A small dynamic leaf-level model predicting photosynthesis in greenhouse tomatoes

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.

Learning from COVID-19: The inclusion of vulnerable groups in COVID-19 responses across Europe

Background

More than two years into the pandemic, many European countries have begun to evaluate their COVID-19 public health responses and draw lessons for future preparedness. As the COVID-19 crisis has exacerbated intersectional social and health inequalities, it is pertinent to evaluate the extent to which COVID-19 responses have successfully responded to the diverse needs of various vulnerable groups. We present a comparative analysis of how evaluations of European COVID-19 responses have assessed efforts to adapt or tailor COVID-19 responses to vulnerable groups, focusing on public testing and tracing strategies and vaccination campaigns.

Methods

We draw on data collected in the H2020 project COVINFORM. We combine insights from qualitative interviews conducted with public health policy- and decision makers in COVINFORM partner countries with a document review of available evaluations of COVID-19 responses published by both government and academic actors between March 2020 and June 2022.

Results

Across countries, evaluations of COVID-19 responses show that efforts to adapt or target public health responses to specific vulnerable groups became more common as the pandemic stretched on. Differences across countries were observed in relation to which groups were considered particularly vulnerable; the types of responses considered successful; as well as the organisational/governmental level at which responses were coordinated. Analyses reveal that the heavy emphasis on medical vulnerability distracted from efforts to address broader, structural inequalities, complicating the development of tailor-made policies.

Conclusions

The results inform ongoing policies that deal with the long-term consequences of the COVID-19 pandemic and aim to reduce disproportionate impacts faced by vulnerable groups. Our findings also add to a better understanding of how future preparedness structures should take into account how pandemic measures have unequal impacts.

Key messages

• As the COVID-19 crisis has exacerbated intersectional social and health inequalities, it is important to learn from efforts to adapt or tailor COVID-19 responses to vulnerable groups.

• The findings demonstrate how across Europe, the combination of particular sets of country-specific COVID-19 responses, tailor-made or not, yield specific consequences for vulnerable groups.

Robust banded protoxylem pattern formation through microtubule-based directional ROP diffusion restriction

In plant vascular tissue development, different cell wall patterns are formed, offering different mechanical properties optimised for different growth stages. Critical in these patterning processes are Rho of Plants (ROP) proteins, a class of evolutionarily conserved small GTPase proteins responsible for local membrane domain formation in many organisms. While te spotted metaxylem pattern can easily be understood as a result of a Turing-style reaction-diffusion mechanism, it remains an open question how the consistent orientation of evenly spaced bands and spirals as found in protoxylem is achieved. We hypothesise that this orientation results from an interaction between ROPs and an array of transversely oriented cortical microtubules that acts as a directional diffusion barrier. Here, we explore this hypothesis using partial differential equation models with anisotropic ROP diffusion and show that a horizontal microtubule array acting as a vertical diffusion barrier to active ROP can yield a horizontally banded ROP pattern. We then study the underlying mechanism in more detail, finding that it can only orient curved pattern features but not straight lines. This implies that, once formed, banded and spiral patterns cannot be reoriented by this mechanism. Finally, we observe that ROPs and microtubules together only form ultimately static patterns if the interaction is implemented with sufficient biological realism.

Small GTPase patterning: How to stabilise cluster coexistence

Many biological processes have to occur at specific locations on the cell membrane. These locations are often specified by the localised activity of small GTPase proteins. Some processes require the formation of a single cluster of active GTPase, also called unipolar polarisation (here “polarisation”), whereas others need multiple coexisting clusters. Moreover, sometimes the pattern of GTPase clusters is dynamically regulated after its formation. This raises the question how the same interacting protein components can produce such a rich variety of naturally occurring patterns. Most currently used models for GTPase-based patterning inherently yield polarisation. Such models may at best yield transient coexistence of at most a few clusters, and hence fail to explain several important biological phenomena. These existing models are all based on mass conservation of total GTPase and some form of direct or indirect positive feedback. Here, we show that either of two biologically plausible modifications can yield stable coexistence: including explicit GTPase turnover, i.e., breaking mass conservation, or negative feedback by activation of an inhibitor like a GAP. Since we start from two different polarising models our findings seem independent of the precise self-activation mechanism. By studying the net GTPase flows among clusters, we provide insight into how these mechanisms operate. Our coexistence models also allow for dynamical regulation of the final pattern, which we illustrate with examples of pollen tube growth and the branching of fungal hyphae. Together, these results provide a better understanding of how cells can tune a single system to generate a wide variety of biologically relevant patterns.

