On testing structural identifiability by a simple scaling method: Relying on scaling symmetries can be misleading

A recent paper published in PLOS Computational Biology [1] introduces the Scaling Invariance Method (SIM) for analysing structural local identifiability and observability. These two properties define mathematically the possibility of determining the values of the parameters (identifiability) and states (observability) of a dynamic model by observing its output. In this note we warn that SIM considers scaling symmetries as the only possible cause of non-identifiability and non-observability. We show that other types of symmetries can cause the same problems without being detected by SIM, and that in those cases the method may lead one to conclude that the model is identifiable and observable when it is actually not.

The limitations, dangers, and benefits of simple methods for testing identifiability

In their Commentary paper, Villaverde and Massonis (On testing structural identifiability by a simple scaling method: relying on scaling symmetries can be misleading) have commented on our paper in which we proposed a simple scaling method to test structural identifiability. Our scaling invariance method (SIM) tests for scaling symmetries only, and Villaverde and Massonis correctly show the SIM may fail to detect identifiability problems when a model has other types of symmetries. We agree with the limitations raised by these authors but, also, we emphasize that the method is still valuable for its applicability to a wide variety of models, its simplicity, and even as a tool to introduce the problem of identifiability to investigators with little training in mathematics.

Assessing the role of initial conditions in the local structural identifiability of large dynamic models

Structural identifiability is a binary property that determines whether or not unique parameter values can, in principle, be estimated from error-free input–output data. The many papers that have been written on this topic collectively stress the importance of this a priori analysis in the model development process. The story however, often ends with a structurally unidentifiable model. This may leave a model developer with no plan of action on how to address this potential issue. We continue this model exploration journey by identifying one of the possible sources of a model’s unidentifiability: problematic initial conditions. It is well-known that certain initial values may result in the loss of local structural identifiability. Nevertheless, literature on this topic has been limited to the analysis of small toy models. Here, we present a systematic approach to detect problematic initial conditions of real-world systems biology models, that are usually not small. A model’s identifiability can often be reinstated by changing the value of such problematic initial conditions. This provides modellers an option to resolve the “unidentifiable model” problem. Additionally, a good understanding of which initial values should rather be avoided can be very useful during experimental design. We show how our approach works in practice by applying it to five models. First, two small benchmark models are studied to get the reader acquainted with the method. The first one shows the effect of a zero-valued problematic initial condition. The second one illustrates that the approach also yields correct results in the presence of input signals and that problematic initial conditions need not be zero-values. For the remaining three examples, we set out to identify key initial values which may result in the structural unidentifiability. The third and fourth examples involve a systems biology Epo receptor model and a JAK/STAT model, respectively. In the final Pharmacokinetics model, of which its global structural identifiability has only recently been confirmed, we indicate that there are still sets of initial values for which this property does not hold.

Structural identifiability of the generalized Lotka–Volterra model for microbiome studies

Population dynamic models can be used in conjunction with time series of species abundances to infer interactions. Understanding microbial interactions is a prerequisite for numerous goals in microbiome research, including predicting how populations change over time, determining how manipulations of microbiomes affect dynamics and designing synthetic microbiomes to perform tasks. As such, there is great interest in adapting population dynamic theory for microbial systems. Despite the appeal, numerous hurdles exist. One hurdle is that the data commonly obtained from DNA sequencing yield estimates of relative abundances, while population dynamic models such as the generalized Lotka–Volterra model track absolute abundances or densities. It is not clear whether relative abundance data alone can be used to infer parameters of population dynamic models such as the Lotka–Volterra model. We used structural identifiability analyses to determine the extent to which a time series of relative abundances can be used to parametrize the generalized Lotka–Volterra model. We found that only with absolute abundance data to accompany relative abundance estimates from sequencing can all parameters be uniquely identified. However, relative abundance data alone do contain information on relative interaction strengths, which is sufficient for many studies where the goal is to estimate key interactions and their effects on dynamics. Using synthetic data of a simple community for which we know the underlying structure, local practical identifiability analysis showed that modest amounts of both process and measurement error do not fundamentally affect these identifiability properties.

Assessing the Role of Initial Conditions in the Local Structural Identifiability of Large Dynamic Models

Structural identifiability is a binary property that determines whether or not unique parameter values can, in principle, be estimated from error-free input-output data. The many papers that have been written on this topic collectively stress theimportance of this a priori analysis in the model development process. The story however, often ends with a structurallyunidentifiable model. This may leave a model developer with no plan of action on how to address this potential issue. We continue this model exploration journey by identifying one of the possible sources of a model’s unidentifiability: problematic initial conditions. It is well-known that certain initial values may result in the loss of local structural identifiability. Nevertheless, literature on this topic has been limited to the analysis of small toy models. Here, we present a systematic approach to detect problematic initial conditions of real-world systems biology models, that are usually not small. A model’s identifiability can often be reinstated by changing the value of such problematic initial conditions. This provides modellers an option to resolve the “unidentifiablemodel” problem. Additionally, a good understanding of which initial values should rather be avoided can be very useful during experimental design. We show how our approach works in practice by applying it to five models. First, two small benchmark models are studied toget the reader acquainted with the method. The first one shows the effect of a zero-valued problematic initial condition. The second one illustrates that the approach also yields correct results in the presence of input signals and that problematic initial conditions need not be zero-values. For the remaining three examples, we set out to identify key initial values which may result in the structural unidentifiability. The third and fourth examples involve a systems biology Epo receptor model and a JAK/STAT model, respectively. In the final Pharmacokinetics model, of which its global structural identifiability has only recently been confirmed, we indicate that there are still sets of initial values for which this property does not hold.

On Role of S-Synchronizability and Excitation Constancy in Structural Identifiability Problem of Nonlinear Systems

A class of dynamical systems with a single nonlinearity considered. The S-synchronizability concept of input introduced. It is shown that S-synchronizability is a condition for the structural identifiability of a nonlinear system. The decisionmaking on structural identifiability based on the properties analysis for a special class of geometric frameworks. Geometric frameworks reflect properties of the nonlinear dynamic system. Requirements for the model allowed us to obtain a geometric structure based on the input and output data considered. The constant excitation effect of input on the structural identifiability of the system is studied. The constant excitation effect of input studied on the structural identifiability of the system. Nonfulfillment the constant excitation condition gives a nonsignificant geometric framework. Various types of structural identifiability based on structure analysis considered. The concept of d-optimality described properties of the geometric structure introduced. Conditions for non-identifiability of nonlinear system structure obtained if the d-optimality of the geometric framework does not hold for the given properties of the input. Methods for estimating identifiability of the system and determining the identifiability area under uncertainty proposed. The proposed approach is generalized to the system having two nonlinearities. Conditions for partial structural identifiability obtained. Structural identifiability features of this class systems noted. The method for estimating the structure of the system proposed when the condition of structural identifiability satisfied. It has shown how the phase portrait used to estimate the system non-identifiability. A method proposed for constructing the structural identifiability domain of the system. Proposed methods and procedures are applied to study systems with Bouc-Wen hysteresis and two nonlinearity.