Getting started with r2sbml

r2sbml is a thin R interface to libSBML, built with Rcpp. It does two things:

  1. Reads an SBML model and lets you query its components from R — species, compartments, parameters, reactions, rules, events and function definitions.
  2. Exports the model’s mass balances as ready-to-simulate code for six ODE targets: deSolve, mrgsolve, rxode2/nlmixr2, MATLAB, Julia and ubiquity.

It does not let you modify a model. There is no setter API and no way to write SBML back out; r2sbml reads and exports.

libSBML itself is bundled with the package and compiled from source during installation, so nothing needs to be installed separately and the build downloads nothing. See the README for the compiler and header prerequisites.

library(r2sbml)

Ten small example models ship with the package and are used throughout this vignette:

basename(list.files(system.file("examples", package = "r2sbml"), pattern = "[.]xml$"))
#>  [1] "sbmlalgebraicrules.xml"              
#>  [2] "sbmlassignmentrules.xml"             
#>  [3] "sbmlboundaryconditions.xml"          
#>  [4] "sbmlconversionfactor-alternative.xml"
#>  [5] "sbmlconversionfactor.xml"            
#>  [6] "sbmldelay.xml"                       
#>  [7] "sbmlevent.xml"                       
#>  [8] "sbmlfunctiondefinition.xml"          
#>  [9] "sbmlmutlicompartment.xml"            
#> [10] "sbmlsimple.xml"

Reading a model

Everything except convertReactions() works in two phases. First getModel() reads the file, keeps the underlying SBMLDocument alive, and hands back an external pointer:

sbml_file <- system.file("examples", "sbmlsimple.xml", package = "r2sbml")
model <- getModel(sbml_file)
#> 
#>   filename: /tmp/RtmpBPkfzA/Rinst1a8b63fe45a0f/r2sbml/examples/sbmlsimple.xml
#>   error(s): 0
#> 
#> 
#> File: /tmp/RtmpBPkfzA/Rinst1a8b63fe45a0f/r2sbml/examples/sbmlsimple.xml (Level 3, version 2)
class(model)
#> [1] "externalptr"

getModel() prints a short header as a side effect — the file it read, how many SBML errors it found, and the Level/Version of the document. Errors are fatal: it prints them and stops, naming the file, rather than handing back a pointer you cannot trust. Warnings and informational diagnostics are not fatal — they are reported as an R warning and the model still loads, which is the same rule convertReactions() applies.

Reading is not validation. libSBML reports parse-level and structural problems as it reads, but getModel() does not run a consistency check, so a file that loads cleanly can still be semantically questionable — inconsistent units, say. r2sbml never validates a model.

Every query function then takes that pointer as its only argument.

Functions that return data

getSpeciesTable(model)
#>   Number Name ID InitialConcentration InitialAmount Compartment CompartmentVol
#> 1      1       E                  NaN         5e-21        comp          1e-14
#> 2      2       S                  NaN         1e-20        comp          1e-14
#> 3      3       P                  NaN         0e+00        comp          1e-14
#> 4      4      ES                  NaN         0e+00        comp          1e-14
#>   BoundaryCondition Constant
#> 1                 0    FALSE
#> 2                 0    FALSE
#> 3                 0    FALSE
#> 4                 0    FALSE

getReactionTable(model)
#>   Number   ID Name Reversible                          RateLaw
#> 1      1  veq            TRUE comp * (kon * E * S - koff * ES)
#> 2      2 vcat           FALSE                 comp * kcat * ES

getSpeciesTable() reports both InitialConcentration and InitialAmount columns. An SBML species carries one or the other, never both, and the unset one reads back as NaN — so the NaN column above is telling you this model is amount-based, not that anything is wrong.

