Search

For dynamic natural resource models a few fundamental questions are often omitted in practice such as (i) “Is it possible to calibrate the model?” and (ii) “Can we reconstruct all unknown dynamic state variables given a certain data record?” Other related questions are (iii) “Does the system allow the state variables to be controlled (or managed) to desired optimal values (e.g., in case of maximum sustainable yield)?” In this paper we highlight and discuss a software tool (the StrucID App) that allows a rapid evaluation of these fundamental and structural model properties that are important to study before a calibration and subsequent simulation of the model.

The conversion of supplemental greenhouse light energy into biomass is not always optimal. Recent trends in global energy prices and discussions on climate change highlight the need to reduce our energy footprint associated with the use of supplemental light in greenhouse crop production. This can be achieved by implementing “smart” lighting regimens which in turn rely on a good understanding of how fluctuating light influences photosynthetic physiology. Here, a simple fit-for-purpose dynamic model is presented. It accurately predicts net leaf photosynthesis under natural fluctuating light. It comprises two ordinary differential equations predicting: 1) the total stomatal conductance to CO2 diffusion and 2) the CO2 concentration inside a leaf. It contains elements of the Farquhar-von Caemmerer-Berry model and the successful incorporation of this model suggests that for tomato (Solanum lycopersicum L.), it is sufficient to assume that Rubisco remains activated despite rapid fluctuations in irradiance. Furthermore, predictions of the net photosynthetic rate under both 400ppm and enriched 800ppm ambient CO2 concentrations indicate a strong correlation between the dynamic rate of photosynthesis and the rate of electron transport. Finally, we are able to indicate whether dynamic photosynthesis is Rubisco or electron transport rate limited.

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

A fundamental principle of systems biology is its perpetual need for new technologies that can solve challenging biological questions. This precept will continue to drive the development of novel analytical tools. The virtuous cycle of biological progress can therefore only exist when experts from different disciplines including biology, chemistry, computer science, engineering, mathematics, and medicine collaborate.General opinion is however that one of the challenges facing the systems biology community is the lag in the development of such technologies. The topic of structural identifiability in particular has been of interest to the systems biology community. This is because researchers in this field often face experimental limitations. These limitations, combined with the fact that systems biology models can contain vast numbers of unknown parameters, necessitate an identifiability analysis. In reality, analysing the structural identifiability of systems biology models, even when they contain only a few states and system parameters, may be challenging. As these models increase in size and complexity, this difficulty is exasperated, and one becomes limited to only a few methods capable of analysing large ordinary differential equation models.In this thesis I study the use of a computationally efficient algorithm, well suited to the analysis of large models, in the model development process. The three related objectives of this thesis are: 1) develop an accurate method to asses the structural identifiability of large possibly nonlinear ordinary differential models, 2) implement thismethod in the preliminary design of experiments, and 3) use the method to address the topic of structural unidentifiability.To improve the method’s accuracy, I systematically study the role of individual factors, such as the number of experimentally measured sensors, on the sharpness of results. Based on the findings, I propose measures that can improve numerical accuracy.To address th

An efficient method that assists in the re-parametrization of structurally unidentifiable models is introduced. It significantly reduces computational demand by combining numerical and symbolic identifiability calculations. This hybrid approach facilitates the re-parametrization of large unidentifiable ordinary differential equation models, including models where state transformations are required. A model is first assessed numerically, to discover potential structurally unidentifiable parameters. We then use symbolic calculations to confirm the numerical results, after which we describe the algebraic relationships between the unidentifiable parameters. Finally, the unidentifiable parameters are substituted with new parameters and simplification ensures that all the unidentifiable parameters are eliminated from the original model structure. The novelty of this method is its utilisation of numerical results, which notably reduces the number of symbolic calculations required. We illustrate our procedure and the detailed re-parametrization process in 5 examples: (1) an immunological model, (2) a microbial growth model, (3) a lung cancer model, (4) a JAK/STAT model, and (5) a small linear model with a non-scalable re-parametrization.

The process of inferring parameter values from experimental data can be a cumbersome task. In addition, the collection of experimental data can be time consuming and costly. This paper covers both these issues by addressing the following question: "Which experimental outputs should be measured to ensure that unique model parameters can be calculated?". Stated formally, we examine the topic of minimal output sets that guarantee a model's structural identifiability. To that end, we introduce an algorithm that guides a researcher as to which model outputs to measure. Our algorithm consists of an iterative structural identifiability analysis and can determine multiple minimal output sets of a model. This choice in different output sets offers researchers flexibility during experimental design. Our method can determine minimal output sets of large differential equation models within short computational times.

