A coordinated switch in sucrose and callose metabolism enables enhanced symplastic unloading in potato tubers.

One of the early changes upon tuber induction is the switch from apoplastic to symplastic unloading. Whether and how this change in unloading mode contributes to sink strength has remained unclear. In addition, developing tubers also change from energy to storage-based sucrose metabolism. Here, we investigated the coordination between changes in unloading mode and sucrose metabolism and their relative role in tuber sink strength by looking into callose and sucrose metabolism gene expression combined with a model of apoplastic and symplastic unloading. Gene expression analysis suggests that callose deposition in tubers is decreased by lower callose synthase expression. Furthermore, changes in callose and sucrose metabolism are strongly correlated, indicating a well-coordinated developmental switch. Modelling indicates that symplastic unloading is not the most efficient unloading mode per se. Instead, it is the concurrent metabolic switch that provides the physiological conditions necessary to potentiate symplastic transport and thereby enhance tuber sink strength .

Parallels between drought and flooding: An integrated framework for plant eco-physiological responses to water stress.

Drought and flooding occur at opposite ends of the soil moisture spectrum yet their resulting stress responses in plants share many similarities. Drought limits root water uptake to which plants respond with stomatal closure and reduced leaf gas exchange. Flooding limits root metabolism due to soil oxygen deficiency, which also limits root water uptake and leaf gas exchange. As drought and flooding can occur consecutively in the same system and resulting plant stress responses share similar mechanisms, a single theoretical framework that integrates plant responses over a continuum of soil water conditions from drought to flooding is attractive. Based on a review of recent literature, we integrated the main plant eco-physiological mechanisms in a single theoretical framework with a focus on plant water transport, plant oxygen dynamics, and leaf gas exchange. We used theory from the soil-plant-atmosphere continuum modeling as "backbone" for our framework, and subsequently incorporated interactions between processes that regulate plant water and oxygen status, abscisic acid and ethylene levels, and the resulting acclimation strategies in response to drought, waterlogging, and complete submergence. Our theoretical framework provides a basis for the development of mathematical models to describe plant responses to the soil moisture continuum from drought to flooding.

Bootstrapping and Pinning down the Root Meristem; the Auxin-PLT-ARR Network Unites Robustness and Sensitivity in Meristem Growth Control.

After germination, the meristem of the embryonic plant root becomes activated, expands in size and subsequently stabilizes to support post-embryonic root growth. The plant hormones auxin and cytokinin, together with master transcription factors of the PLETHORA (PLT) family have been shown to form a regulatory network that governs the patterning of this root meristem. Still, which functional constraints contributed to shaping the dynamics and architecture of this network, has largely remained unanswered. Using a combination of modeling approaches we reveal how the interplay between auxin and PLTs enables meristem activation in response to above-threshold stimulation, while its embedding in a PIN-mediated auxin reflux loop ensures localized PLT transcription and thereby, a finite meristem size. We furthermore demonstrate how this constrained PLT transcriptional domain enables independent control of meristem size and division rates, further supporting a division of labor between auxin and PLT. We subsequently reveal how the weaker auxin antagonism of the earlier active Arabidopsis response regulator 12 (ARR12) may arise from the absence of a DELLA protein interaction domain. Our model indicates that this reduced strength is essential to prevent collapse in the early stages of meristem expansion while at later stages the enhanced strength of Arabidopsis response regulator 1 (ARR1) is required for sufficient meristem size control. Summarizing, our work indicates that functional constraints significantly contribute to shaping the auxin-cytokinin-PLT regulatory network.

Quantitative plant biology-Old and new.

Quantitative approaches in plant biology have a long history that have led to several ground-breaking discoveries and given rise to new principles, new paradigms and new methodologies. We take a short historical trip into the past to explore some of the many great scientists and influences that have led to the development of quantitative plant biology. We have not been constrained by historical fact, although we have tried not to deviate too much. We end with a forward look, expressing our hopes and ambitions for this exciting interdisciplinary field.

Local auxin competition explains fragmented differentiation patterns.

