Global Identifiability of Differential Models

Many real-world processes and phenomena are modeled using systems of ordinary differential equations with parameters. Given such a system, we say that a parameter is globally identifiable if it can be uniquely recovered from input and output data. The main contribution of this paper is to provide theory, an algorithm, and software for deciding global identifiability. First, we rigorously derive an algebraic criterion for global identifiability (this is an analytic property), which yields a deterministic algorithm. Second, we improve the efficiency by randomizing the algorithm while guaranteeing the probability of correctness. With our new algorithm, we can tackle problems that could not be tackled before. A software based on the algorithm (called SIAN) is available at https://github.com/pogudingleb/SIAN

Web-based Structural Identifiability Analyzer

Parameter identifiability describes whether, for a given differential model, one can determine parameter values from model equations. Knowing global or local identifiability properties allows construction of better practical experiments to identify parameters from experimental data. In this work, we present a web-based software tool that allows to answer specific identifiability queries. Concretely, our toolbox can determine identifiability of individual parameters of the model and also provide all functions of parameters that are identifiable (also called identifiable combinations) from single or multiple experiments. The program is freely available at https://maple.cloud/app/6509768948056064

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

Observability and Structural Identifiability of Nonlinear Biological Systems

Observability is a modelling property that describes the possibility of inferring the internal state of a system from observations of its output. A related property, structural identifiability, refers to the theoretical possibility of determining the parameter values from the output. In fact, structural identifiability becomes a particular case of observability if the parameters are considered as constant state variables. It is possible to simultaneously analyse the observability and structural identifiability of a model using the conceptual tools of differential geometry. Many complex biological processes can be described by systems of nonlinear ordinary differential equations, and can therefore be analysed with this approach. The purpose of this review article is threefold: (I) to serve as a tutorial on observability and structural identifiability of nonlinear systems, using the differential geometry approach for their analysis; (II) to review recent advances in the field; and (III) to identify open problems and suggest new avenues for research in this area.Comment: Accepted for publication in the special issue "Computational Methods for Identification and Modelling of Complex Biological Systems" of Complexit

Modeling Doxorubicin Pharmacokinetics in Multiple Myeloma Suggests Mechanism of Drug Resistance

Objective: Multiple myeloma (MM) is a plasma cell malignancy often treated with chemotherapy drugs. Among these, doxorubicin (DOXO) is commonly employed, sometimes in combined-drug therapies, but it has to be optimally administered in order to maximize its efficacy and reduce possible side effects. To support DOXO studies and treatment optimization, here we propose an experimental/modeling approach to establish a model describing DOXO pharmacokinetics (PK) in MM cells. Methods: A series of in vitro experiments were performed in MM1R and MOLP-2 cells. DOXO was administered at two dosages (200 nM, 450 nM) at [Formula: see text]=0 and removed at [Formula: see text]=3 hrs. Intracellular DOXO concentration was measured via fluorescence microscopy during both drug uptake ([Formula: see text]=0-3 hrs) and release phases ([Formula: see text]=3-8 hrs). Four PK candidate models were identified, and were compared and selected based on their ability to describe DOXO data and numerical parameter identification. Results: The most parsimonious model consists of three compartments describing DOXO distribution between the extracellular space, the cell cytoplasm and the nucleus, and defines the intracellular DOXO efflux rate through a Hill function, simulating a threshold/saturation drug resistance mechanism. This model predicted DOXO data well in all the experiments and provided precise parameter estimates (mean ± standard deviation coefficient of variation: 15.8±12.2%). Conclusions: A reliable PK model describing DOXO uptake and release in MM cells has been successfully developed. Significance: The proposed PK model, once integrated with DOXO pharmacodynamics, has the potential of allowing the study and the optimization of DOXO treatment strategies in MM

On the origins and rarity of locally but not globally identifiable parameters in biological modeling

Structural identifiability determines the possibility of estimating the parameters of a model by observing its output in an ideal experiment. If a parameter is structurally locally identifiable, but not globally (SLING), its true value cannot be uniquely inferred because several equivalent solutions exist. In biological modeling it is sometimes assumed that local identifiability entails global identifiability, which is convenient because local identifiability tests are typically less computationally demanding than global tests. However, this assumption has never been investigated beyond demonstrating the existence of counter-examples. To clarify this matter, in this paper we began by asking how often a structurally locally identifiable parameter is not globally identifiable in systems biology. To answer this question empirically we assembled a collection of 102 mathematical models from the literature, with a total of 763 parameters. We analysed their identifiability, determining that approximately 5% of the parameters are SLING. Next we investigated how the SLING parameters arise, tracing their origin to particular features of the model equations. Finally, we investigated the possibility of obtaining false estimates. Some of the solutions that are mathematically equivalent to the true one involved parameters and/or initial conditions with negative values, which are not biologically meaningful. In other cases the true solution and the equivalent one were in the same range. These results provide insight about a previously unexplored hypothesis, and suggest that in most (albeit not all) systems biology applications it suffices to test for structural local identifiability.MCIN/AEI/ 10.13039/50110001103300004837 | Ref. PID2020-113992RA-I00MCIN/AEI/ 10.13039/50110001103300004837 | Ref. RYC-2019-027537-IXunta de Galicia | Ref. ED431F 2021/00

Structural identifiability analysis of epidemic models based on differential equations: A Primer

The successful application of epidemic models hinges on our ability to estimate model parameters from limited observations reliably. An often-overlooked step before estimating model parameters consists of ensuring that the model parameters are structurally identifiable from a given dataset. Structural identifiability analysis uncovers any existing parameter correlations that preclude their estimation from the observed variables. Here we review and illustrate methods for structural identifiability analysis based on a differential algebra approach using DAISY and Mathematica (Wolfram Research). We demonstrate this approach through examples of compartmental epidemic models previously employed to study transmission dynamics and control. We show that lack of structural identifiability may be remedied by incorporating additional observations from different model states or fixing some parameters based on existing parameter correlations, or by reducing the number of parameters or state variables involved in the system dynamics. We also underscore how structural identifiability analysis can help improve compartmental diagrams of differential-equation models by indicating the observed variables and the results of the structural identifiability analysis