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Units

SBML has support for units in all quantities. The units are specified using these 4 properties: kind, scale, multiplier, and exponent . These unit attributes are interpreted like this:

(multiplier * kind * 10^scale)^exponent

or, if you prefer:

power(prod(multiplier,kind,power(10.0,scale)),exponent)

The kind can be any SI base unit, e.g. second. Other units can be derived using products of these base units, liter/(nanomole millisecond) is expressed as:

<unitDefinition id="liter_per_nanomole_millisecond">
 <listOfUnits>
  <unit kind="litre" exponent="1" scale="0" multiplier="1"/>
  <unit kind="mole" exponent="-1" scale="-9" multiplier="1"/>
  <unit kind="second" exponent="-1" scale="-3" multiplier="1"/>
 </listOfUnits>
</unitDefinition>

In SBtab files, units are written in a more human readable form (!Unit column) and it is not always trivial to interpret those units. The R program in this repository attempts to read the units using a regular expression with sub-groups. To make it somewhat doable, we have additional rules on unit-strings:

  1. Only SI base units are allowed for now
    • derived units such as Newton or Hz are not understood (liter is the only exception)
    • not all SI prefixes are understood, but the most common ones are (G,M,k,c,m,µ,n,p,f)
  2. Only one slash is allowed (the slash has the lowest precedence)
    • liter / mole second is ok
    • 1/((mole/liter) * second) is not ok (because it has two slashes)
    • multiplication has higher precedence than division
  3. All parentheses are ignored
    • (mole/liter)^(-1) is not interpreted correctly, because parentheses will be ignored
    • liter/mole second is the same as liter/(mole second)
    • * and ␣ are the same (blank space is interpreted as multiplication)
  4. Powers cannot have spaces between base and exponent, the ^ is optional
    • s^2 is ok
    • s2 is ok and means the same thing
    • kg m s^(-2) is ok and the same as kg m s^-2
    • kg m s-2 is also ok and means the same as kg m s^-2
    • cm2 is ok and means square centimeters
    • kg m s^( -2 ) is not ok (spaces)
  5. The literal "1" is interpreted as: this quantity is dimensionless (in sbml this is actually called dimensionless)
    • a 1 in a unit will reappear in sbml, even if unnecessary
    • 1 m / 1 s will have 4 entries in the sbml unit definition, with two unnecessary dimensionless units
    • 1/s will be the same as s^-1 in effect, but 1/s will have an unnecessary dimensionless unit entry in the definition
    • no simplification of the unit is performed, so meter/meter is not simplified to 1
  6. long words can be used as well as abbreviations
    • millisecond is ok
    • ms is also ok
    • msecond (probably) also ok (but weird)
  7. we don't have a system for multipliers. They are used to convert to and from non SI systems (imperial)
    • inches and feet are not multiples of SI base units, so are not processed by this parser.
    • we don't plan to support non SI units later, unless it becomes necessary
  8. The units that are not understood, but don't lead to a crash/error in the R code are interpreted as 1
    • the user can later correct those definitions in the output (sbml) file by hand (using a normal text editor)

Because we use a simple regular expression to parse units, the base unit for mass is g (not kg, it's a bit of an exception in the système international). Here is the regular expression, possibly not up to date:

pat <- paste0("^(G|giga|M|mega|k|kilo|c|centi|m|milli|u|μ|micro|n|nano|p|pico|f|femto)?",
	          "(l|L|liter|litre|g|gram|mole?|s|second|m|meter|metre|K|kelvin|cd|candela|A|ampere)",
	          "\\^?([-+]?[0-9]+)?$")

A list of perfectly fine units

Newton, Hertz and M are not parsed automatically, use the long form in column 2.

meaning suggested string kind scale exponent
Newton kg m s-2 "gram" +3 1
"metre" 1 1
"second" 1 -2
nanomolarity (nM) nmol/l "mole" -9 1
"litre" 1 -1
kHz ms^-1 "second" -3 -1

Please be aware that the SBML units themselves are not always interpreted right by SBML importers (in other software). So, not always is it an error of this script if a different software displays a different unit than was intended.

Note that kHz is a bit unusual as Hertz is reciprocal to a base unit (second), so kHz is written as 1000/s = 1/0.001 s = ms^-1 once broken down to base units.

NEURON

Some software, including NEURON has units imposed by the environment in which the subcellular model is embedded. So the units are expected to be compaible to the simulator.

In this case the user must write a model file using those imposed units.

Of course, this becomes impossible, once a second simulator imposes a different set of units. To maintain compatibilty between the two, using only one model file, it is perhaps possible to use the Expression mechanism. But the model will become a lot less readable.

So, it would be better, if an output unit could be requested (for autmoatic transformation). This is not easy and currently not implemented.