Trajectories of cellular ontogeny are tightly controlled and often involve feedback-regulated molecular antagonism. For example, sieve element differentiation along developing protophloem cell files of Arabidopsis roots requires two antagonistic regulators of auxin efflux. Paradoxically, loss-of-function in either regulator triggers similar, seemingly stochastic differentiation failures of individual sieve element precursors. Here we show that these patterning defects are distinct and non-random. They can be explained by auxin-dependent bistability that emerges from competition for auxin between neighboring cells. This bistability depends on the presence of an auxin influx facilitator, and can be triggered by either flux enhancement or repression. Our results uncover a hitherto overlooked aspect of auxin uptake, and highlight the contributions of local auxin influx, efflux and biosynthesis to protophloem formation. Moreover, the combined experimental-modeling approach suggests that without auxin efflux homeostasis, auxin influx interferes with coordinated differentiation.

Modeling of Root Nitrate Responses Suggests Preferential Foraging Arises From the Integration of Demand, Supply and Local Presence Signals.

A plants' fitness to a large extent depends on its capacity to adapt to spatio-temporally varying environmental conditions. One such environmental condition to which plants display extensive phenotypic plasticity is soil nitrate levels and patterns. In response to heterogeneous nitrate distribution, plants show a so-called preferential foraging response. Herein root growth is enhanced in high nitrate patches and repressed in low nitrate locations beyond a level that can be explained from local nitrate sensing. Although various molecular players involved in this preferential foraging behavior have been identified, how these together shape root system adaptation has remained unresolved. Here we use a simple modeling approach in which we incrementally incorporate the known molecular pathways to investigate the combination of regulatory mechanisms that underly preferential root nitrate foraging. Our model suggests that instead of involving a growth suppressing supply signal, growth reduction on the low nitrate side may arise from reduced root foraging and increased competition for carbon. Additionally, our work suggests that the long distance CK signaling involved in preferential root foraging may function as a supply signal modulating demand signaling strength. We illustrate how this integration of demand and supply signals prevents excessive preferential foraging under conditions in which demand is not met by sufficient supply and a more generic foraging in search of nitrate should be maintained.

Halotropism requires phospholipase Dζ1-mediated modulation of cellular polarity of auxin transport carriers.

Endocytosis and relocalization of auxin carriers represent important mechanisms for adaptive plant growth and developmental responses. Both root gravitropism and halotropism have been shown to be dependent on relocalization of auxin transporters. Following their homology to mammalian phospholipase Ds (PLDs), plant PLDζ-type enzymes are likely candidates to regulate auxin carrier endocytosis. We investigated root tropic responses for an Arabidopsis pldζ1-KO mutant and its effect on the dynamics of two auxin transporters during salt stress, that is, PIN2 and AUX1. We found altered root growth and halotropic and gravitropic responses in the absence of PLDζ1 and report a role for PLDζ1 in the polar localization of PIN2. Additionally, irrespective of the genetic background, salt stress induced changes in AUX1 polarity. Utilizing our previous computational model, we found that these novel salt-induced AUX1 changes contribute to halotropic auxin asymmetry. We also report the formation of "osmotic stress-induced membrane structures." These large membrane structures are formed at the plasma membrane shortly after NaCl or sorbitol treatment and have a prolonged presence in a pldζ1 mutant. Taken together, these results show a crucial role for PLDζ1 in both ionic and osmotic stress-induced auxin carrier dynamics during salt stress.

Discrete mechanical growth model for plant tissue.

We present a discrete mechanical model to study plant development. The method is built up of mass points, springs and hinges mimicking the plant cell wall's microstructure. To model plastic growth the resting lengths of springs are adjusted; when springs exceed a threshold length, new mass points, springs and hinges, are added. We formulate a stiffness tensor for the springs and hinges as a function of the fourth rank tensor of elasticity and the geometry of the mesh. This allows us to approximate the material law as a generalized orthotropic Hooke's law, and control material properties during growth. The material properties of the model are illustrated in numerical simulations for finite strain and plastic growth. To solve the equations of motion of mass points we assume elastostatics and use Verlet integration. The method is demonstrated in simulations when anisotropic growth causes emergent residual strain fields in cell walls and a bending of tissue. The method can be used in multilevel models to study plant development, for example by coupling it to models for cytoskeletal, hormonal and gene regulatory processes.

