Iconic symbols

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Iconic symbols

Description

Iconic symbols are used in ergodynamics to indicate more explicitely — compared to standard SI or IUPAC symbols — 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 further improved by showing the unit of a quantity together with the iconic symbol of the quantity.

Reference: Gnaiger 2020 MitoPathways

Communicated by Gnaiger E 2020-11-29

Abbreviation of iconic symbols

Exmaple

• The symbol Δ_mF_nH⁺ [kJ·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 Δ_mF_H⁺ [kJ·mol^-1]. This opens up an ambiguity, since in another context the same abbreviated symbol Δ_mF_H⁺ would indicate the pmF in the electrical format e with electrical units [V].
• Even the symbol Δ_mF_nH⁺ is ambiguous, since the compartmental direction of the pmF is not specified. A positive or negative numerical value of Δ_mF_nH⁺, therefore, cannot be interpreted without further specification. This is achieved by canonical extension of the iconic symbol as Δ_mF_nH⁺pos, which indicates the direction from the negative compartment (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

• protonmotive force Δ_mF_eH+ = pmF [V]
• proton charge Q_UH⁺ = e [C·x^-1]
• particle charge Q_UX [C·x^-1]

Iconic symbols show the quantity, the format of the normalization in the subscript (U, n, e), and the entity specified in the subscript (X). The normalized quantities are per X. In the quantities Q_elX, N_X, n_X, V_X, m_X, 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 [C·x^-1], which is charge per count of protons.

Qel ≝ Qelp+ [C]

e ≝ QNp+ = Qel·Np+-1  [C∙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" — 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 ρ [C·m^-3]. Dividing ρ by the count concentration of electrons [x·m^-3], we obtain the unit [C·x^-1] for the electron charge. Therefore, electron charge (or proton charge) is clearly the charge per particle.

Ambiguity of Q_B

IUPAC (Cohen 2008 IUPAC Green Book) defines the charge number as

IUPAC:  zB = QB·e-1

Therefore, Q_B = z_B∙e. The subscript in Q_B indicates per elementary entity B. This is opposite to the subscript in V_B as the symbol for the volume of a substance of type B (e.g. V_O2 [L]). For consistency with this convention, the symbol Q_elB or Q_elX [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 Q_NX [C∙x^-1]. To avoid too long and multiple subscript levels, Q_NX is used instead of Q_UX, and the ‘el’ is dropped from Q_elNX. The particle charge Q_NH⁺ per hydrogen ion is identical to the definition of the elementary charge e. Therefore, the charge number of the hydrogen ion is z_H⁺ = Q_NH⁺/e = 1. In summary:

zB = QNB·e-1

QNB = QelB·NB-1 [C∙x-1]

Keywords

» charge Q_elX

» charge number z_X

» electrochemical constant f

» elementary charge e

» Faraday constant F

» hydrogen ion versus proton

» iconic symbols

» motive entity

» particle charge Q_NX

Bioblast links: Charge - >>>>>>> - Click on [Expand] or [Collapse] - >>>>>>>

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 Q_elX, N_X, n_X, V_X, m_X, 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	[C·x-1]		particle charge (IUPAC: QB)
charge QelX	[C]	/ amount nX	[mol]	= QnX	[C·mol-1]		charge number times Faraday constant
charge QelX	[C]	/ volume VX	[m3]	= QVX	[C·m-3]	ρel	charge density
charge QelX	[C]	/ mass mX	[kg]	= QmX	[C·kg-1]		specific charge
count NX	[x]	/ charge QelX	[C]	= NeX	[x·C-1]
amount nX	[mol]	/ charge QelX	[C]	= neX	[mol·C-1]
volume VX	[m3]	/ charge QelX	[C]	= VeX	[m3·C-1]	ρel-1
mass mX	[kg]	/ charge QelX	[C]	= meX	[kg·C-1]

References

1. Gnaiger E (2020) Mitochondrial pathways and respiratory control. An introduction to OXPHOS analysis. 5th ed. Bioenerg Commun 2020.2. - »Bioblast link«
2. 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.
3. Grosholz Emily R (2007) Representation and productive ambiguity in mathematics and the sciences. Oxford Univ Press 312 pp. - »Bioblast link«

MitoPedia concepts: Ergodynamics