SBML Systems Biology & Biochemical Kinetics (.sbml, .xml)

@modelscript/sbml (languages/sbml) provides zero-regex streaming XML parsing, biochemical reaction network kinetics solving, 4th-order Runge-Kutta ODE simulation, linear DAE lowering, and Modelica 3.x projection for Systems Biology Markup Language (SBML Level 2 & 3 Core) cellular, metabolic, and signaling network models.

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Supported Extensions & Standards

Extension	Format	Description
.sbml	SBML Model File	Standard biochemical XML schema encoding compartments, species, parameters, and reactions
.xml	SBML XML Document	General XML format containing standard SBML Level 2/3 definitions

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Key Capabilities

1. Biochemical Reaction Networks & Stoichiometry

• Parses hierarchical multi-compartment biochemical reaction networks:
  • Compartments: Cellular volumes (cytosol, mitochondria, extracellular space) with spatial dimensions (0D, 2D membrane, 3D volume).
  • Species: Chemical and protein concentrations or particle amounts ($[S_i]\ge 0$).
  • Parameters: Kinetic rate constants ($k_{\text{fwd}},k_{\text{rev}}$), Michaelis constants ($K_m$), and Hill coefficients ($n$).
  • Reactions: Reversible and irreversible reaction fluxes ($v_j$) with stoichiometric coefficient matrices $N=[{\nu }_{ij}]$:$$\sum _i{s}_{ij}{S}_i\stackrel{v_j}{\to }\sum _k{p}_{kj}{P}_k$$

2. Kinetic Law Formulations & ODE Solver

• Evaluates dynamic reaction velocities across standard enzyme kinetics:
  • Mass-Action Kinetics:$$v=k_{\text{fwd}}\prod [R_i{]}^{s_i}-k_{\text{rev}}\prod [P_j{]}^{p_j}$$
  • Michaelis-Menten Enzymatic Saturation:$$v=\frac{V_{\text{max}}[S]}{K_m+[S]}$$
  • Hill Cooperativity:$$v=\frac{V_{\text{max}}[S{]}^n}{K_{0.5}^n+[S{]}^n}$$
• Solves the resulting non-linear ordinary differential equations (ODEs):$$\frac{d[S_i]}{dt}=\frac{1}{V_{\text{comp}}}\sum _{j=1}^R{\nu }_{ij}\cdot v_j([S],p)$$using embedded 4th-order Runge-Kutta (RK4) integration or stiff SUNDIALS CVODE solvers.

3. Direct DAE Lowering

• Lowers reaction stoichiometric matrices and flux equations into @modelscript/runtime's DAEBuilder linear memory arena.
• Enables co-simulation between cellular metabolic networks and pharmacokinetics / drug delivery fluid pipelines (@modelscript/aspen).

4. Bidirectional Modelica 3.x Projection

• Projects SBML reaction systems into Modelica biochemical components and acausal substance substance-flow models.

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Pre-Flight Diagnostics

The SBML analyzer validates stoichiometric consistency, undefined references, and physical rate bounds:

10 rules7 error2 warning1 info Run with msx sbml lint

Code	Rule	Severity	Message
M8801	missing-model-id	error	SBML <model> element is missing required 'id' attribute.
M8802	undefined-compartment-reference	error	Species '<speciesId>' references undefined compartment '<compartmentId>'.
M8803	undefined-species-reference	error	Reaction '<reactionId>' references undefined <role> species '<speciesId>'.
M8804	negative-compartment-size	error	Compartment '<compartmentId>' defines non-positive size (<size>).
M8805	negative-initial-amount-concentration	error	Species '<speciesId>' specifies negative initial amount/concentration (<val>).
M8806	empty-reaction	error	Reaction '<reactionId>' must define at least one reactant or product.
M8807	missing-kinetic-law	warning	Reaction '<reactionId>' does not define a kineticLaw rate law equation.
M8808	negative-stoichiometry	error	Species reference for '<speciesId>' in reaction '<reactionId>' specifies non-positive stoichiometry (<stoich>).
M8809	undefined-kinetic-parameter	warning	Kinetic law formula in reaction '<reactionId>' references identifier '<id>' not found in parameters or species.
M8810	circular-species-assignment	info	Reaction '<reactionId>' lists '<speciesId>' as both reactant and product with identical stoichiometry; consider defining as modifier.

Generated from languages/sbml/src/errors.ts. All languages →

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CLI Usage

# Inspect compartments, species, parameters, and reactions
msx sbml inspect GlycolyticPathway.sbml

# Run pre-flight linting and stoichiometric validation
msx sbml lint GlycolyticPathway.sbml

# Simulate biochemical reaction kinetics ODEs with RK4
msx sbml simulate GlycolyticPathway.sbml --duration=20.0

# Lower biochemical reaction network to ModelScript linear DAE arena
msx sbml to-dae GlycolyticPathway.sbml

# Project into Modelica 3.x biochemical network model
msx sbml to-modelica GlycolyticPathway.sbml -o GlycolysisModel.mo