Structural Identifiability and Observability of Microbial Community Models
Abstract
:1. Introduction
2. Materials and Methods
2.1. Definitions
2.2. Analysis Methods
Algorithm 1: Probabilistic algorithm to test local algebraic observability in polynomial time |
Preprocesing Construct a straight-line program encoding the variational system with and the expressions used during its integration. Specialization Specialisation of the parameters, , and the inputs, Power Series Solution Computation of the power series solution of at order with a specialised value for the states Jacobian computation Evaluation of on the previous results, giving the coefficients of the Jacobian matrix Rank computation Calculation of the matrix rank and transcendence degree if transcendence degree = 0 then | System is algebraically observable else | Determine which variable or variables are not observable. end |
3. Models
3.1. Species–Species Interaction Models (SSI)
3.1.1. Generalized Lotka–Volterra Models (gLV)
3.1.2. Composite Lotka–Volterra Models (cLV)
3.2. Species–Metabolite Interaction Models (SMI)
3.2.1. Quadratic Species–Metabolite Interaction Models (QSMI)
3.2.2. SMI Models with Simple Monod Growth Kinetics (MSMI)
3.3. A Phage Cocktail Model (PC)
4. Results
5. Discussion and Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
ODE | Ordinary Differential Equation |
SIO | Structural Identifiability and Observability |
gLV | generalized Lotka–Volterra |
SLI | Structurally Locally Identifiable |
SU | Structurally Unidentifiable |
SSI | Species–Species Interaction |
SMI | Species–Metabolite Interaction |
QSMI | Quadratic Species–Metabolite Interaction |
MSMI | SMI model with Monod growth kinetics |
cLV | composite Lotka–Volterra |
PC | Phage Cocktail |
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Díaz-Seoane, S.; Sellán, E.; Villaverde, A.F. Structural Identifiability and Observability of Microbial Community Models. Bioengineering 2023, 10, 483. https://doi.org/10.3390/bioengineering10040483
Díaz-Seoane S, Sellán E, Villaverde AF. Structural Identifiability and Observability of Microbial Community Models. Bioengineering. 2023; 10(4):483. https://doi.org/10.3390/bioengineering10040483
Chicago/Turabian StyleDíaz-Seoane, Sandra, Elena Sellán, and Alejandro F. Villaverde. 2023. "Structural Identifiability and Observability of Microbial Community Models" Bioengineering 10, no. 4: 483. https://doi.org/10.3390/bioengineering10040483