Simpler accessors return plain vectors:

getCmtNames(model)
#> [1] "comp"
getCmtSizes(model)
#> [1] 1e-14
getNumSpecies(model)
#> [1] 4

The full set of data-returning functions:

Function Returns
getSpeciesTable(), getParameterTable(), getReactionTable() a data.frame
getSpeciesNames(), getCmtNames() a character vector
getSpeciesIC(), getCmtSizes() a numeric vector
getNumSpecies() an integer

getSpeciesIC() reports whichever of initialAmount or initialConcentration the model sets, named by species id, and applies no unit conversion — unlike convertReactions(), which must divide an amount by the compartment volume because the ODE it writes integrates concentrations. getSpeciesNames() and getCmtNames() return the SBML name where one is set and fall back to the id otherwise. See vignette("limitations", package = "r2sbml") for both.

Functions that print

A second family writes to the console and returns 0 invisibly. Assigning them gets you the 0, not the text, so capture them instead:

rules_model <- getModel(system.file("examples", "sbmlassignmentrules.xml",
                                    package = "r2sbml"))
#> 
#>   filename: /tmp/RtmpBPkfzA/Rinst1a8b63fe45a0f/r2sbml/examples/sbmlassignmentrules.xml
#>   error(s): 0
#> 
#> 
#> File: /tmp/RtmpBPkfzA/Rinst1a8b63fe45a0f/r2sbml/examples/sbmlassignmentrules.xml (Level 3, version 2)
getRuleMath(rules_model)
#> Rule 0, formula: S1 = T / (1 + Keq)
#> Rule 1, formula: S2 = Keq * S1
#> [1] 0
txt <- capture.output(getReactionMath(model))
txt
#> [1] "Reaction 0, formula: comp * (kon * E * S - koff * ES)"
#> [2] "Reaction 1, formula: comp * kcat * ES"                
#> [3] "[1] 0"
Function Prints
getRuleMath() assignment, rate and algebraic rules
getReactionMath() kinetic laws
getFunctionDefinition() function definitions
getEventMath() event triggers, delays and assignments
printSBML(), echoSBML() the document itself

printSBML() and echoSBML() are the exception to the two-phase rule: they take a filename, not a model pointer.

Absent components are an error, not an empty result

A query for a component the model does not have raises an error. It does not return a zero-row data frame or a zero-length vector:

# sbmlsimple.xml has no rules at all
getRuleMath(model)
#> Error:
#> ! No Rules present in the model.

The error names the component that was missing, so a caller can tell the cases apart. If you are looping over many models, wrap the call:

safely <- function(expr) tryCatch(expr, error = function(e) NULL)
files  <- list.files(system.file("examples", package = "r2sbml"),
                     pattern = "[.]xml$", full.names = TRUE)

has_rules <- vapply(files, function(f) {
  !is.null(safely(capture.output(getRuleMath(getModel(f)))))
}, logical(1))
data.frame(model = basename(files), has_rules = unname(has_rules))
#>                                   model has_rules
#> 1                sbmlalgebraicrules.xml      TRUE
#> 2               sbmlassignmentrules.xml      TRUE
#> 3            sbmlboundaryconditions.xml      TRUE
#> 4  sbmlconversionfactor-alternative.xml     FALSE
#> 5              sbmlconversionfactor.xml     FALSE
#> 6                         sbmldelay.xml      TRUE
#> 7                         sbmlevent.xml      TRUE
#> 8            sbmlfunctiondefinition.xml     FALSE
#> 9              sbmlmutlicompartment.xml     FALSE
#> 10                       sbmlsimple.xml     FALSE

The same applies to getParameterTable() on a model whose parameters are all local to its kinetic laws — sbmlsimple.xml is exactly that case.

Exporting mass balances

convertReactions() is the other half of the package, and the one function that does not take a model pointer. It reads the SBML file itself and writes a code file, returning NULL invisibly:

out_r <- tempfile(fileext = ".R")
convertReactions(sbml_file, out_r, format = "R")
#> Conversion completed.
#> Number of ODEs - 4
format Target
"R" or "deSolve" (default) deSolve
"mrgsolve" mrgsolve
"nlmixr2" or "rxode2" rxode2 / nlmixr2
"MATLAB" or "matlab" a function file for ode15s
"Julia" or "julia" an ODEProblem for DifferentialEquations.jl
"ubiquity" or "Ubiquity" a ubiquity system file

An unrecognised format is an error, so a typo cannot leave you with an empty file that looks like a successful conversion:

convertReactions(sbml_file, tempfile(), format = "fortran")
#> Conversion completed.
#> Number of ODEs - 4
#> Error:
#> ! Unknown format 'fortran'. Use one of 'R'/'deSolve', 'mrgsolve', 'nlmixr2'/'rxode2', 'MATLAB', 'Julia' or 'ubiquity'.