Determining minimal output sets that ensure structural identifiability

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.

Algorithm for a particle-based growth model for plant tissues

We have developed an algorithm for a particle-based model for the growth of plant tissues in three dimensions in which each cell is represented by a single particle, and connecting cell walls are represented as permanent bonds between particles. A sample of plant tissue is represented by a fixed network of bonded particles. If, and only if a cell divides, this network is updated locally. The update algorithm is implemented in a model where cell growth and division gives rise to forces between the cells, which are relaxed in steepest descent minimization. The same forces generate a pressure inside the cells, which moderates growth. The local nature of the algorithm makes it efficient computationally, so the model can deal with a large number of cells. We used the model to study the growth of plant tissues for a variety of model parameters, to show the viability of the algorithm.

Dynamic modelling of limitations on improving leaf CO2 assimilation under fluctuating irradiance

A dynamic model of leaf CO₂ assimilation was developed as an extension of the canonical steady-state model, by adding the effects of energy-dependent non-photochemical quenching (qE), chloroplast movement, photoinhibition, regulation of enzyme activity in the Calvin cycle, metabolite concentrations, and dynamic CO₂ diffusion. The model was calibrated and tested successfully using published measurements of gas exchange and chlorophyll fluorescence on Arabidopsis thaliana ecotype Col-0 and several photosynthetic mutants and transformants affecting the regulation of Rubisco activity (rca-2 and rwt43), non-photochemical quenching (npq4-1 and npq1-2), and sucrose synthesis (spsa1). The potential improvements on CO₂ assimilation under fluctuating irradiance that can be achieved by removing the kinetic limitations on the regulation of enzyme activities, electron transport, and stomatal conductance were calculated in silico for different scenarios. The model predicted that the rates of activation of enzymes in the Calvin cycle and stomatal opening were the most limiting (up to 17% improvement) and that effects varied with the frequency of fluctuations. On the other hand, relaxation of qE and chloroplast movement had a strong effect on average low-irradiance CO₂ assimilation (up to 10% improvement). Strong synergies among processes were found, such that removing all kinetic limitations simultaneously resulted in improvements of up to 32%.

R0: Host Longevity Matters

The basic reproduction ratio, R₀, is a fundamental concept in epidemiology. It is defined as the total number of secondary infections brought on by a single primary infection, in a totally susceptible population. The value of R₀ indicates whether a starting epidemic reaches a considerable part of the population and causes a lot of damage, or whether it remains restricted to a relatively small number of individuals. To calculate R₀ one has to evaluate an integral that ranges over the duration of the infection of the host. This duration is, of course, limited by remaining host longevity. So, R₀ depends on remaining host longevity and in this paper we show that for long-lived hosts this aspect may not be ignored for long-lasting infections. We investigate in particular how this epidemiological measure of pathogen fitness depends on host longevity. For our analyses we adopt and combine a generic within- and between-host model from the literature. To find the optimal strategy for a pathogen from an evolutionary point of view, we focus on the indicator \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0^{{opt}}$$\end{document}R0opt, i.e., the optimum of R₀ as a function of its replication and mutation rates. These are the within-host parameters that the pathogen has at its disposal to optimize its strategy. We show that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$R_0^{{opt}}$$\end{document}R0opt is highly influenced by remaining host longevity in combination with the contact rate between hosts in a susceptible population. In addition, these two parameters determine whether a killer-like or a milker-like strategy is optimal for a given pathogen. In the killer-like strategy the pathogen has a high rate of reproduction within the host in a short time span causing a relatively short disease, whereas in the milker-like strategy the pathogen multiplies relatively slowly, producing a continuous small amount of offspring over time with a small effect on host health. The present research allows for the determination of a bifurcation line in the plane of host longevity versus contact rate that forms the boundary between the milker-like and killer-like regions. This plot shows that for short remaining host longevities the killer-like strategy is optimal, whereas for very long remaining host longevities the milker-like strategy is advantageous. For in-between values of host longevity, the contact rate determines which of both strategies is optimal.

