How grass keeps growing: an integrated analysis of hormonal crosstalk in the maize leaf growth zone.

We studied the maize leaf to understand how long-distance signals, auxin and cytokinin, control leaf growth dynamics. We constructed a mathematical model describing the transport of these hormones along the leaf growth zone and their interaction with the local gibberellin (GA) metabolism in the control of cell division. Assuming gradually declining auxin and cytokinin supply at the leaf base, the model generated spatiotemporal hormone distribution and growth patterns that matched experimental data. At the cellular level, the model predicted a basal leaf growth as a result of cell division driven by auxin and cytokinin. Superimposed on this, GA synthesis regulated growth through the control of the size of the region of active cell division. The predicted hormone and cell length distributions closely matched experimental data. To correctly predict the leaf growth profiles and final organ size of lines with reduced or elevated GA production, the model required a signal proportional to the size of the emerged part of the leaf that inhibited the basal leaf growth driven by auxin and cytokinin. Excision and shading of the emerged part of the growing leaf allowed us to demonstrate that this signal exists and depends on the perception of light intensity.

Multiple mechanisms explain how reduced KRP expression increases leaf size of Arabidopsis thaliana.

Although cell number generally correlates with organ size, the role of cell cycle control in growth regulation is still largely unsolved. We studied kip related protein (krp) 4, 6 and 7 single, double and triple mutants of Arabidopsis thaliana to understand the role of cell cycle inhibitory proteins in leaf development. We performed leaf growth and seed size analysis, kinematic analysis, flow cytometery, transcriptome analysis and mathematical modeling of G1/S and G2/M checkpoint progression of the mitotic and endoreplication cycle. Double and triple mutants progressively increased mature leaf size, because of elevated expression of cell cycle and DNA replication genes stimulating progression through the division and endoreplication cycle. However, cell number was also already increased before leaf emergence, as a result of an increased cell number in the embryo. We show that increased embryo and seed size in krp4/6/7 results from seed abortion, presumably reducing resource competition, and that seed size differences contribute to the phenotype of several large-leaf mutants. Our results provide a new mechanistic understanding of the role of cell cycle regulation in leaf development and highlight the contribution of the embryo to the development of leaves after germination in general.

Optimizing agent-based transmission models for infectious diseases.

BACKGROUND: Infectious disease modeling and computational power have evolved such that large-scale agent-based models (ABMs) have become feasible. However, the increasing hardware complexity requires adapted software designs to achieve the full potential of current high-performance workstations. RESULTS: We have found large performance differences with a discrete-time ABM for close-contact disease transmission due to data locality. Sorting the population according to the social contact clusters reduced simulation time by a factor of two. Data locality and model performance can also be improved by storing person attributes separately instead of using person objects. Next, decreasing the number of operations by sorting people by health status before processing disease transmission has also a large impact on model performance. Depending of the clinical attack rate, target population and computer hardware, the introduction of the sort phase decreased the run time from 26% up to more than 70%. We have investigated the application of parallel programming techniques and found that the speedup is significant but it drops quickly with the number of cores. We observed that the effect of scheduling and workload chunk size is model specific and can make a large difference. CONCLUSIONS: Investment in performance optimization of ABM simulator code can lead to significant run time reductions. The key steps are straightforward: the data structure for the population and sorting people on health status before effecting disease propagation. We believe these conclusions to be valid for a wide range of infectious disease ABMs. We recommend that future studies evaluate the impact of data management, algorithmic procedures and parallelization on model performance.

Active learning to understand infectious disease models and improve policy making.

Modeling plays a major role in policy making, especially for infectious disease interventions but such models can be complex and computationally intensive. A more systematic exploration is needed to gain a thorough systems understanding. We present an active learning approach based on machine learning techniques as iterative surrogate modeling and model-guided experimentation to systematically analyze both common and edge manifestations of complex model runs. Symbolic regression is used for nonlinear response surface modeling with automatic feature selection. First, we illustrate our approach using an individual-based model for influenza vaccination. After optimizing the parameter space, we observe an inverse relationship between vaccination coverage and cumulative attack rate reinforced by herd immunity. Second, we demonstrate the use of surrogate modeling techniques on input-response data from a deterministic dynamic model, which was designed to explore the cost-effectiveness of varicella-zoster virus vaccination. We use symbolic regression to handle high dimensionality and correlated inputs and to identify the most influential variables. Provided insight is used to focus research, reduce dimensionality and decrease decision uncertainty. We conclude that active learning is needed to fully understand complex systems behavior. Surrogate models can be readily explored at no computational expense, and can also be used as emulator to improve rapid policy making in various settings.

Putting theory to the test: which regulatory mechanisms can drive realistic growth of a root?

In recent years there has been a strong development of computational approaches to mechanistically understand organ growth regulation in plants. In this study, simulation methods were used to explore which regulatory mechanisms can lead to realistic output at the cell and whole organ scale and which other possibilities must be discarded as they result in cellular patterns and kinematic characteristics that are not consistent with experimental observations for the Arabidopsis thaliana primary root. To aid in this analysis, a 'Uniform Longitudinal Strain Rule' (ULSR) was formulated as a necessary condition for stable, unidirectional, symplastic growth. Our simulations indicate that symplastic structures are robust to differences in longitudinal strain rates along the growth axis only if these differences are small and short-lived. Whereas simple cell-autonomous regulatory rules based on counters and timers can produce stable growth, it was found that steady developmental zones and smooth transitions in cell lengths are not feasible. By introducing spatial cues into growth regulation, those inadequacies could be avoided and experimental data could be faithfully reproduced. Nevertheless, a root growth model based on previous polar auxin-transport mechanisms violates the proposed ULSR due to the presence of lateral gradients. Models with layer-specific regulation or layer-driven growth offer potential solutions. Alternatively, a model representing the known cross-talk between auxin, as the cell proliferation promoting factor, and cytokinin, as the cell differentiation promoting factor, predicts the effect of hormone-perturbations on meristem size. By down-regulating PIN-mediated transport through the transcription factor SHY2, cytokinin effectively flattens the lateral auxin gradient, at the basal boundary of the division zone, (thereby imposing the ULSR) to signal the exit of proliferation and start of elongation. This model exploration underlines the value of generating virtual root growth kinematics to dissect and understand the mechanisms controlling this biological system.