What happens before anything is written

convertReactions() applies four libSBML converters in sequence:

  1. replaceReactions — every reaction becomes a rate rule
  2. promoteLocalParameters — parameters local to a kinetic law become global
  3. expandInitialAssignments — initial assignments are folded into values
  4. expandFunctionDefinitions — user-defined functions are inlined

By the time a writer runs, the model is in rate-rule form with no local parameters and no function definitions left. That is why the generated code never contains a function definition, and why parameters that were buried inside a kinetic law appear as top-level constants.

The deSolve output

cat(readLines(out_r), sep = "\n")
#> ## Automatically generated model file by r2sbml at 
#> ## Writing the model ODEs for solving in R
#> ## Solving the model requires desolve package 
#> 
#> ## Model Summary 
#> ## functionDefinitions: 0
#> ##     unitDefinitions: 2
#> ##    compartmentTypes: 0
#> ##        speciesTypes: 0
#> ##        compartments: 1
#> ##             species: 4
#> ##          parameters: 3
#> ##  initialAssignments: 0
#> ##               rules: 4
#> ##         constraints: 0
#> ##           reactions: 0
#> ##              events: 0
#> 
#> ## Load required packages
#> library(deSolve)
#> 
#> ## Units Definitions
#> ## per_second: Kind=, : Exponent=-1
#> ## litre_per_mole_second: Kind=, : Exponent=-1
#> ## litre_per_mole_second: Kind=, : Exponent=1
#> ## litre_per_mole_second: Kind=, : Exponent=-1
#> 
#> ## Compartments 
#> comp = 1e-14
#> 
#> ## Initial Amounts
#> InitialAmounts <- c(
#>          E = 5e-07,
#>          S = 1e-06,
#>          P = 0,
#>          ES = 0
#>                     )
#> 
#> ## Parameters
#> parameters <- c(
#>          veq_koff = 0.2,
#>          veq_kon = 1e+06,
#>          vcat_kcat = 0.1
#>                )
#> 
#> ## Reactions 
#> 
#> ## Mass-Balances (ODEs)
#> massBalances <- function(time, states, params){
#> 
#>    ## Get States Names 
#>    E = states[["E"]]
#>    S = states[["S"]]
#>    P = states[["P"]]
#>    ES = states[["ES"]]
#> 
#>    ## Get Parameter Names 
#>    veq_koff = params[["veq_koff"]]
#>    veq_kon = params[["veq_kon"]]
#>    vcat_kcat = params[["vcat_kcat"]]
#> 
#>    ## Mass Balances
#>    dE_dt = -1 * (comp * (veq_kon * E * S - veq_koff * ES) / comp) + comp * vcat_kcat * ES / comp
#>    dS_dt = -1 * (comp * (veq_kon * E * S - veq_koff * ES) / comp)
#>    dP_dt = comp * vcat_kcat * ES / comp
#>    dES_dt = comp * (veq_kon * E * S - veq_koff * ES) / comp + -1 * (comp * vcat_kcat * ES / comp)
#> 
#>    ## Make a list of Mass Balances
#>    MassBalances <- c(
#>      dE_dt ,
#>      dS_dt ,
#>      dP_dt ,
#>      dES_dt
#>    )
#>    return(list(MassBalances))
#> 
#> }

Three things in that file are worth pointing out.

The state vector is decided deliberately. It is not simply “one equation per rule”. A species set by an assignment rule is computed inside the right-hand side and given no slot, because its value follows from the rule at every time point. A species with no rate rule — a boundary condition, or one in no reaction — keeps its slot with a zero derivative so it still appears in the solution.