In Silico Analysis of the Regulation of the Photosynthetic Electron Transport Chain in C3 Plants

We present a new simulation model of the reactions in the photosynthetic electron transport chain of C3 species. We show that including recent insights about the regulation of the thylakoid proton motive force, ATP/NADPH balancing mechanisms (cyclic and noncyclic alternative electron transport), and regulation of Rubisco activity leads to emergent behaviors that may affect the operation and regulation of photosynthesis under different dynamic environmental conditions. The model was parameterized with experimental results in the literature, with a focus on Arabidopsis (Arabidopsis thaliana). A dataset was constructed from multiple sources, including measurements of steady-state and dynamic gas exchange, chlorophyll fluorescence, and absorbance spectroscopy under different light intensities and CO2, to test predictions of the model under different experimental conditions. Simulations suggested that there are strong interactions between cyclic and noncyclic alternative electron transport and that an excess capacity for alternative electron transport is required to ensure adequate redox state and lumen pH. Furthermore, the model predicted that, under specific conditions, reduction of ferredoxin by plastoquinol is possible after a rapid increase in light intensity. Further analysis also revealed that the relationship between ATP synthesis and proton motive force was highly regulated by the concentrations of ATP, ADP, and inorganic phosphate, and this facilitated an increase in nonphotochemical quenching and proton motive force under conditions where metabolism was limiting, such as low CO2, high light intensity, or combined high CO2 and high light intensity. The model may be used as an in silico platform for future research on the regulation of photosynthetic electron transport.

Observability of Complex Systems: Finding the Gap

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.

Floral pathway integrator gene expression mediates gradual transmission of environmental and endogenous cues to flowering time

The appropriate timing of flowering is crucial for the reproductive success of plants. Hence, intricate genetic networks integrate various environmental and endogenous cues such as temperature or hormonal statues. These signals integrate into a network of floral pathway integrator genes. At a quantitative level, it is currently unclear how the impact of genetic variation in signaling pathways on flowering time is mediated by floral pathway integrator genes. Here, using datasets available from literature, we connect Arabidopsis thaliana flowering time in genetic backgrounds varying in upstream signalling components with the expression levels of floral pathway integrator genes in these genetic backgrounds. Our modelling results indicate that flowering time depends in a quite linear way on expression levels of floral pathway integrator genes. This gradual, proportional response of flowering time to upstream changes enables a gradual adaptation to changing environmental factors such as temperature and light.

A quantitative and dynamic model of the Arabidopsis flowering time gene regulatory network

Various environmental signals integrate into a network of floral regulatory genes leading to the final decision on when to flower. Although a wealth of qualitative knowledge is available on how flowering time genes regulate each other, only a few studies incorporated this knowledge into predictive models. Such models are invaluable as they enable to investigate how various types of inputs are combined to give a quantitative readout. To investigate the effect of gene expression disturbances on flowering time, we developed a dynamic model for the regulation of flowering time in Arabidopsis thaliana. Model parameters were estimated based on expression time-courses for relevant genes, and a consistent set of flowering times for plants of various genetic backgrounds. Validation was performed by predicting changes in expression level in mutant backgrounds and comparing these predictions with independent expression data, and by comparison of predicted and experimental flowering times for several double mutants. Remarkably, the model predicts that a disturbance in a particular gene has not necessarily the largest impact on directly connected genes. For example, the model predicts that SUPPRESSOR OF OVEREXPRESSION OF CONSTANS (SOC1) mutation has a larger impact on APETALA1 (AP1), which is not directly regulated by SOC1, compared to its effect on LEAFY (LFY) which is under direct control of SOC1. This was confirmed by expression data. Another model prediction involves the importance of cooperativity in the regulation of APETALA1 (AP1) by LFY, a prediction supported by experimental evidence. Concluding, our model for flowering time gene regulation enables to address how different quantitative inputs are combined into one quantitative output, flowering time.

A New Modified Histogram Matching Normalization for Time Series Microarray Analysis

Microarray data is often utilized in inferring regulatory networks. Quantile normalization (QN) is a popular method to reduce array-to-array variation. We show that in the context of time series measurements QN may not be the best choice for this task, especially not if the inference is based on continuous time ODE model. We propose an alternative normalization method that is better suited for network inference from time series data.

Prediction uncertainty assessment of a systems biology model requires a sample of the full probability distribution of its parameters

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.

Inferring the gene network underlying the branching of tomato inflorescence

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.