Around the clock: gradient shape and noise impact the evolution of oscillatory segmentation dynamics.

BACKGROUND: Segmentation, the subdivision of the major body axis into repeated elements, is considered one of the major evolutionary innovations in bilaterian animals. In all three segmented animal clades, the predominant segmentation mechanism is sequential segmentation, where segments are generated one by one in anterior-posterior order from a posterior undifferentiated zone. In vertebrates and arthropods, sequential segmentation is thought to arise from a clock-and-wavefront-type mechanism, where oscillations in the posterior growth zone are transformed into a segmental prepattern in the anterior by a receding wavefront. Previous evo-devo simulation studies have demonstrated that this segmentation type repeatedly arises, supporting the idea of parallel evolutionary origins in these animal clades. Sequential segmentation has been studied most extensively in vertebrates, where travelling waves have been observed that reflect the slowing down of oscillations prior to their cessation and where these oscillations involve a highly complex regulatory network. It is currently unclear under which conditions this oscillator complexity and slowing should be expected to evolve, how they are related and to what extent similar properties should be expected for sequential segmentation in other animal species. RESULTS: To investigate these questions, we extend a previously developed computational model for the evolution of segmentation. We vary the slope of the posterior morphogen gradient and the strength of gene expression noise. We find that compared to a shallow gradient, a steep morphogen gradient allows for faster evolution and evolved oscillator networks are simpler. Furthermore, under steep gradients, damped oscillators often evolve, whereas shallow gradients appear to require persistent oscillators which are regularly accompanied by travelling waves, indicative of a frequency gradient. We show that gene expression noise increases the likelihood of evolving persistent oscillators under steep gradients and of evolving frequency gradients under shallow gradients. Surprisingly, we find that the evolutions of oscillator complexity and travelling waves are not correlated, suggesting that these properties may have evolved separately. CONCLUSIONS: Based on our findings, we suggest that travelling waves may have evolved in response to shallow morphogen gradients and gene expression noise. These two factors may thus also be responsible for the observed differences between different species within both the arthropod and chordate phyla.

Auxin Information Processing; Partners and Interactions beyond the Usual Suspects.

Auxin plays a major role in a variety of processes involved in plant developmental patterning and its adaptation to environmental conditions. Therefore, an important question is how specificity in auxin signalling is achieved, that is, how a single signalling molecule can carry so many different types of information. In recent years, many studies on auxin specificity have been published, unravelling increasingly more details on differential auxin sensitivity, expression domains and downstream partners of the auxin receptors (transport inhibitor response 1 (TIR1) and other auxin signaling F-box proteins (AFB)), transcriptional repressors that are degraded in response to auxin (AUX/IAA) and downstream auxin response factors (ARF) that together constitute the plant's major auxin response pathways. These data are critical to explain how, in the same cells, different auxin levels may trigger different responses, as well as how in different spatial or temporal contexts similar auxin signals converge to different responses. However, these insights do not yet answer more complex questions regarding auxin specificity. As an example, they leave open the question of how similar sized auxin changes at similar locations result in different responses depending on the duration and spatial extent of the fluctuation in auxin levels. Similarly, it leaves unanswered how, in the case of certain tropisms, small differences in signal strength at both sides of a plant organ are converted into an instructive auxin asymmetry that enables a robust tropic response. Finally, it does not explain how, in certain cases, substantially different auxin levels become translated into similar cellular responses, while in other cases similar auxin levels, even when combined with similar auxin response machinery, may trigger different responses. In this review, we illustrate how considering the regulatory networks and contexts in which auxin signalling takes place helps answer these types of fundamental questions.

Modelling asymmetric somitogenesis: Deciphering the mechanisms behind species differences.