Initial conditions are converted into the units the ODE integrates. An SBML species symbol is a concentration unless hasOnlySubstanceUnits is set, and the rate rules are divided by the compartment volume to match. sbmlsimple.xml declares initialAmount = 5e-21 in a 1e-14 compartment, so the generated initial condition is 5e-07, not 5e-21. The volume used is the species’ own compartment’s, so a multi-compartment model rescales species individually.

Compartment volumes are emitted as plain constants when they are constant. If a compartment carries a rate rule instead, it joins the state vector and is integrated — see “Changing compartment volumes” below.

You can run the result directly:

library(deSolve)

env <- new.env()
source(out_r, local = env)

solution <- ode(y     = env$InitialAmounts,
                times = seq(0, 5, by = 1),
                func  = env$massBalances,
                parms = env$parameters)
round(solution, 9)
#>   time        E        S        P       ES
#> 1    0 5.00e-07 1.00e-06 0.00e+00 0.00e+00
#> 2    1 2.51e-07 7.36e-07 1.60e-08 2.49e-07
#> 3    2 1.90e-07 6.46e-07 4.40e-08 3.10e-07
#> 4    3 1.74e-07 5.98e-07 7.60e-08 3.26e-07
#> 5    4 1.72e-07 5.63e-07 1.09e-07 3.28e-07
#> 6    5 1.75e-07 5.34e-07 1.42e-07 3.25e-07
# free + bound enzyme is conserved, and so is total substrate
d <- as.data.frame(solution)
range(d$E + d$ES)
#> [1] 5e-07 5e-07
range(d$S + d$ES + d$P)
#> [1] 1e-06 1e-06

The other five targets

Each target gets its own spelling of the same mathematics.

out_mrg <- tempfile(fileext = ".cpp")
convertReactions(sbml_file, out_mrg, format = "mrgsolve")
#> Conversion completed.
#> Number of ODEs - 4
cat(readLines(out_mrg), sep = "\n")
#> ## Automatically generated mrgsolve model file by r2sbml
#> 
#> $PROB
#> 
#> $PARAM
#> veq_koff = 0.2
#> veq_kon = 1e+06
#> vcat_kcat = 0.1
#> 
#> $CMT
#> E
#> S
#> P
#> ES
#> 
#> $MAIN
#> E_0 = 5e-07;
#> S_0 = 1e-06;
#> P_0 = 0;
#> ES_0 = 0;
#> double comp = 1e-14;
#> 
#> $ODE
#> dxdt_E = -1.0 * (comp * (veq_kon * E * S - veq_koff * ES) / comp) + comp * vcat_kcat * ES / comp;
#> dxdt_S = -1.0 * (comp * (veq_kon * E * S - veq_koff * ES) / comp);
#> dxdt_P = comp * vcat_kcat * ES / comp;
#> dxdt_ES = comp * (veq_kon * E * S - veq_koff * ES) / comp + -1.0 * (comp * vcat_kcat * ES / comp);

mrgsolve model blocks are C++, where ^ is bitwise XOR and does not compile for doubles, so powers are written pow(a, b) for this target alone.