For a reconstruction of state and parameter values in a dynamic system model, first the question whether these values can be uniquely determined from the data must be answered. This structural model property is known as observability or, in case of parameter calibration only, identifiability. Testing a given model for observability is a well studied problem in the systems and control sciences. However, it is increasingly difficult, if not impossible, to address this property for large size models that, nowadays, are frequently used. We demonstrate the application of a recently developed algorithm that overcomes this problem and is remarkably efficient. As an illustration we show how an observability analysis for a Chinese Hamster Ovary Cell model (34 states, 117 parameters), a JAKSTAT signalling model (31 states, 51 parameters), and a MAP Kinase model (100 states, 88 parameters) can be established in a very short time.

The architecture of tomato inflorescence strongly affects flower production and subsequent crop yield. To understand the genetic activities involved, insight into the underlying network of genes that initiate and control the sympodial growth in the tomato is essential. In this paper, we show how the structure of this network can be derived from available data of the expressions of the involved genes. Our approach starts from employing biological expert knowledge to select the most probable gene candidates behind branching behavior. To find how these genes interact, we develop a stepwise procedure for computational inference of the network structure. Our data consists of expression levels from primary shoot meristems, measured at different developmental stages on three different genotypes of tomato. With the network inferred by our algorithm, we can explain the dynamics corresponding to all three genotypes simultaneously, despite their apparent dissimilarities. We also correctly predict the chronological order of expression peaks for the main hubs in the network. Based on the inferred network, using optimal experimental design criteria, we are able to suggest an informative set of experiments for further investigation of the mechanisms underlying branching behavior.

The architecture of tomato inflorescence strongly affects flower production and subsequent crop yield. To understand the genetic activities involved, insight into the underlying network of genes that initiate and control the sympodial growth in the tomato is essential. In this paper, we show how the structure of this network can be derived from available data of the expressions of the involved genes. Our approach starts from employing biological expert knowledge to select the most probable gene candidates behind branching behavior. To find how these genes interact, we develop a stepwise procedure for computational inference of the network structure. Our data consists of expression levels from primary shoot meristems, measured at different developmental stages on three different genotypes of tomato. With the network inferred by our algorithm, we can explain the dynamics corresponding to all three genotypes simultaneously, despite their apparent dissimilarities. We also correctly predict the chronological order of expression peaks for the main hubs in the network. Based on the inferred network, using optimal experimental design criteria, we are able to suggest an informative set of experiments for further investigation of the mechanisms underlying branching behavior

Multi-parameter models in systems biology are typically ‘sloppy’: some parameters or combinations of parameters may be hard to estimate from data, whereas others are not. One might expect that parameter uncertainty automatically leads to uncertain predictions, but this is not the case. We illustrate this by showing that the prediction uncertainty of each of six sloppy models varies enormously among different predictions. Statistical approximations of parameter uncertainty may lead to dramatic errors in prediction uncertainty estimation. We argue that prediction uncertainty assessment must therefore be performed on a per-prediction basis using a full computational uncertainty analysis. In practice this is feasible by providing a model with a sample or ensemble representing the distribution of its parameters. Within a Bayesian framework, such a sample may be generated by a Markov Chain Monte Carlo (MCMC) algorithm that infers the parameter distribution based on experimental data. Matlab code for generating the sample (with the Differential Evolution Markov Chain sampler) and the subsequent uncertainty analysis using such a sample, is supplied as Supplemental Information.

Flavonoids are secondary metabolites present in all terrestrial plants. The flavonoid pathway has been extensively studied, and many of the involved genes and metabolites have been described in the literature. Despite this extensive knowledge, the functioning of the pathway in vivo is still poorly understood. Here, we study the flavonoid pathway using both experiments and mathematical models. We measured flavonoid metabolite dynamics in two tissues, hypocotyls and cotyledons, during tomato seedling development. Interestingly, the same backbone of interactions leads to very different accumulation patterns in the different tissues. Initially, we developed a mathematical model with constant enzyme concentrations that described the metabolic networks separately in both tissues. This model was unable to fit the measured flavonoid dynamics in the hypocotyls, even if we allowed unrealistic parameter values. This suggested us to investigate the effect of transcript abundance on flavonoid accumulation. We found that the expression of candidate flavonoid genes varies considerably with time. Variation in transcript abundance results in enzymatic variation, which could have a large effect on metabolite accumulation. Candidate transcript abundance was included in the mathematical model as representative for enzyme concentration. We fitted the resulting model to the flavonoid dynamics in the cotyledons, and tested it by applying it to the data from hypocotyls. When transcript abundance is included, we are indeed able to explain flavonoid dynamics in both tissues. Importantly, this is possible under the biologically relevant restriction that the enzymatic properties estimated by the model are conserved between the tissues.