Somitogenesis is one of the major hallmarks of bilateral symmetry in vertebrates. This symmetry is lost when retinoic acid (RA) signalling is inhibited, allowing the left-right determination pathway to influence somitogenesis. In all three studied vertebrate model species, zebrafish, chicken and mouse, the frequency of somite formation becomes asymmetric, with slower gene expression oscillations driving somitogenesis on the right side. Still, intriguingly, the resulting left-right asymmetric phenotypes differ significantly between these model species. While somitogenesis is generally considered as functionally equivalent among different vertebrates, substantial differences exist in the subset of oscillating genes between different vertebrate species. Variation also appears to exist in the way oscillations cease and somite boundaries become patterned. In addition, in absence of RA, the FGF8 gradient thought to constitute the determination wavefront becomes asymmetric in zebrafish and mouse, extending more anteriorly to the right, while remaining symmetric in chicken. Here we use a computational modelling approach to decipher the causes underlying species differences in asymmetric somitogenesis. Specifically, we investigate to what extent differences can be explained from observed differences in FGF asymmetry and whether differences in somite determination dynamics may also be involved. We demonstrate that a simple clock-and-wavefront model incorporating the observed left-right differences in somitogenesis frequency readily reproduces asymmetric somitogenesis in chicken. However, incorporating asymmetry in FGF signalling was insufficient to robustly reproduce mouse or zebrafish asymmetry phenotypes. In order to explain these phenoptypes we needed to extend the basic model, incorporating species-specific details of the somitogenesis determination mechanism. Our results thus demonstrate that a combination of differences in FGF dynamics and somite determination cause species differences in asymmetric somitogenesis. In addition,they highlight the power of using computational models as well as studying left-right asymmetry to obtain more insight in somitogenesis.

Periodic Lateral Root Priming: What Makes It Tick?

Conditioning small groups of root pericycle cells for future lateral root formation has a major impact on overall plant root architecture. This priming of lateral roots occurs rhythmically, involving temporal oscillations in auxin response in the root tip. During growth, this process generates a spatial pattern of prebranch sites, an early stage in lateral root formation characterized by a stably maintained high auxin response. To date, the molecular mechanism behind this rhythmicity has remained elusive. Some data implicate a cell-autonomous oscillation in gene expression, while others strongly support the importance of tissue-level modulations in auxin fluxes. Here, we summarize the experimental data on periodic lateral root priming. We present a theoretical framework that distinguishes between a priming signal and its subsequent memorization and show how major roles for auxin fluxes and gene expression naturally emerge from this framework. We then discuss three mechanisms that could potentially induce oscillations of auxin response: cell-autonomous oscillations, Turing-type patterning, and tissue-level oscillations in auxin fluxes, along with specific properties of lateral root priming that may be used to discern which type of mechanism is most likely to drive lateral root patterning. We conclude with suggestions for future experiments and modeling studies.

In silico evo-devo: reconstructing stages in the evolution of animal segmentation.

BACKGROUND: The evolution of animal segmentation is a major research focus within the field of evolutionary-developmental biology. Most studied segmented animals generate their segments in a repetitive, anterior-to-posterior fashion coordinated with the extension of the body axis from a posterior growth zone. In the current study we ask which selection pressures and ordering of evolutionary events may have contributed to the evolution of this specific segmentation mode. RESULTS: To answer this question we extend a previous in silico simulation model of the evolution of segmentation by allowing the tissue growth pattern to freely evolve. We then determine the likelihood of evolving oscillatory sequential segmentation combined with posterior growth under various conditions, such as the presence or absence of a posterior morphogen gradient or selection for determinate growth. We find that posterior growth with sequential segmentation is the predominant outcome of our simulations only if a posterior morphogen gradient is assumed to have already evolved and selection for determinate growth occurs secondarily. Otherwise, an alternative segmentation mechanism dominates, in which divisions occur in large bursts through the entire tissue and all segments are created simultaneously. CONCLUSIONS: Our study suggests that the ancestry of a posterior signalling centre has played an important role in the evolution of sequential segmentation. In addition, it suggests that determinate growth evolved secondarily, after the evolution of posterior growth. More generally, we demonstrate the potential of evo-devo simulation models that allow us to vary conditions as well as the onset of selection pressures to infer a likely order of evolutionary innovations.