out_rx <- tempfile(fileext = ".R")
convertReactions(sbml_file, out_rx, format = "nlmixr2")
#> Conversion completed.
#> Number of ODEs - 4
cat(readLines(out_rx), sep = "\n")
#> ## Automatically generated nlmixr2/rxode model file by r2sbml
#> 
#> model <- function() {
#>   ini({
#>     veq_koff <- 0.2
#>     veq_kon <- 1e+06
#>     vcat_kcat <- 0.1
#>   })
#>   model({
#>     comp <- 1e-14
#>     E(0) <- 5e-07
#>     S(0) <- 1e-06
#>     P(0) <- 0
#>     ES(0) <- 0
#> 
#>     d/dt(E) <- -1 * (comp * (veq_kon * E * S - veq_koff * ES) / comp) + comp * vcat_kcat * ES / comp
#>     d/dt(S) <- -1 * (comp * (veq_kon * E * S - veq_koff * ES) / comp)
#>     d/dt(P) <- comp * vcat_kcat * ES / comp
#>     d/dt(ES) <- comp * (veq_kon * E * S - veq_koff * ES) / comp + -1 * (comp * vcat_kcat * ES / comp)
#>   })
#> }
out_m <- tempfile(fileext = ".m")
convertReactions(sbml_file, out_m, format = "MATLAB")
#> Conversion completed.
#> Number of ODEs - 4
cat(readLines(out_m), sep = "\n")
#> % Automatically generated MATLAB model file by r2sbml
#> %
#> % Save as file1b952307e6d.m, then solve with:  [t, y] = file1b952307e6d();
#> % Columns of y are, in order: E, S, P, ES
#> %
#> % Model Summary
#> %        compartments: 1
#> %             species: 4
#> %          parameters: 3
#> %               rules: 4
#> %              events: 0
#> 
#> function [t, y] = file1b952307e6d(tspan, y0)
#> 
#>     if nargin < 1 || isempty(tspan)
#>         tspan = [0 10];
#>     end
#> 
#>     % Compartments
#>     comp = 1e-14;
#> 
#>     % Parameters
#>     veq_koff = 0.2;
#>     veq_kon = 1000000;
#>     vcat_kcat = 0.1;
#> 
#>     % Initial amounts
#>     if nargin < 2 || isempty(y0)
#>         y0 = [ ...
#>             5e-07; % E
#>             1e-06; % S
#>             0; % P
#>             0; % ES
#>         ];
#>     end
#> 
#>     [t, y] = ode15s(@massBalances, tspan, y0);
#> 
#>     function dydt = massBalances(time, states)
#> 
#>         % States
#>         E = states(1);
#>         S = states(2);
#>         P = states(3);
#>         ES = states(4);
#> 
#>         % Mass balances
#>         dydt = zeros(4, 1);
#>         dydt(1) = -1 * (comp * (veq_kon * E * S - veq_koff * ES) / comp) + comp * vcat_kcat * ES / comp; % E
#>         dydt(2) = -1 * (comp * (veq_kon * E * S - veq_koff * ES) / comp); % S
#>         dydt(3) = comp * vcat_kcat * ES / comp; % P
#>         dydt(4) = comp * (veq_kon * E * S - veq_koff * ES) / comp + -1 * (comp * vcat_kcat * ES / comp); % ES
#> 
#>     end
#> end

MATLAB resolves a function by file name, so the generated function is named after the output path you gave. Renaming the .m file breaks it — regenerate instead of renaming.