Background Current research in network reverse engineering for genetic or metabolic networks very often does not include a proper experimental and/or input design. In this paper we address this issue in more detail and suggest a method that includes an iterative design of experiments based, on the most recent data that become available. The presented approach allows a reliable reconstruction of the network and addresses an important issue, i.e., the analysis and the propagation of uncertainties as they exist in both the data and in our own knowledge. These two types of uncertainties have their immediate ramifications for the uncertainties in the parameter estimates and, hence, are taken into account from the very beginning of our experimental design. Findings The method is demonstrated for two small networks that include a genetic network for mRNA synthesis and degradation and an oscillatory network describing a molecular network underlying adenosine 3'-5' cyclic monophosphate (cAMP) as observed in populations of Dyctyostelium cells. In both cases a substantial reduction in parameter uncertainty was observed. Extension to larger scale networks is possible but needs a more rigorous parameter estimation algorithm that includes sparsity as a constraint in the optimization procedure. Conclusion We conclude that a careful experiment design very often (but not always) pays off in terms of reliability in the inferred network topology. For large scale networks a better parameter estimation algorithm is required that includes sparsity as an additional constraint. These algorithms are available in the literature and can also be used in an adaptive optimal design setting as demonstrated in this paper

Autonomous robots for agricultural practices will become reality soon. These mobile robots could take over regular tasks such as scouting for weeds and diseases, plant specific applications, yield and field mapping and for instance the release of info-chemicals for attracting predators of pests. This paper presents WURking, a small sized sub-canopy autonomous robot that can be used for a wide range of tasks on the farm of the future. WURking was designed for navigating within row crops like corn. It consists of a mobile platform with three independently driven steerable wheels. The robot carries ultrasound sensors and a gyroscope used for navigation between the crop rows, end of row detection and headland turning. A camera is mounted to detect objects like weeds. High level control of this robot was implemented using the visual programming language LabView. A data fusion technique is used to extract the position and orientation of the robot relative to the crop rows, from the redundant set of sensor data. Feedback linearization of the non-linear system dynamics yielded a simple linear controller structure which was fed by state estimates generated by a Kalman filter using the raw ultrasound sensor data. The headland turning was based on a proportional controller using data from the gyroscope. This paper contains a description of the robot as well as results of a performance test performed in 2008. This test revealed that the robot was able to navigate through the corn field with a maximum offset of ±10 cm from the centre of the rows and an maximum orientation error of ±0.15 rad.

The paper presents a method to derive an optimal parametric sensitivity controller for optimal estimation of a set of parameters in an experiment. The method is demonstrated for a fed batch bio-reactor case study for optimal estimation of the saturation constant Ks and, albeit intuitively, the parameter combination "mu-max X/Y" where mu-max is the maximum growth rate [g/min], Y is the yield coefficient [g/g], and X is the (constant) biomass [g].

The paper aims to develop a more systematic approach to the problem of model structure identification for continuous time (physically based) mathematical models with discrete observations. An introduction to the model structure identification problem is first presented. The approach to this problem is the application of a modified version of the extended Kalman filter, originally defined in [23]. This filter is tested using artificial data. The results obtained lead to a further discussion of the filter's stability properties and also to a metaphor for model structures. Further study of the numerical properties of the algorithm reveal that its stability can be improved. An alternative algorithm, the so called recursive prediction error algorithm, is modified to a Kalman-like algorithm in continuous-discrete formulation. This algorithm is also tested using artificial data. The RPE-type of filter has better stability properties and appears to be very robust to initial conditions. Its applicability to environmental case studies is set out through the application of the filter to a familiar case study. Applications of this type of filter is valuable for validation/verification of environmental and/or economical models that include a set of ordinary differential equations.