Dynamical compensation and structural identifiability: analysis, implications, and reconciliation

The concept of dynamical compensation has been recently introduced to describe the ability of a biological system to keep its output dynamics unchanged in the face of varying parameters. Here we show that, according to its original definition, dynamical compensation is equivalent to lack of structural identifiability. This is relevant if model parameters need to be estimated, which is often the case in biological modelling. This realization prompts us to warn that care should we taken when using an unidentifiable model to extract biological insight: the estimated values of structurally unidentifiable parameters are meaningless, and model predictions about unmeasured state variables can be wrong. Taking this into account, we explore alternative definitions of dynamical compensation that do not necessarily imply structural unidentifiability. Accordingly, we show different ways in which a model can be made identifiable while exhibiting dynamical compensation. Our analyses enable the use of the new concept of dynamical compensation in the context of parameter identification, and reconcile it with the desirable property of structural identifiability

Parameter identifiability analysis and visualization in large-scale kinetic models of biosystems

[Background] Kinetic models of biochemical systems usually consist of ordinary differential equations that have many unknown parameters. Some of these parameters are often practically unidentifiable, that is, their values cannot be uniquely determined from the available data. Possible causes are lack of influence on the measured outputs, interdependence among parameters, and poor data quality. Uncorrelated parameters can be seen as the key tuning knobs of a predictive model. Therefore, before attempting to perform parameter estimation (model calibration) it is important to characterize the subset(s) of identifiable parameters and their interplay. Once this is achieved, it is still necessary to perform parameter estimation, which poses additional challenges.[Methods] We present a methodology that (i) detects high-order relationships among parameters, and (ii) visualizes the results to facilitate further analysis. We use a collinearity index to quantify the correlation between parameters in a group in a computationally efficient way. Then we apply integer optimization to find the largest groups of uncorrelated parameters. We also use the collinearity index to identify small groups of highly correlated parameters. The results files can be visualized using Cytoscape, showing the identifiable and non-identifiable groups of parameters together with the model structure in the same graph.[Results] Our contributions alleviate the difficulties that appear at different stages of the identifiability analysis and parameter estimation process. We show how to combine global optimization and regularization techniques for calibrating medium and large scale biological models with moderate computation times. Then we evaluate the practical identifiability of the estimated parameters using the proposed methodology. The identifiability analysis techniques are implemented as a MATLAB toolbox called VisId, which is freely available as open source from GitHub ( https://github.com/gabora/visid ).[Conclusions] Our approach is geared towards scalability. It enables the practical identifiability analysis of dynamic models of large size, and accelerates their calibration. The visualization tool allows modellers to detect parts that are problematic and need refinement or reformulation, and provides experimentalists with information that can be helpful in the design of new experiments.This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 686282 (“CANPATHPRO”), from the EU FP7 project "NICHE" (ITN Grant number 289384), and from the Spanish MINECO project "SYNBIOFACTORY" (grant number DPI2014-55276-C5-2-R).Peer reviewe

PREMER: Parallel reverse engineering of biological networks with information theory

A common approach for reverse engineering biological networks from data is to deduce the existence of interactions among nodes from information theoretic measures. Estimating these quantities in a multidimensional space is computationally demanding for large datasets. This hampers the application of elaborate algorithms which are crucial for discarding spurious interactions and determining causal relationships  to large-scale network inference problems. To alleviate this issue we have developed PREMER, a software tool which can automatically run in parallel and sequential environments, thanks to its implementation of OpenMP directives. It recovers network topology and estimates the strength and causality of interactions using information theoretic criteria, and allowing the incorporation of prior knowledge. A preprocessing module takes care of imputing missing data and correcting outliers if needed. PREMER (https://sites.google.com/site/premertoolbox/) runs on Windows, Linux and OSX, it is implemented in Matlab/Octave and Fortran 90, and it does not require any commercial software.AFV acknowledges funding from the Galician government (Xunta de Galiza) through the I2C fellowship ED481B2014/133-0. KB was supported by the German Federal Ministry of Research and Education (BMBF, OncoPath consortium). JRB acknowledges funding from the Spanish government (MINECO) and the European Regional Development Fund (ERDF) through the project “SYNBIOFACTORY” (grant number DPI2014-55276-C5-2-R). This project has received funding from the European Unions Horizon 2020 research and innovation programme under grant agreement No 686282 (CanPathPro). We thank David R. Penas and David Henriques for assistance with the implementation