out_jl <- tempfile(fileext = ".jl")
convertReactions(sbml_file, out_jl, format = "Julia")
#> Conversion completed.
#> Number of ODEs - 4
cat(readLines(out_jl), sep = "\n")
#> # Automatically generated Julia model file by r2sbml
#> #
#> # Solve with:  using DifferentialEquations; sol = solve(prob)
#> # Elements of u are, in order: E, S, P, ES
#> #
#> # Model Summary
#> #        compartments: 1
#> #             species: 4
#> #          parameters: 3
#> #               rules: 4
#> #              events: 0
#> 
#> using DifferentialEquations
#> 
#> function massbalances!(du, u, p, t)
#> 
#>     time = t
#> 
#>     # Compartments
#>     comp = 1e-14
#> 
#>     # Parameters
#>     veq_koff = p[1]
#>     veq_kon = p[2]
#>     vcat_kcat = p[3]
#> 
#>     # States
#>     E = u[1]
#>     S = u[2]
#>     P = u[3]
#>     ES = u[4]
#> 
#>     # Mass balances
#>     du[1] = -1 * (comp * (veq_kon * E * S - veq_koff * ES) / comp) + comp * vcat_kcat * ES / comp  # E
#>     du[2] = -1 * (comp * (veq_kon * E * S - veq_koff * ES) / comp)  # S
#>     du[3] = comp * vcat_kcat * ES / comp  # P
#>     du[4] = comp * (veq_kon * E * S - veq_koff * ES) / comp + -1 * (comp * vcat_kcat * ES / comp)  # ES
#> 
#>     return nothing
#> end
#> 
#> u0 = Float64[5e-07, 1e-06, 0, 0]
#> p = Float64[0.2, 1000000, 0.1]
#> tspan = (0.0, 10.0)
#> prob = ODEProblem(massbalances!, u0, tspan, p)
out_ub <- tempfile(fileext = ".txt")
convertReactions(sbml_file, out_ub, format = "ubiquity")
#> Conversion completed.
#> Number of ODEs - 4
cat(readLines(out_ub), sep = "\n")
#> # Automatically generated ubiquity system file by r2sbml
#> #
#> # Build with:  cfg <- build_system(system_file = "<this file>")
#> #
#> # Model Summary
#> #        compartments: 1
#> #             species: 4
#> #          parameters: 3
#> #               rules: 4
#> #              events: 0
#> 
#> # Compartment volumes
#> <P> comp 1e-14 -inf inf litre yes System
#> 
#> # Parameters
#> <P> veq_koff 0.2 -inf inf per_second yes System
#> <P> veq_kon 1000000 -inf inf litre_per_mole_second yes System
#> <P> vcat_kcat 0.1 -inf inf per_second yes System
#> 
#> # Initial conditions
#> <I> E = 5e-07
#> <I> S = 1e-06
#> <I> P = 0
#> <I> ES = 0
#> 
#> # Mass balances
#> <ODE:E> (((-1.0)*((comp*(((veq_kon*E)*S)-(veq_koff*ES)))/comp))+(((comp*vcat_kcat)*ES)/comp))
#> <ODE:S> ((-1.0)*((comp*(((veq_kon*E)*S)-(veq_koff*ES)))/comp))
#> <ODE:P> (((comp*vcat_kcat)*ES)/comp)
#> <ODE:ES> (((comp*(((veq_kon*E)*S)-(veq_koff*ES)))/comp)+((-1.0)*(((comp*vcat_kcat)*ES)/comp)))
#> 
#> # Outputs
#> <O> E_out = E
#> <O> S_out = S
#> <O> P_out = P
#> <O> ES_out = ES

ubiquity has no compartment concept of its own, so a compartment volume becomes an ordinary <P> constant that the rate expressions divide by. It also spells exponentiation, the transcendental functions and every comparison as bracketed prefix calls — SIMINT_POWER[a][b], SIMINT_LOGN[a], SIMINT_GT[a][b] — which is why its output looks so different from the rest.

Parameter bounds are written -inf inf rather than the eps inf you may have seen in hand-written ubiquity systems: an SBML value may legitimately be zero or negative, and a lower bound above the value would be inconsistent. They matter only for estimation.

Model features that change the shape of the output

Assignment rules

A species driven by an assignment rule is not integrated. It is recomputed inside the right-hand side, before the derivatives that read it:

assign_file <- system.file("examples", "sbmlassignmentrules.xml", package = "r2sbml")
out_assign  <- tempfile(fileext = ".R")
convertReactions(assign_file, out_assign, format = "R")
#> Conversion completed.
#> Number of ODEs - 5

lines <- readLines(out_assign)
cat(lines[grep("Assignment Rules", lines):length(lines)], sep = "\n")
#>    ## Assignment Rules
#>    S1 = T / (1 + Keq)
#>    S2 = Keq * S1
#> 
#>    ## Mass Balances
#>    dX0_dt = -1 * (in_k1 * X0 * cell / cell)
#>    dX1_dt = out_k2 * S2 * cell / cell
#>    dT_dt = in_k1 * X0 * cell / cell + -1 * (out_k2 * S2 * cell / cell)
#> 
#>    ## Make a list of Mass Balances
#>    MassBalances <- c(
#>      dX0_dt ,
#>      dX1_dt ,
#>      dT_dt
#>    )
#>    return(list(MassBalances, c(S1 = S1, S2 = S2)))
#> 
#> }

S1 and S2 have no slot in the state vector and no derivative; they are locals. Giving them slots would leave the solver carrying copies that never update while the rules recompute different values beside them.

Algebraic rules make the model a DAE

An algebraic rule is a constraint, 0 = f(...), not a derivative. A rule that names a single undetermined variable and is linear in it is simply solved for that variable and written as an assignment rule, in every target. The rules in sbmlalgebraicrules.xml each name both E and ES, so they cannot be solved one at a time: the model is a differential-algebraic system, and where the target can solve one, r2sbml emits it.