Numerical bifurcation analysis of the pattern formation in a cell based auxin transport model.

Transport models of growth hormones can be used to reproduce the hormone accumulations that occur in plant organs. Mostly, these accumulation patterns are calculated using time step methods, even though only the resulting steady state patterns of the model are of interest. We examine the steady state solutions of the hormone transport model of Smith et al. (Proc Natl Acad Sci USA 103(5):1301-1306, 2006) for a one-dimensional row of plant cells. We search for the steady state solutions as a function of three of the model parameters by using numerical continuation methods and bifurcation analysis. These methods are more adequate for solving steady state problems than time step methods. We discuss a trivial solution where the concentrations of hormones are equal in all cells and examine its stability region. We identify two generic bifurcation scenarios through which the trivial solution loses its stability. The trivial solution becomes either a steady state pattern with regular spaced peaks or a pattern where the concentration is periodic in time.

Towards mechanistic models of plant organ growth.

Modelling and simulation are increasingly used as tools in the study of plant growth and developmental processes. By formulating experimentally obtained knowledge as a system of interacting mathematical equations, it becomes feasible for biologists to gain a mechanistic understanding of the complex behaviour of biological systems. In this review, the modelling tools that are currently available and the progress that has been made to model plant development, based on experimental knowledge, are described. In terms of implementation, it is argued that, for the modelling of plant organ growth, the cellular level should form the cornerstone. It integrates the output of molecular regulatory networks to two processes, cell division and cell expansion, that drive growth and development of the organ. In turn, these cellular processes are controlled at the molecular level by hormone signalling. Therefore, combining a cellular modelling framework with regulatory modules for the regulation of cell division, expansion, and hormone signalling could form the basis of a functional organ growth simulation model. The current state of progress towards this aim is that the regulation of the cell cycle and hormone transport have been modelled extensively and these modules could be integrated. However, much less progress has been made on the modelling of cell expansion, which urgently needs to be addressed. A limitation of the current generation models is that they are largely qualitative. The possibilities to characterize existing and future models more quantitatively will be discussed. Together with experimental methods to measure crucial model parameters, these modelling techniques provide a basis to develop a Systems Biology approach to gain a fundamental insight into the relationship between gene function and whole organ behaviour.

Clustering of susceptible individuals within households can drive measles outbreaks: an individual-based model exploration.

When estimating important measures such as the herd immunity threshold, and the corresponding efforts required to eliminate measles, it is often assumed that susceptible individuals are uniformly distributed throughout populations. However, unvaccinated individuals may be clustered in a variety of ways, including by geographic location, by age, in schools, or in households. Here, we investigate to which extent different levels of within-household clustering of susceptible individuals may impact the risk and persistence of measles outbreaks. To this end, we apply an individual-based model, Stride, to a population of 600,000 individuals, using data from Flanders, Belgium. We construct a metric to estimate the level of within-household susceptibility clustering in the population. Furthermore, we compare realistic scenarios regarding the distribution of susceptible individuals within households in terms of their impact on epidemiological measures for outbreak risk and persistence. We find that higher levels of within-household clustering of susceptible individuals increase the risk, size and persistence of measles outbreaks. Ignoring within-household clustering thus leads to underestimations of required measles elimination and outbreak mitigation efforts.

Virtual Plant Tissue: Building Blocks for Next-Generation Plant Growth Simulation.

Motivation: Computational modeling of plant developmental processes is becoming increasingly important. Cellular resolution plant tissue simulators have been developed, yet they are typically describing physiological processes in an isolated way, strongly delimited in space and time. Results: With plant systems biology moving toward an integrative perspective on development we have built the Virtual Plant Tissue (VPTissue) package to couple functional modules or models in the same framework and across different frameworks. Multiple levels of model integration and coordination enable combining existing and new models from different sources, with diverse options in terms of input/output. Besides the core simulator the toolset also comprises a tissue editor for manipulating tissue geometry and cell, wall, and node attributes in an interactive manner. A parameter exploration tool is available to study parameter dependence of simulation results by distributing calculations over multiple systems. Availability: Virtual Plant Tissue is available as open source (EUPL license) on Bitbucket (https://bitbucket.org/vptissue/vptissue). The project has a website https://vptissue.bitbucket.io.

Modified J-matrix method for scattering.

We modify the J-matrix technique for scattering so that problems with long-range interactions are easily solved. This is done by introducing additional terms in the asymptotic three-term recurrence relation that take into account asymptotic effects of the potential. The solutions of this modified recurrence relation are a very good approximation of the exact scattering solution. Only a small number of residual coefficients need to be calculated. As a result, the numerical effort to solve the scattering problem is seriously reduced. The technique is illustrated with a Yukawa potential.