Phase segregation through transient network formation in a binary particle suspension in simple shear: application to dough

In this paper we describe a viscoelastic type of phase separation in a simulated binary fluid with a sticky and an inert component, without any external gradients. Phase segregation under simple shear occurs due to transient network formation of the sticky component, expelling the inert particles from the network. When model parameters are adjusted to reduce network formation and rearrangement, the segregation effect is significantly smaller or absent. The behavior is independent of shear rate; segregation increases mainly with shear strain. The model is applied to wheat dough. Recent experiments have shown that prolonged shear flow of wheat dough can even give macroscopic segregation.

Modelling the impact of HIV on the populations of South Africa and Botswana

We develop and use mathematical models that describe changes in the South African population over the last decades, brought on by HIV and AIDS. We do not model all the phases in HIV progression but rather, we show that a relatively simple model is sufficient to represent the data and allows us to investigate important aspects of HIV infection: firstly, we are able to investigate the effect of awareness on the prevalence of HIV and secondly, it enables us to make a comparison between South Africa and Botswana. A comparison is made between two models: a model that does not reflect awareness of the devastating impact of HIV and AIDS, and a model with an added psychological awareness factor. Both models are fitted to data that reflects the incidence of HIV and AIDS within South Africa. This allows us to examine the impact of psychological awareness. We show that inclusion of the effect of awareness is absolutely necessary to arrive at a model description that satisfactorily fits the available HIV and AIDS data for South Africa. We also show that a relatively simple modelling of awareness (as opposed to more complex mathematical techniques that have been used in past studies) is sufficient to accurately describe the observed patterns in the data. Even though awareness alone is not sufficient to eradicate any disease and other control strategies should be explored and implemented concurrently with educational campaigns, we are able to conclude (through thorough model analyses procedures) that the current level of awareness in South Africa is far below the level that is effectively required to eradicate HIV from the South African population. The awareness model is also fitted to HIV-related data for Botswana and we compare the results with the South African case. Though the effect of awareness is currently estimated at a much higher level in Botswana, other factors such as poorer health care and cultural differences may play a role in limiting the ability of awareness to combat HIV in Botswana.

Modelling cell division and endoreduplication in tomato fruit pericarp

In many developing plant tissues and organs, differentiating cells switch from the classical cell cycle to an alternative partial cycle. This partial cycle bypasses mitosis and allows for multiple rounds of genome duplication without cell division, giving rise to cells with high ploidy numbers. This partial cycle is referred to as endoreduplication. Cell division and endoreduplication are important processes for biomass allocation and yield in tomato. Quantitative trait loci for tomato fruit size or weight are frequently associated with variations in the pericarp cell number, and due to the tight connection between endoreduplication and cell expansion and the prevalence of polyploidy in storage tissues, a functional correlation between nuclear ploidy number and cell growth has also been implicated (karyoplasmic ratio theory). In this paper, we assess the applicability of putative mechanisms for the onset of endoreduplication in tomato pericarp cells via development of a mathematical model for the cell cycle gene regulatory network. We focus on targets for regulation of the transition to endoreduplication by the phytohormone auxin, which is known to play a vital role in the onset of cell expansion and differentiation in developing tomato fruit. We show that several putative mechanisms are capable of inducing the onset of endoreduplication. This redundancy in explanatory mechanisms is explained by analysing system behaviour as a function of their combined action. Namely, when all these routes to endoreduplication are used in a combined fashion, robustness of the regulation of the transition to endoreduplication is greatly improved.

Work satisfaction at a multidisciplinary gastrointestinal oncology fast-track outpatient clinic