For deSolve that changes the shape of the generated function entirely: it becomes a residual function for daspk of (time, states, derivs, params), not a derivative function for ode:

alg_file <- system.file("examples", "sbmlalgebraicrules.xml", package = "r2sbml")
out_alg  <- tempfile(fileext = ".R")
convertReactions(alg_file, out_alg, format = "R")
#> Conversion completed.
#> Number of ODEs - 4

lines <- readLines(out_alg)
cat(lines[grep("Residuals:", lines)[1]:(grep("return\\(list\\(Residuals", lines))], sep = "\n")
#>    ## Residuals: 0 = d<state>/dt - f() for an integrated state,
#>    ##            0 = g()               for one fixed by an algebraic rule
#>    res_E = k1_on * E * S - (k1_off + k2) * ES  ## algebraic rule fixing E
#>    res_S = derivs[["S"]] - (-1 * (cell * (k1_on * E * S - k1_off * ES) / cell))
#>    res_ES = E + ES - E_total  ## algebraic rule fixing ES
#>    res_P = derivs[["P"]] - (cell * k2 * ES / cell)
#>    res_E_total = derivs[["E_total"]]  ## E_total is constant
#> 
#>    ## Make a list of Residuals
#>    Residuals <- c(
#>      res_E ,
#>      res_S ,
#>      res_ES ,
#>      res_P ,
#>      res_E_total
#>    )
#>    return(list(Residuals))

The file also defines InitialDerivatives, because daspk needs y' at t = 0 consistent with the residuals:

env <- new.env()
source(out_alg, local = env)

sol <- deSolve::daspk(y     = env$InitialAmounts,
                      dy    = env$InitialDerivatives,
                      times = seq(0, 10, by = 2),
                      res   = env$massBalances,
                      parms = env$parameters)
round(sol, 6)
#>   time        E        S       ES        P E_total
#> 1    0 0.500000 1.000000 0.500000 0.000000       1
#> 2    2 0.638103 0.567146 0.361897 0.432854       1
#> 3    4 0.782187 0.278465 0.217813 0.721535       1
#> 4    6 0.892834 0.120029 0.107166 0.879971       1
#> 5    8 0.954673 0.047479 0.045327 0.952521       1
#> 6   10 0.982329 0.017989 0.017671 0.982011       1
d <- as.data.frame(sol)
# both algebraic rules hold along the whole trajectory
max(abs(d$E + d$ES - d$E_total))
#> [1] 1.511014e-13
max(abs(1 * d$E * d$S - (0.5 + 0.5) * d$ES))
#> [1] 4.561434e-07

MATLAB and Julia keep the ordinary derivative shape and use a singular mass matrix instead: M * y' = f, with a zero row wherever a constraint sits, so that row reads 0 = f_i.

out_alg_m <- tempfile(fileext = ".m")
convertReactions(alg_file, out_alg_m, format = "MATLAB")
#> Conversion completed.
#> Number of ODEs - 4
lines <- readLines(out_alg_m)
cat(grep("M = eye|M\\(|MassSingular|ode15s", lines, value = TRUE), sep = "\n")
#>     M = eye(5);
#>     M(1, 1) = 0; % E
#>     M(3, 3) = 0; % ES
#>     opts = odeset('Mass', M, 'MassSingular', 'yes');
#>     [t, y] = ode15s(@massBalances, tspan, y0, opts);

Julia needs both the mass matrix and a solver that accepts one, so the generated header names Rodas5() rather than a bare solve(prob):

out_alg_jl <- tempfile(fileext = ".jl")
convertReactions(alg_file, out_alg_jl, format = "Julia")
#> Conversion completed.
#> Number of ODEs - 4
lines <- readLines(out_alg_jl)
cat(grep("Solve with|^M |^M\\[|mass_matrix|ODEProblem", lines, value = TRUE), sep = "\n")
#> # Solve with:  using DifferentialEquations; sol = solve(prob, Rodas5())
#> M = zeros(5, 5)
#> M[2, 2] = 1.0  # S
#> M[4, 4] = 1.0  # P
#> M[5, 5] = 1.0  # E_total
#> massbalances = ODEFunction(massbalances!; mass_matrix = M)
#> prob = ODEProblem(massbalances, u0, tspan, p)

mrgsolve, rxode2 and ubiquity integrate ODEs only. For those, a rule that could not be solved is written out as a comment and convertReactions() warns — see the limitations vignette.

