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89
Structural Identifiability of Systems Biology Models: A Critical Comparison of Methods
, 2011
"... 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 timeseries data of appropriate quality w ..."
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Cited by 24 (2 self)
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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 timeseries 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 nonlinear 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
A: Glocal Robustness Analysis and Model Discrimination for Circadian Oscillators
 PLoS Comput Biol
"... To characterize the behavior and robustness of cellular circuits with many unknown parameters is a major challenge for systems biology. Its difficulty rises exponentially with the number of circuit components. We here propose a novel analysis method to meet this challenge. Our method identifies the ..."
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Cited by 17 (3 self)
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To characterize the behavior and robustness of cellular circuits with many unknown parameters is a major challenge for systems biology. Its difficulty rises exponentially with the number of circuit components. We here propose a novel analysis method to meet this challenge. Our method identifies the region of a highdimensional parameter space where a circuit displays an experimentally observed behavior. It does so via a Monte Carlo approach guided by principal component analysis, in order to allow efficient sampling of this space. This ‘global ’ analysis is then supplemented by a ‘local ’ analysis, in which circuit robustness is determined for each of the thousands of parameter sets sampled in the global analysis. We apply this method to two prominent, recent models of the cyanobacterial circadian oscillator, an autocatalytic model, and a model centered on consecutive phosphorylation at two sites of the KaiC protein, a key circadian regulator. For these models, we find that the twosites architecture is much more robust than the autocatalytic one, both globally and locally, based on five different quantifiers of robustness, including robustness to parameter perturbations and to molecular noise. Our ‘glocal’ combination of global and local analyses can also identify key causes of high or low robustness. In doing so, our approach helps to unravel the architectural origin of robust circuit behavior. Complementarily, identifying fragile aspects of system behavior can aid in designing perturbation experiments that may discriminate between competing mechanisms and
Executing multicellular differentiation: quantitative predictive modelling of c. elegans vulval development
 Bioinformatics
, 2009
"... Motivation: Understanding the processes involved in multicellular pattern formation is a central problem of developmental biology, hopefully leading to many new insights, e.g., in the treatment of various diseases. Defining suitable computational techniques for development modelling, able to perf ..."
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Cited by 14 (4 self)
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Motivation: Understanding the processes involved in multicellular pattern formation is a central problem of developmental biology, hopefully leading to many new insights, e.g., in the treatment of various diseases. Defining suitable computational techniques for development modelling, able to perform in silico simulation experiments, is an open and challenging problem. Results: Previously, we proposed a coarsegrained, quantitative approach based on the basic Petri net formalism, to mimic the behaviour of the biological processes during multicellular differentiation. Here we apply our modelling approach to the wellstudied process of C. elegans vulval development. We show that our model correctly reproduces a large set of in vivo experiments with statistical accuracy. It also generates gene expression time series in accordance with recent biological evidence. Finally, we modelled the role of microRNA mir61 during vulval development and predict its contribution in stabilising cell pattern formation. Contact:
Understanding Modularity in Molecular Networks Requires Dynamics
, 2009
"... Visit the online version of this article to access the personalization and article tools: ..."
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Cited by 9 (0 self)
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Visit the online version of this article to access the personalization and article tools:
An Integrated Strategy for Prediction Uncertainty Analysis (Supplement)
"... As mentioned in the main paper, we ran Profile Likelihoods for each mode detected with the Monte Carlo Multiple Minimisation. The reason for this is that the method by which these profiles are computed are local (reoptimising from the current point at each step). The result is that one runs the risk ..."
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Cited by 7 (0 self)
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As mentioned in the main paper, we ran Profile Likelihoods for each mode detected with the Monte Carlo Multiple Minimisation. The reason for this is that the method by which these profiles are computed are local (reoptimising from the current point at each step). The result is that one runs the risk that the profile likelihood fails to leave a mode before the error reaches the threshold (see for example the green profile for parameter 4 in the top row). It is therefore important to validate that all modes have been reached after running the Profile Likelihoods. Mode switches can also be observed (for an example, see the blue profile for parameter 1 in the bottom row). The profiles can subsequently be merged afterwards. Note that some of the parameters were structurally nonidentifiable and showed clear relationships between the parameters when plotted in a scatter plot (see Figure 1). Shown in Figure 2 are the three separate Profile Likelihoods performed in order to obtain the merged version
From Molecules to Organisms: Towards Multiscale Integrated Models of Biological Systems, in "Theoretical Biology Insights
"... Abstract: A consensus has recently emerged that further progress in understanding human physiopathology will demand integrative views of biological systems. In this context, complex systems and related interdisciplinary approaches of biology are expected to help. The aim of this collective paper is ..."
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Abstract: A consensus has recently emerged that further progress in understanding human physiopathology will demand integrative views of biological systems. In this context, complex systems and related interdisciplinary approaches of biology are expected to help. The aim of this collective paper is basically to provide a starting point for further discussions and interactions within the community of complex systems biologists. After brie y introducing some general concepts, we present four major challenges that should be tackled in the next years. These represent future directions that we isolated as priority concerns for modern biology. Suggestions of how to reach these destinations are provided, with the hope that they will soon lead to concrete advances towards fully consistent multiscale models of biological systems and a better understanding of physiopathology.