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Background: Physician and nurse satisfaction is positively correlated with patient satisfaction. In our university centre we have established the Gastrointestinal Oncology Clinic Amsterdam (GIOCA), a patient centred multidisciplinary one day diagnostics and fast track treatment planning outpatient clinic for gastrointestinal malignancies. The GIOCA team consists of dedicated surgeons, gastroenterologists, medical oncologists, radiation oncologists, radiologists, nuclear radiologists, pathologists, and specialized nurses. We have measured a high patient satisfaction. However to our knowledge there are no studies that focus on the satisfaction of physicians and nurses working within a multidisciplinary team. Our aim was to evaluate the experience and work satisfaction of the physicians and nurses at GIOCA. Methods: A qualitative observational study was performed to compose a questionnaire. This questionnaire was then sent to every physician (specialist, fellow, and resident) and nurse (n=77) working at the outpatient clinic. Answers were given on a 5-point Likert scale. Data were analysed using non-parametric tests. Results: The questionnaire was answered by 73 respondents, of whom 8.2% were nurses and 91.8% were physicians (95% overall response rate). Overall satisfaction with the fast track outpatient clinic was high for all groups (4; 3-5). The workload was experienced as average by physicians and high by nurses (p<0.001). The highest emotional strain was reported by nurses and residents. The emotional strain reported by residents was significantly higher compared to the level of emotional strain reported by specialists (p=0.034). The quality of the multidisciplinary meeting was rated high by both physicians and nurses. The importance of a multidisciplinary one day diagnostics outpatient clinic was invariably rated high to very high by all physicians and nurses. Conclusions: The overall work satisfaction at GIOCA is high. A patient centred one day diagnostics and fast track treatment outpatient clinic for gastrointestinal malignancies is indispensible according to the physicians and nurses. This may have contributed to a high patient satisfaction and a high overall work satisfaction.

Crop management impacts the efficiency of quantitative trait loci (QTL) detection and use: case study of fruit load×QTL interactions

Mapping studies using populations with introgressed marker-defined genomic regions are continuously increasing knowledge about quantitative trait loci (QTL) that correlate with variation in important crop traits. This knowledge is useful for plant breeding, although combining desired traits in one genotype might be complicated by the mode of inheritance and co-localization of QTL with antagonistic effects, and by physiological trade-offs, and feed-back or feed-forward mechanisms. Therefore, integrating advances at the genetic level with insight into influences of environment and crop management on crop performance remains difficult. Whereas mapping studies can pinpoint correlations between QTL and phenotypic traits for specific conditions, ignoring or overlooking the importance of environment or crop management can jeopardize the relevance of such assessments. Here, we focus on fruit load (a measure determining competition among fruits on one plant) and its strong modulation of QTL effects on fruit size and composition. Following an integral approach, we show which fruit traits are affected by fruit load, to which underlying processes these traits can be linked, and which processes at lower and higher integration levels are affected by fruit load (and subsequently influence fruit traits). This opinion paper (i) argues that a mechanistic framework to interpret interactions between fruit load and QTL effects is needed, (ii) pleads for consideration of the context of agronomic management when detecting QTL, (iii) makes a case for incorporating interacting factors in the experimental set-up of QTL mapping studies, and (iv) provides recommendations to improve efficiency in QTL detection and use, with particular focus on model-based marker-assisted breeding.

Predictive modelling of complex agronomic and biological systems

Biological systems are tremendously complex in their functioning and regulation. Studying the multifaceted behaviour and describing the performance of such complexity has challenged the scientific community for years. The reduction of real-world intricacy into simple descriptive models has therefore convinced many researchers of the usefulness of introducing mathematics into biological sciences. Predictive modelling takes such an approach another step further in that it takes advantage of existing knowledge to project the performance of a system in alternating scenarios. The ever growing amounts of available data generated by assessing biological systems at increasingly higher detail provide unique opportunities for future modelling and experiment design. Here we aim to provide an overview of the progress made in modelling over time and the currently prevalent approaches for iterative modelling cycles in modern biology. We will further argue for the importance of versatility in modelling approaches, including parameter estimation, model reduction and network reconstruction. Finally, we will discuss the difficulties in overcoming the mathematical interpretation of in vivo complexity and address some of the future challenges lying ahead.

The flavonoid pathway in tomato seedlings: transcript abundance and the modeling of metabolite dynamics

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.