Changing compartment volumes

If a compartment carries a rate rule, its volume is integrated alongside the species, and every species inside it picks up a dilution term. Since a species symbol is a concentration, [S] = n/V, the derivative is

\[\frac{d[S]}{dt} \;=\; \frac{1}{V}\frac{dn}{dt} \;-\; \frac{[S]}{V}\frac{dV}{dt}\]

and libSBML’s converter supplies only the first term. r2sbml adds the second.

The example models all have constant compartments, so here is a small model written out by hand — a species sitting in a compartment that grows at a constant rate, with no reactions at all:

growing <- tempfile(fileext = ".xml")
writeLines('<?xml version="1.0" encoding="UTF-8" ?>
<sbml xmlns="http://www.sbml.org/sbml/level3/version2/core" level="3" version="2">
<model substanceUnits="mole" volumeUnits="litre" timeUnits="second" extentUnits="mole">
<listOfCompartments>
<compartment id="c" size="1" spatialDimensions="3" constant="false"/>
</listOfCompartments>
<listOfSpecies>
<species id="A" compartment="c" initialConcentration="2" boundaryCondition="false"
hasOnlySubstanceUnits="false" constant="false"/>
</listOfSpecies>
<listOfParameters>
<parameter id="g" value="1" constant="true"/>
</listOfParameters>
<listOfRules>
<rateRule variable="c">
<math xmlns="http://www.w3.org/1998/Math/MathML"><ci>g</ci></math>
</rateRule>
</listOfRules>
</model>
</sbml>', growing)

out_grow <- tempfile(fileext = ".R")
convertReactions(growing, out_grow, format = "R")
#> Conversion completed.
#> Number of ODEs - 1
lines <- readLines(out_grow)
cat(grep("InitialAmounts|^ +[Ac] =|_dt|states\\[", lines, value = TRUE), sep = "\n")
#> InitialAmounts <- c(
#>          A = 2,
#>          c = 1   ## compartment volume, integrated
#>    A = states[["A"]]
#>    c = states[["c"]]
#>    dA_dt = -A * (g) / c  ## includes dilution by the changing volume
#>    dc_dt = g  ## compartment volume
#>      dA_dt ,
#>      dc_dt

c is a state, not a constant, and A has a non-zero derivative despite taking part in no reaction — its concentration falls because its container is growing. The exact solution is [A](t) = 2 / (1 + t), with the amount A * c fixed at 2:

env <- new.env()
source(out_grow, local = env)

times <- c(0, 1, 3, 7)
d <- as.data.frame(deSolve::ode(y = env$InitialAmounts, times = times,
                                func = env$massBalances, parms = env$parameters,
                                rtol = 1e-10, atol = 1e-10))
data.frame(time = times, A = d$A, exact = 2 / (1 + times), amount = d$A * d$c)
#>   time    A exact amount
#> 1    0 2.00  2.00      2
#> 2    1 1.00  1.00      2
#> 3    3 0.50  0.50      2
#> 4    7 0.25  0.25      2

Practical notes

Write to tempfile() in examples and tests. convertReactions() overwrites its output path without asking.

Expect console output. convertReactions() prints Conversion completed. and the number of ODEs; getModel() prints its header. Wrap calls in invisible(capture.output(...)) if that noise is unwelcome.

Watch for warnings. Several model features cannot be expressed in every target. Where that is true, convertReactions() raises an R warning rather than silently emitting code that runs but computes the wrong thing. The next vignette lists every such case, and — just as importantly — the cases where no warning is raised.

Where to go next

vignette("limitations", package = "r2sbml")

covers what r2sbml does not do: unsupported SBML constructs, the per-target capability matrix, which limitations are announced and which are silent, and the known quirks of the query functions.