charge) is clearly the charge per particle.

Ambiguity of QB

IUPAC (Cohen 2008 IUPAC Green Book) defines the charge number as
IUPAC:  zB = QBĀ·e-1
Therefore, QB = zBāˆ™e. The subscript in QB indicates per elementary entity B. This is opposite to the subscript in VB as the symbol for the volume of a substance of type B (e.g. VO2 [L]). For consistency with this convention, the symbol QelB or QelX [C] is used for indicating charge of a substance of type B or X, distinguished from particle charge as the quantity of charge per elementary entity X with symbol QNX [Cāˆ™x-1]. To avoid too long and multiple subscript levels, QNX is used instead of QUX, and the ā€˜elā€™ is dropped from QelNX. The particle charge QNH+ per hydrogen ion is identical to the definition of the elementary charge e. Therefore, the charge number of the hydrogen ion is zH+ = QNH+/e = 1. In summary:
zB = QNBĀ·e-1
QNB = QelBĀ·NB-1 [Cāˆ™x-1]


Keywords

Ā» charge QelX
Ā» charge number zX
Ā» electrochemical constant f
Ā» elementary charge e
Ā» Faraday constant F
Ā» hydrogen ion versus proton
Ā» iconic symbols
Ā» motive entity
Ā» particle charge QNX


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Normalization of charge and iconic symbols
Iconic symbols show the quantity, the format of the normalization in the subscript (N, n, e), and the entity specified in the subscript (X). The normalized quantities are per X. In the quantities QelX, NX, nX, VX, mX, the subscript X without attachment to a format indicates the quantity of X.
Quantity Unit Normalized for quantity Unit Iconic symbol Unit Practical symbol Quantity
charge QelX [C] / count NX [x] = QNX [CĀ·x-1] particle charge (IUPAC: QB)
charge QelX [C] / amount nX [mol] = QnX [CĀ·mol-1] charge number times Faraday constant
charge QelX [C] / volume VX [m3] = QVX [CĀ·m-3] Ļel charge density
charge QelX [C] / mass mX [kg] = QmX [CĀ·kg-1] specific charge
count NX [x] / charge QelX [C] = NeX [xĀ·C-1]
amount nX [mol] / charge QelX [C] = neX [molĀ·C-1]
volume VX [m3] / charge QelX [C] = VeX [m3Ā·C-1] Ļel-1
mass mX [kg] / charge QelX [C] = meX [kgĀ·C-1]



References

  1. Bureau International des Poids et Mesures (2019) The International System of Units (SI). 9th edition:117-216 ISBN 978-92-822-2272-0. - Ā»Bioblast linkĀ«
  2. Cohen ER, Cvitas T, Frey JG, Holmstrƶm B, Kuchitsu K, Marquardt R, Mills I, Pavese F, Quack M, Stohner J, Strauss HL, Takami M, Thor HL (2008) Quantities, Units and Symbols in Physical Chemistry. IUPAC Green Book 3rd Edition, 2nd Printing, IUPAC & RSC Publishing, Cambridge. - Ā»Bioblast linkĀ«
  3. Gnaiger E (2020) Mitochondrial pathways and respiratory control. An introduction to OXPHOS analysis. 5th ed. Bioenerg Commun 2020.2. - Ā»Bioblast linkĀ«
  4. Gnaiger E (2021) The elementary unit ā€” canonical reviewer's comments on: Bureau International des Poids et Mesures (2019) The International System of Units (SI) 9th ed. MitoFit Preprints 2020.4.v2. https://doi.org/10.26124/mitofit:200004.v2.
  5. Grosholz ER (2007) Representation and productive ambiguity in mathematics and the sciences. Oxford Univ Press:312 pp. - Ā»Bioblast linkĀ«
  6. Mitchell P (1966) Chemiosmotic coupling in oxidative and photosynthetic phosphorylation. Biochim Biophys Acta Bioenergetics 1807 (2011):1507-38. - Ā»Bioblast linkĀ« ā€“ The Grey Book



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