Systematic construction of kinetic models from genomescale metabolic networks
 PLOS ONE
, 2013
"... The quantitative effects of environmental and genetic perturbations on metabolism can be studied in silico using kinetic models. We present a strategy for largescale model construction based on a logical layering of data such as reaction fluxes, metabolite concentrations, and kinetic constants. The ..."
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Cited by 6 (0 self)
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The quantitative effects of environmental and genetic perturbations on metabolism can be studied in silico using kinetic models. We present a strategy for largescale model construction based on a logical layering of data such as reaction fluxes, metabolite concentrations, and kinetic constants. The resulting models contain realistic standard rate laws and plausible parameters, adhere to the laws of thermodynamics, and reproduce a predefined steady state. These features have not been simultaneously achieved by previous workflows. We demonstrate the advantages and limitations of the workflow by translating the yeast consensus metabolic network into a kinetic model. Despite crudely selected data, the model shows realistic control behaviour, a stable dynamic, and realistic response to perturbations in extracellular glucose concentrations. The paper concludes by outlining how new data can continuously be fed into the workflow and how iterative model
Memory lower bounds for randomized collaborative search and implications for biology
 In Distributed Computing
, 2012
"... Abstract. Initial knowledge regarding group size can be crucial for collective performance. We study this relation in the context of the Ants Nearby Treasure Search (ANTS) problem [18], which models natural cooperative foraging behavior such as that performed by ants around their nest. In this pro ..."
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Abstract. Initial knowledge regarding group size can be crucial for collective performance. We study this relation in the context of the Ants Nearby Treasure Search (ANTS) problem [18], which models natural cooperative foraging behavior such as that performed by ants around their nest. In this problem, k (probabilistic) agents, initially placed at some central location, collectively search for a treasure on the twodimensional grid. The treasure is placed at a target location by an adversary and the goal is to find it as fast as possible as a function of both k and D, where D is the (unknown) distance between the central location and the target. It is easy to see that T = Ω(D+D2/k) time units are necessary for finding the treasure. Recently, it has been established that O(T) time is sufficient if the agents know their total number k (or a constant approximation of it), and enough memory bits are available at their disposal [18]. In this paper, we establish lower bounds on the agent memory size required for achieving certain running time performances. To the best our knowledge, these bounds are the first nontrivial lower bounds for the memory size of probabilistic searchers. For example, for every given positive constant , terminating the search by time O(log1− k · T) requires agents to use Ω(log log k) memory bits. From a high level perspective, we illustrate how methods from distributed computing can be useful in generating lower bounds for cooperative biological ensembles. Indeed, if experiments that comply with our setting reveal that the ants ’ search is time efficient, then our theoretical lower bounds can provide some insight on the memory ants use for this task.
A bayesian approach to targeted experiment design
 Bioinformatics
, 2012
"... Motivation: Systems biology employs mathematical modelling to further our understanding of biochemical pathways. Since the amount of experimental data on which the models are parameterized is often limited, these models exhibit large uncertainty in both parameters and predictions. Statistical meth ..."
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Cited by 5 (0 self)
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Motivation: Systems biology employs mathematical modelling to further our understanding of biochemical pathways. Since the amount of experimental data on which the models are parameterized is often limited, these models exhibit large uncertainty in both parameters and predictions. Statistical methods can be used to select experiments that will reduce such uncertainty in an optimal manner. However, existing methods for Optimal Experiment Design (OED) rely on assumptions that are inappropriate when data is scarce considering model complexity. Results: We have developed a novel method to perform OED for models that cope with large parameter uncertainty. We employ a Bayesian approach involving importance sampling of the Posterior Predictive Distribution to predict the efficacy of a new measurement at reducing the uncertainty of a selected prediction. We demonstrate the method by applying it to a case where we show that specific combinations of experiments result in more precise predictions. Availability: Source code is available at:
Identification of nonlinear systems with stable oscillations
 in 50th IEEE Conference on Decision and Control (CDC). IEEE
, 2011
"... Abstract — We propose a convex optimization procedure for identification of nonlinear systems that exhibit stable limit cycles. It extends the “robust identification error ” framework in which a convex upper bound on simulation error is optimized to fit rational polynomial models with a strong stabi ..."
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Cited by 5 (4 self)
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Abstract — We propose a convex optimization procedure for identification of nonlinear systems that exhibit stable limit cycles. It extends the “robust identification error ” framework in which a convex upper bound on simulation error is optimized to fit rational polynomial models with a strong stability guarantee. In this work, we relax the stability constraint using the concepts of transverse dynamics and orbital stability, thus allowing systems with autonomous oscillations to be identified. The resulting optimization problem is convex, and an approximate simulationerror bound is proved without assuming that the true system is in the model class, or that the number of measurements goes to infinity. The method is illustrated by identifying a highfidelity model from experimental recordings of a live rat hippocampal neuron in culture. I.