Fast track multidisciplinary approach for gastrointestinal tumours

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Background: The incidence of gastrointestinal (GI) tract tumours in the Netherlands is rising. However, GI oncological medical care is still delayed and fragmented. There is a need for better and faster diagnostic work-up, faster start of treatment, but also for expert multidisciplinary deliberation. Therefore, the GIOCA, Gastro Intestinal Oncological Centre Amsterdam, started in 2009 as a one day fast track multidisciplinary outpatient clinic for patients with GI malignancies. The goal was an admission time (AT, time from referral to consultation) of < 1 week and a run through time (RTT, time from multidisciplinary meeting to start of treatment) of < 3 weeks. The aim of this study was first to evaluate the AT and RTT at GIOCA and secondly to evaluate the subjective impact of this novel strategy on patients burden and satisfaction. Methods: Patients were seen at GIOCA in the morning on a colorectal (CRC ), an oesophago/gastric (OES) or a hepatopancreaticobiliary (HPB) day. That same morning (additional) diagnostics were performed. At the multidisciplinary meeting afterwards, a final diagnosis and treatment plan was made, which was later communicated to the patient. The patient then met all involved specialists. AT and RTT were prospectively recorded for all GIOCA patients. For HPB malignancies, AT and RTT could be compared to historical controls from the preceding year. Patient impact and satisfaction was evaluated using a before/after cohort study design, with a written questionnaire prospectively administered to all GIOCA patients and compared to data obtained 3 months prior to GIOCA start. Results: Analyses of 2009 and 2010 showed the following results: The average AT for CRC, OES and HPB was 7.6, 9.5 and 9 days respectively. The average RTT for CRC, OES and HPB was 20.8, 24 and 25 days respectively. For HPB malignancies, this was 10.4 days (AT) and 59.8 days (RTT) in the year preceding GIOCA. Higher levels of patient satisfaction were obtained in GIOCA patients compared to controls. More than 90% of the patients interviewed would advice the GIOCA outpatient approach to other patients. Conclusions: Progress has been made in the AT and RTT in GI malignancies in GIOCA, but the goals were still not all reached. Patients were very satisfied with this novel approach.

Network inference via adaptive optimal design

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.

A mathematical model for BRASSINOSTEROID INSENSITIVE1-mediated signaling in root growth and hypocotyl elongation

Brassinosteroid (BR) signaling is essential for plant growth and development. In Arabidopsis (Arabidopsis thaliana), BRs are perceived by the BRASSINOSTEROID INSENSITIVE1 (BRI1) receptor. Root growth and hypocotyl elongation are convenient downstream physiological outputs of BR signaling. A computational approach was employed to predict root growth solely on the basis of BRI1 receptor activity. The developed mathematical model predicts that during normal root growth, few receptors are occupied with ligand. The model faithfully predicts root growth, as observed in bri1 loss-of-function mutants. For roots, it incorporates one stimulatory and two inhibitory modules, while for hypocotyls, a single inhibitory module is sufficient. Root growth as observed when BRI1 is overexpressed can only be predicted assuming that a decrease occurred in the BRI1 half-maximum response values. Root growth appears highly sensitive to variation in BR concentration and much less to reduction in BRI1 receptor level, suggesting that regulation occurs primarily by ligand availability and biochemical activity.

Integrating two patterning processes in the flower

Spatial organ arrangement plays an important role in flower development. The position and the identity of floral organs is influenced by various processes, in particular the expression of MADS-box transcription factors for identity and dynamics of the plant hormone auxin for positioning. We are currently integrating patterning processes of MADS and auxin into our computational models, based on interactions that are known from experiments, in order to get insight in how these define the floral body plan. The resulting computational model will help to explore hypothetical interactions between the MADS and auxin regulation networks in floral organ patterning.

MYCN and ALKF1174L are sufficient to drive neuroblastoma development from neural crest progenitor cells

Neuroblastoma is an embryonal tumor with a heterogeneous clinical course. The tumor is presumed to be derived from the neural crest, but the cells of origin remain to be determined. To date, few recurrent genetic changes contributing to neuroblastoma formation, such as amplification of the MYCN oncogene and activating mutations of the ALK oncogene, have been identified. The possibility to model neuroblastoma in mice allows investigation of the cell of origin hypothesis in further detail. Here we present the evidence that murine neural crest progenitor cells can give rise to neuroblastoma upon transformation with MYCN or ALK(F1174L). For this purpose we used JoMa1, a multipotent neural crest progenitor cell line, which is kept in a viable and undifferentiated state by a tamoxifen-activated c-Myc transgene (c-MycER(T)). Expression of MYCN or ALK(F1174L), one of the oncogenic ALK variants identified in primary neuroblastomas, enabled these cells to grow independently of c-MycER(T) activity in vitro and caused formation of neuroblastoma-like tumors in vivo in contrast to parental JoMa1 cells and JoMa1 cells-expressing TrkA or GFP. Tumorigenicity was enhanced upon serial transplantation of tumor-derived cells, and tumor cells remained susceptible to the MYC-inhibitor, NBT-272, indicating that cell growth depended on functional MYCN. Our findings support neural crest progenitor cells as the precursor cells of neuroblastoma, and indicate that neuroblastomas arise as their malignant progeny.

