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.
Under natural conditions, irradiance frequently fluctuates, causing net photosynthesis rate (A) to respond slowly and reducing the yields. We quantified the genotypic variation of photosynthetic induction in 19 genotypes among the following six horticultural crops: basil, chrysanthemum, cucumber, lettuce, tomato, and rose. Kinetics of photosynthetic induction and the stomatal opening were measured by exposing shade-adapted leaves (50 μmol m–2 s–1) to a high irradiance (1000 μmol m–2 s–1) until A reached a steady state. Rubisco activation rate was estimated by the kinetics of carboxylation capacity, which was quantified using dynamic A vs. [CO2] curves. Generally, variations in photosynthetic induction kinetics were larger between crops and smaller between cultivars of the same crop. Time until reaching 20–90% of full A induction varied by 40–60% across genotypes, and this was driven by a variation in the stomatal opening rather than Rubisco activation kinetics. Stomatal conductance kinetics were partly determined by differences in the stomatal size and density; species with densely packed, smaller stomata (e.g., cucumber) tended to open their stomata faster, adapting stomatal conductance more rapidly and efficiently than species with larger but fewer stomata (e.g., chrysanthemum). We conclude that manipulating stomatal traits may speed up photosynthetic induction and growth of horticultural crops under natural irradiance fluctuations.
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.
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