760 research outputs found
Structural Identifiability of Systems Biology Models: A Critical Comparison of Methods
Analysing the properties of a biological system through in silico experimentation requires a satisfactory mathematical representation of the system including accurate values of the model parameters. Fortunately, modern experimental techniques allow obtaining time-series data of appropriate quality which may then be used to estimate unknown parameters. However, in many cases, a subset of those parameters may not be uniquely estimated, independently of the experimental data available or the numerical techniques used for estimation. This lack of identifiability is related to the structure of the model, i.e. the system dynamics plus the observation function. Despite the interest in knowing a priori whether there is any chance of uniquely estimating all model unknown parameters, the structural identifiability analysis for general non-linear dynamic models is still an open question. There is no method amenable to every model, thus at some point we have to face the selection of one of the possibilities. This work presents a critical comparison of the currently available techniques. To this end, we perform the structural identifiability analysis of a collection of biological models. The results reveal that the generating series approach, in combination with identifiability tableaus, offers the most advantageous compromise among range of applicability, computational complexity and information provided
Identifiability of large nonlinear biochemical networks
Dynamic models formulated as a set of ordinary differential equations provide a detailed description of the time-evolution of a system. Such models of (bio)chemical reaction networks have contributed to important advances in biotechnology and biomedical applications, and their impact is foreseen to increase in the near future. Hence, the task of dynamic model building has attracted much attention from scientists working at the intersection of biochemistry, systems theory, mathematics, and computer science, among other disciplines-an area sometimes called systems biology. Before a model can be effectively used, the values of its unknown parameters have to be estimated from experimental data. A necessary condition for parameter estimation is identifiability, the property that, for a certain output, there exists a unique (or finite) set of parameter values that produces it. Identifiability can be analysed from two complementary points of view: structural (which searches for symmetries in the model equations that may prevent parameters from being uniquely determined) or practical (which focuses on the limitations introduced by the quantity and quality of the data available for parameter estimation). Both types of analyses are often difficult for nonlinear models, and their complexity increases rapidly with the problem size. Hence, assessing the identifiability of realistic dynamic models of biochemical networks remains a challenging task. Despite the fact that many methods have been developed for this purpose, it is still an open problem and an active area of research. Here we review the theory and tools available for the study of identifiability, and discuss some closely related concepts such as sensitivity to parameter perturbations, observability, distinguishability, and optimal experimental design, among others.This work was funded by the Galician government (Xunta de Galiza) through the I2C postdoctoral program (fellowship ED481B2014/133-0), and by the Spanish Ministry of Economy and Competitiveness (grant DPI2013-47100-C2-2-P)
Review: to be or not to be an identifiable model. Is this a relevant question in animal science modelling?
International audienceWhat is a good (useful) mathematical model in animal science? For models constructed for prediction purposes, the question of model adequacy (usefulness) has been traditionally tackled by statistical analysis applied to observed experimental data relative to model-predicted variables. However, little attention has been paid to analytic tools that exploit the mathematical properties of the model equations. For example, in the context of model calibration, before attempting a numerical estimation of the model parameters, we might want to know if we have any chance of success in estimating a unique best value of the model parameters from available measurements. This question of uniqueness is referred to as structural identifiability; a mathematical property that is defined on the sole basis of the model structure within a hypothetical ideal experiment determined by a setting of model inputs (stimuli) and observable variables (measurements). Structural identifiability analysis applied to dynamic models described by ordinary differential equations (ODE) is a common practice in control engineering and system identification. This analysis demands mathematical technicalities that are beyond the academic background of animal science, which might explain the lack of pervasiveness of identifiability analysis in animal science modelling. To fill this gap, in this paper we address the analysis of structural identifiability from a practitioner perspective by capitalizing on the use of dedicated software tools. Our objectives are (i) to provide a comprehensive explanation of the structural identifiability notion for the community of animal science modelling, (ii) to assess the relevance of identifiability analysis in animal science modelling and (iii) to motivate the community to use identifiability analysis in the modelling practice (when the identifiability question is relevant). We focus our study on ODE models. By using illustrative examples that include published mathematical models describing lactation in cattle, we show how structural identifiability analysis can contribute to advancing mathematical modelling in animal science towards the production of useful models and highly informative experiments. Rather than attempting to impose a systematic identifiability analysis to the modelling community during model developments, we wish to open a window towards the discovery of a powerful tool for model construction and experiment design
Differential elimination for dynamical models via projections with applications to structural identifiability
Elimination of unknowns in a system of differential equations is often
required when analysing (possibly nonlinear) dynamical systems models, where
only a subset of variables are observable. One such analysis, identifiability,
often relies on computing input-output relations via differential algebraic
elimination. Determining identifiability, a natural prerequisite for meaningful
parameter estimation, is often prohibitively expensive for medium to large
systems due to the computationally expensive task of elimination.
We propose an algorithm that computes a description of the set of
differential-algebraic relations between the input and output variables of a
dynamical system model. The resulting algorithm outperforms general-purpose
software for differential elimination on a set of benchmark models from
literature.
We use the designed elimination algorithm to build a new randomized algorithm
for assessing structural identifiability of a parameter in a parametric model.
A parameter is said to be identifiable if its value can be uniquely determined
from input-output data assuming the absence of noise and sufficiently exciting
inputs. Our new algorithm allows the identification of models that could not be
tackled before.
Our implementation is publicly available as a Julia package at
https://github.com/SciML/StructuralIdentifiability.jl
Data-driven modelling of biological multi-scale processes
Biological processes involve a variety of spatial and temporal scales. A
holistic understanding of many biological processes therefore requires
multi-scale models which capture the relevant properties on all these scales.
In this manuscript we review mathematical modelling approaches used to describe
the individual spatial scales and how they are integrated into holistic models.
We discuss the relation between spatial and temporal scales and the implication
of that on multi-scale modelling. Based upon this overview over
state-of-the-art modelling approaches, we formulate key challenges in
mathematical and computational modelling of biological multi-scale and
multi-physics processes. In particular, we considered the availability of
analysis tools for multi-scale models and model-based multi-scale data
integration. We provide a compact review of methods for model-based data
integration and model-based hypothesis testing. Furthermore, novel approaches
and recent trends are discussed, including computation time reduction using
reduced order and surrogate models, which contribute to the solution of
inference problems. We conclude the manuscript by providing a few ideas for the
development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and
Multiscale Dynamics (American Scientific Publishers
Comparative Analysis of Practical Identifiability Methods for an SEIR Model
Identifiability of a mathematical model plays a crucial role in
parameterization of the model. In this study, we establish the structural
identifiability of a Susceptible-Exposed-Infected-Recovered (SEIR) model given
different combinations of input data and investigate practical identifiability
with respect to different observable data, data frequency, and noise
distributions. The practical identifiability is explored by both Monte Carlo
simulations and a Correlation Matrix approach. Our results show that practical
identifiability benefits from higher data frequency and data from the peak of
an outbreak. The incidence data gives the best practical identifiability
results compared to prevalence and cumulative data. In addition, we compare and
distinguish the practical identifiability by Monte Carlo simulations and a
Correlation Matrix approach, providing insights for when to use which method
for other applications.Comment: Minor changes to clarify why structural identifiability with respect
to incidence data was not perfor
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