Simulation of organ patterning on the floral meristem using a polar auxin transport model

An intriguing phenomenon in plant development is the timing and positioning of lateral organ initiation, which is a fundamental aspect of plant architecture. Although important progress has been made in elucidating the role of auxin transport in the vegetative shoot to explain the phyllotaxis of leaf formation in a spiral fashion, a model study of the role of auxin transport in whorled organ patterning in the expanding floral meristem is not available yet. We present an initial simulation approach to study the mechanisms that are expected to play an important role. Starting point is a confocal imaging study of Arabidopsis floral meristems at consecutive time points during flower development. These images reveal auxin accumulation patterns at the positions of the organs, which strongly suggests that the role of auxin in the floral meristem is similar to the role it plays in the shoot apical meristem. This is the basis for a simulation study of auxin transport through a growing floral meristem, which may answer the question whether auxin transport can in itself be responsible for the typical whorled floral pattern. We combined a cellular growth model for the meristem with a polar auxin transport model. The model predicts that sepals are initiated by auxin maxima arising early during meristem outgrowth. These form a pre-pattern relative to which a series of smaller auxin maxima are positioned, which partially overlap with the anlagen of petals, stamens, and carpels. We adjusted the model parameters corresponding to properties of floral mutants and found that the model predictions agree with the observed mutant patterns. The predicted timing of the primordia outgrowth and the timing and positioning of the sepal primordia show remarkable similarities with a developing flower in nature.

Lipid aggregate formation at an oscillating bubble surface: a simulation study

We perform a molecular dynamics simulation study of the behavior of a lipid coating layer on an oscillating bubble surface. Micrometer sized bubbles, stabilized with a lipid monolayer coating, are used in acoustic imaging as a contrast agent. The coating layer is expected to be strongly influenced by the oscillation of the bubble in the high frequency sound field, with a period of a microsecond. The typical time scale of molecular motion, however, is of the order of femtoseconds. One of the challenges is to bridge this nine decade gap in time scales. To this end we have developed a model that is highly coarse grained, but still features the essential mechanisms determining lipid dynamics, with time scales of picoseconds. This approach allows us to severely restrict the computing times, although we make use of very modest computing equipment. We show in our simulation that the amphiphilic monolayer folds upon contraction of the bubble, and forms micellar aggregates at the air-water interface. Some micellar structures survive consecutive re-expansion and indeed remain persistent over several cycles. These structures may add to the anisotropic behavior of the bubbles under oscillating conditions. We also investigated temperature and frequency dependence.

Redefining plant systems biology: from cell to ecosystem

Molecular biologists typically restrict systems biology to cellular levels. By contrast, ecologists define biological systems as communities of interacting individuals at different trophic levels that process energy, nutrient and information flows. Modern plant breeding needs to increase agricultural productivity while decreasing the ecological footprint. This requires a holistic systems biology approach that couples different aggregation levels while considering the variables that affect these biological systems from cell to community. The challenge is to generate accurate experimental data that can be used together with modelling concepts and techniques that allow experimentally verifying in silico predictions. The coupling of aggregation levels in plant sciences, termed Integral Quantification of Biological Organization (IQ(BiO)), might enhance our abilities to generate new desired plant phenotypes.

Continuous-time modeling of cell fate determination in Arabidopsis flowers

Background

The genetic control of floral organ specification is currently being investigated by various approaches, both experimentally and through modeling. Models and simulations have mostly involved boolean or related methods, and so far a quantitative, continuous-time approach has not been explored.

Results

We propose an ordinary differential equation (ODE) model that describes the gene expression dynamics of a gene regulatory network that controls floral organ formation in the model plant Arabidopsis thaliana. In this model, the dimerization of MADS-box transcription factors is incorporated explicitly. The unknown parameters are estimated from (known) experimental expression data. The model is validated by simulation studies of known mutant plants.

Conclusions

The proposed model gives realistic predictions with respect to independent mutation data. A simulation study is carried out to predict the effects of a new type of mutation that has so far not been made in Arabidopsis, but that could be used as a severe test of the validity of the model. According to our predictions, the role of dimers is surprisingly important. Moreover, the functional loss of any dimer leads to one or more phenotypic alterations.

