# Calling complete() adds differential constraints to algebraic extension of ReactionSystem

**URL:** <https://discourse.julialang.org/t/calling-complete-adds-differential-constraints-to-algebraic-extension-of-reactionsystem/131115>\
**Category:** Modelling & Simulations\
**Tags:** question, package, modelingtoolkit, catalyst\
**Created:** [July 27, 2025, 8:20pm UTC](https://discourse.julialang.org/t/calling-complete-adds-differential-constraints-to-algebraic-extension-of-reactionsystem/131115 "2025-07-27T20:20:27Z")\
**Posts on this page:** 3\
**Page:** 1

<div class="post-metadata">

**Author:** ![spackman](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/spackman/32/215941_2.png) [@spackman](https://discourse.julialang.org/u/spackman)\
**Post date:** [July 27, 2025, 8:20pm UTC](https://discourse.julialang.org/t/calling-complete-adds-differential-constraints-to-algebraic-extension-of-reactionsystem/131115/1 "2025-07-27T20:20:27Z")

</div>

Hey guys,

I’m doing some experimentation with Catalyst.jl and algebraic equations to define systems where the system volume is not constant. This can occur when the major solvent is a reactant in appreciable quantities, and it impacts all the rate laws through redefining the species concentration.

I’m having trouble converting my system to an ODEProblem() because calling the `complete()` function appears to add additional equatiosn to my system. Here is an example:

```julia
using Catalyst, ModelingToolkit

@independent_variables t
@parameters k1, k2, k3, rho
@species H2O(t) A(t) B(t) mH2O(t) mA(t) mB(t) V(t)

rxns = [
        Reaction(k1, [H2O], [A , B])
        Reaction(k2, [A], [B])
        Reaction(k3, [B], [H2O])
]

@named rn = ReactionSystem(rxns, combinatoric_ratelaws=false)

# set up a system of equations linking the mass of each species to its concentration
equations = [
        V ~ mH2O / rho
        H2O ~ mH2O / V
        A ~ mA / V
        B ~ mB / V
]

@named alg = ODESystem(equations, t, [mH2O mA mB], [])

rn2 = extend(alg, rn)

rn2 = complete(rn2; sys=rn2)

```

When I display the system ODEs, I get this:

\begin{align} \frac{\mathrm{d} \mathtt{H2O}\left( t \right)}{\mathrm{d}t} &= - \mathtt{k1} \mathtt{H2O}\left( t \right) + \mathtt{k3} B\left( t \right) \\ \frac{\mathrm{d} A\left( t \right)}{\mathrm{d}t} &= \mathtt{k1} \mathtt{H2O}\left( t \right) - \mathtt{k2} A\left( t \right) \\ \frac{\mathrm{d} B\left( t \right)}{\mathrm{d}t} &= \mathtt{k1} \mathtt{H2O}\left( t \right) + \mathtt{k2} A\left( t \right) - \mathtt{k3} B\left( t \right) \\ \frac{\mathrm{d} \mathtt{mH2O}\left( t \right)}{\mathrm{d}t} &= 0 \\ \frac{\mathrm{d} \mathtt{mA}\left( t \right)}{\mathrm{d}t} &= 0 \\ \frac{\mathrm{d} \mathtt{mB}\left( t \right)}{\mathrm{d}t} &= 0 \\ V\left( t \right) &= \frac{\mathtt{mH2O}\left( t \right)}{\mathtt{rho}} \\ \mathtt{H2O}\left( t \right) &= \frac{\mathtt{mH2O}\left( t \right)}{V\left( t \right)} \\ A\left( t \right) &= \frac{\mathtt{mA}\left( t \right)}{V\left( t \right)} \\ B\left( t \right) &= \frac{\mathtt{mB}\left( t \right)}{V\left( t \right)} \end{align}

There are now 3 additional differential equations that were not explicitly specified in the original system. I think these equations are causeing my system to be over-defined when I try to convert it to an ODEProblem:

```julia
u0 = [mA => 0.1, mB => 0, V => 50] #mH2O is fully specified by the volume V and the density rho
ps = [k1 => 1, k2 => 3, k3 => 0.5, rho => 0.99]
oprob = ODEProblem(rn2, u0, (0.0, 5.0), ps, structural_simplify=true)

```

This yields:

```julia
ExtraEquationsSystemException: The system is unbalanced. There are 7 highest order derivative variables and 10 equations.
More equations than variables, here are the potential extra equation(s):
 0 ~ -H2O(t) + mH2O(t) / V(t)
 0 ~ -V(t) + mH2O(t) / rho
 0 ~ mA(t) / V(t) - A(t)
Note that the process of determining extra equations is a best-effort heuristic. The true extra equations are dependent on the model and may not be in this list.

```

Ideally, I want to be able to proceed with a system without these additional equations. This could happen by either

- pruning the system after complete to remove unwanted differential equations (I don’t think this is possible because a complete system is not mutable)
- stopping the generation of unnecessary equations from the start
- explicitly defining these differential equations (possible, but not ideal)

The easiest option would be to prevent their generation in the first place.

Any tips on this problem?

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<div class="post-metadata">

**Author:** ![spackman](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/spackman/32/215941_2.png) [@spackman](https://discourse.julialang.org/u/spackman)\
**Post date:** [July 27, 2025, 9:56pm UTC](https://discourse.julialang.org/t/calling-complete-adds-differential-constraints-to-algebraic-extension-of-reactionsystem/131115/2 "2025-07-27T21:56:34Z")

</div>

I’ve solved the completeness problem -  
The additional equation appear to have been added because the new variables (mH2O, mA, mB) were added using the @species macro.

Re-defining using the @variables macro eliminates the issue:

```julia
using Catalyst, ModelingToolkit

@independent_variables t
@parameters k1 k2 k3 rho
@variables mH2O(t) mA(t) mB(t) V(t)
@species H2O(t) A(t) B(t) 

rxns = [
        Reaction(k1, [H2O], [A , B])
        Reaction(k2, [A], [B])
        Reaction(k3, [B], [H2O])
]

@named rn = ReactionSystem(rxns, combinatoric_ratelaws=false)

equations = [
        V ~ mH2O / rho
        H2O ~ mH2O / V
        A ~ mA / V
        B ~ mB / V
]

@named alg = ODESystem(equations, t, [mH2O mA mB V], [rho])

rn2 = extend(alg, rn)

rn2 = complete(rn2; sys=rn2)

```

Now the system can be defined as fully determined:

```julia
u0 = [mA => 0.1, mB => 0, mH2O => 49.5]
ps = [k1 => 100, k2 => 30, k3 => 0.5, rho => 0.99]
oprob = ODEProblem(rn2, u0, (0.0, 5.0), ps, structural_simplify=true)

```

It happens that the system defined in this example is singular, which appears during the solution step.

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<div class="post-metadata">

**Author:** ![isaacsas](https://avatars.discourse-cdn.com/v4/letter/i/f6c823/32.png) [@isaacsas](https://discourse.julialang.org/u/isaacsas)\
**Post date:** [July 28, 2025, 2:07pm UTC](https://discourse.julialang.org/t/calling-complete-adds-differential-constraints-to-algebraic-extension-of-reactionsystem/131115/3 "2025-07-28T14:07:17Z")

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You could alternatively pass `include_zero_odes = false` to `convert` or pass the `isbcspecies = true` metadata when creating the species. The later is a SBML feature that tags that no equation should be generated for the species from its inclusion as a substrate or product, I.e that the species will have a separate equation given for its dynamics elsewhere.