Urban Cholera transmission hotspots and their implications for Reactive Vaccination: evidence from Bissau city, Guinea Bissau

Use of cholera vaccines in response to epidemics (reactive vaccination) may provide an effective supplement to traditional control measures. In Haiti, reactive vaccination was considered but, until recently, rejected in part due to limited global supply of vaccine. Using Bissau City, Guinea-Bissau as a case study, we explore neighborhood-level transmission dynamics to understand if, with limited vaccine and likely delays, reactive vaccination can significantly change the course of a cholera epidemic

On the relationship between sloppiness and identifiability

25 páginas, 11 figuras, 2 tablasDynamic models of biochemical networks are often formulated as sets of non-linear ordinary differential equations, whose states are the concentrations or abundances of the network components. They typically have a large number of kinetic parameters, which must be determined by calibrating the model with experimental data. In recent years it has been suggested that dynamic systems biology models are universally sloppy, meaning that the values of some parameters can be perturbed by several orders of magnitude without causing significant changes in the model output. This observation has prompted calls for focusing on model predictions rather than on parameters. In this work we examine the concept of sloppiness, investigating its links with the long-established notions of structural and practical identifiability. By analysing a set of case studies we show that sloppiness is not equivalent to lack of identifiability, and that sloppy models can be identifiable. Thus, using sloppiness to draw conclusions about the possibility of estimating parameter values can be misleading. Instead, structural and practical identifiability analyses are better tools for assessing the confidence in parameter estimates. Furthermore, we show that, when designing new experiments to decrease parametric uncertainty, designs that optimize practical identifiability criteria are more informative than those that minimize sloppinessThis project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 686282 (“CANPATHPRO”) and from the Spanish government (MINECO) and the European Regional Development Fund (ERDF) through the projects “SYNBIOFACTORY” (grant number DPI2014-55276-C5-2-R), and “IMPROWINE” (grant number AGL2015-67504-C3-2-R)N

Images in Clinical Urology: Complex open pyeloplasty in a pelvic kidney

A pelvic kidney occurs in between 1 in 2200 and 1 in 3000 people,1 due to failure of ascent during development. It is commonly asymptomatic and usually functions normally. Pelvic ureteral junction obstruction can either be congenital or acquired, and is characterized by intrinsic stenosis or extrinsic compression of the ureter at the junction with the pelvicalyceal renal system. This can cause symptomatic or asymptomatic hydronephrosis. We describe the complex case and management of a patient with a massive pelvic ureteral junction obstruction in a pelvic kidney

Input-dependent structural identifiability of nonlinear systems

A dynamic model is structurally identifiable if it is possible to infer its unknown parameters by observing its output. Structural identifiability depends on the system dynamics, output, and input, as well as on the specific values of initial conditions and parameters. Here we present a symbolic method that characterizes the input that a model requires to be structurally identifiable. It determines which derivatives must be non-zero in order to have a sufficiently exciting input. Our approach considers structural identifiability as a generalization of nonlinear observability and incorporates extended Lie derivatives. The methodology assesses structural identifiability for time-varying inputs and, additionally, it can be used to determine the input profile that is required to make the parameters structurally locally identifiable. Furthermore, it is sometimes possible to replace an experiment with time-varying input with multiple experiments with constant inputs. We implement the resulting method as a MATLAB toolbox named STRIKE-GOLDD2. This tool can assist in the design of new experiments for the purpose of parameter estimation