Flow-induced correlation effects within a linear chain in a polymer melt

A framework for a consistent description of the flow-induced correlation effects within a linear polymer chain in a melt is proposed. The formalism shows how correlations between chain segments in the flow can be incorporated into a hierarchy of distribution functions for tangent vectors. The present model allows one to take into account all the major relaxation mechanisms. Special cases of the derived set of equations are shown to yield existing models and shed some light on the connection between them. Consequences of several assumptions widely used in the literature are analyzed within the developed framework.

A molecular model for cohesive slip at polymer melt/solid interfaces

A molecular model is proposed which predicts wall slip by disentanglement of polymer chains adsorbed on a wall from those in the polymer bulk. The dynamics of the near-wall boundary layer is found to be governed by a nonlinear equation of motion, which accounts for such mechanisms on surface chains as convection, retraction, constraint release, and thermal fluctuations. This equation is valid over a wide range of grafting regimes, including those in which interactions between neighboring adsorbed molecules become essential. It is not closed since the dynamics of adsorbed chains is shown to be coupled to that of polymer chains in the bulk via constraint release. The constitutive equations for the layer and bulk, together with continuity of stress and velocity, are found to form a closed system of equations which governs the dynamics of the whole "bulk+boundary layer" ensemble. Its solution provides a stick-slip law in terms of the molecular parameters and extruder geometry. The model is quantitative and contains only those parameters that can be measured directly, or extracted from independent rheological measurements. The model predictions show a good agreement with available experimental data.

Self-consistent dynamics of wall slip

A simple molecular model is studied to explain wall slip in a polymer melt. We consider a tube model for tethered chains in which the most important relaxation mechanisms: convective constraint release and chain stretching (retraction), are incorporated. Furthermore, we take the interactions between tethered chains and bulk flow self-consistently into account. Numerical simulations show that our model exhibits an entanglement-disentanglement transition, leading to a jump in the slip velocity which increases with the number of entanglements and the grafting density. The wall shear stress is found to be a nonmonotonic function of the slip and plate velocity, yielding the possibility of hysteresis and spurt instabilities. In a simplified version of the model we show via an analytical approach that the stick-slip transition is asymmetrical: the transition from stick to slip is much faster than the slip to stick transition. Our analysis reveals the existence of a dimensionless parameter that determines the time scale of the dynamics for the slowing down of the bulk flow. The relative rate at which relaxation of the tethered chains and slowing down of the bulk take place, seems to be quintessential for the slip behavior of the melt.

Prediction of survival in patients with head and neck cancer

BACKGROUND

In patients with head and neck squamous cell carcinoma (HNSCC) the estimated prognosis is usually based on the TNM classification. The relative weight of the three contributing parameters is often not completely clear. Moreover, the impact of other important clinical variables such as age, gender, prior malignancies, etc is very difficult to substantiate in daily clinical practice. The Cox-regression model allows us to estimate the effect of different variables simultaneously. The purpose of this study was to design a model for application in new HNSCC patients. In our historical data-base of patients with HNSCC, patient, treatment, and follow-up data are stored by trained oncological data managers. With these hospital-based data, we developed a statistical model for risk assessment and prediction of overall survival. This model serves in clinical decision making and appropriate counseling of patients with HNSCC.

PATIENTS AND METHODS

All patients with HNSCC of the oral cavity, the pharynx, and the larynx diagnosed in our hospital between 1981 and 1998 were included. In these 1396 patients, the prognostic value of site of the primary tumor, age at diagnosis, gender, T-, N-, and M-stage, and prior malignancies were studied univariately by Kaplan-Meier curves and the log-rank test. The Cox-regression model was used to investigate the effect of these variables simultaneously on overall survival and to develop a prediction model for individual patients.

RESULTS

In the univariate analyses, all variables except gender contributed significantly to overall survival. Their contribution remained significant in the multivariate Cox model. Based on the relative risks and the baseline survival curve, the expected survival for a new HNSCC patient can be calculated.

CONCLUSIONS

It is possible to predict survival probabilities in a new patient with HNSCC based on historical results from a data-set analyzed with the Cox-regression model. The model is supplied with hospital-based data. Our model can be extended by other prognostic factors such as co-morbidity, histological data, molecular biology markers, etc. The results of the Cox-regression may be used in patient counseling, clinical decision making, and quality maintenance.