Modeling halotropism: a key role for root tip architecture and reflux loop remodeling in redistributing auxin.

A key characteristic of plant development is its plasticity in response to various and dynamically changing environmental conditions. Tropisms contribute to this flexibility by allowing plant organs to grow from or towards environmental cues. Halotropism is a recently described tropism in which plant roots bend away from salt. During halotropism, as in most other tropisms, directional growth is generated through an asymmetric auxin distribution that generates differences in growth rate and hence induces bending. Here, we develop a detailed model of auxin transport in the Arabidopsis root tip and combine this with experiments to investigate the processes generating auxin asymmetry during halotropism. Our model points to the key role of root tip architecture in allowing the decrease in PIN2 at the salt-exposed side of the root to result in a re-routing of auxin to the opposite side. In addition, our model demonstrates how feedback of auxin on the auxin transporter AUX1 amplifies this auxin asymmetry, while a salt-induced transient increase in PIN1 levels increases the speed at which this occurs. Using AUX1-GFP imaging and pin1 mutants, we experimentally confirmed these model predictions, thus expanding our knowledge of the cellular basis of halotropism.

Effects of Heterogeneous Diffuse Fibrosis on Arrhythmia Dynamics and Mechanism.

Myocardial fibrosis is an important risk factor for cardiac arrhythmias. Previous experimental and numerical studies have shown that the texture and spatial distribution of fibrosis may play an important role in arrhythmia onset. Here, we investigate how spatial heterogeneity of fibrosis affects arrhythmia onset using numerical methods. We generate various tissue textures that differ by the mean amount of fibrosis, the degree of heterogeneity and the characteristic size of heterogeneity. We study the onset of arrhythmias using a burst pacing protocol. We confirm that spatial heterogeneity of fibrosis increases the probability of arrhythmia induction. This effect is more pronounced with the increase of both the spatial size and the degree of heterogeneity. The induced arrhythmias have a regular structure with the period being mostly determined by the maximal local fibrosis level. We perform ablations of the induced fibrillatory patterns to classify their type. We show that in fibrotic tissue fibrillation is usually of the mother rotor type but becomes of the multiple wavelet type with increase in tissue size. Overall, we conclude that the most important factor determining the formation and dynamics of arrhythmia in heterogeneous fibrotic tissue is the value of maximal local fibrosis.

Segment-specific adhesion as a driver of convergent extension.

Convergent extension, the simultaneous extension and narrowing of tissues, is a crucial event in the formation of the main body axis during embryonic development. It involves processes on multiple scales: the sub-cellular, cellular and tissue level, which interact via explicit or intrinsic feedback mechanisms. Computational modelling studies play an important role in unravelling the multiscale feedbacks underlying convergent extension. Convergent extension usually operates in tissue which has been patterned or is currently being patterned into distinct domains of gene expression. How such tissue patterns are maintained during the large scale tissue movements of convergent extension has thus far not been investigated. Intriguingly, experimental data indicate that in certain cases these tissue patterns may drive convergent extension rather than requiring safeguarding against convergent extension. Here we use a 2D Cellular Potts Model (CPM) of a tissue prepatterned into segments, to show that convergent extension tends to disrupt this pre-existing segmental pattern. However, when cells preferentially adhere to cells of the same segment type, segment integrity is maintained without any reduction in tissue extension. Strikingly, we demonstrate that this segment-specific adhesion is by itself sufficient to drive convergent extension. Convergent extension is enhanced when we endow our in silico cells with persistence of motion, which in vivo would naturally follow from cytoskeletal dynamics. Finally, we extend our model to confirm the generality of our results. We demonstrate a similar effect of differential adhesion on convergent extension in tissues that can only extend in a single direction (as often occurs due to the inertia of the head region of the embryo), and in tissues prepatterned into a sequence of domains resulting in two opposing adhesive gradients, rather than alternating segments.

Evolution of networks for body plan patterning; interplay of modularity, robustness and evolvability.

A major goal of evolutionary developmental biology (evo-devo) is to understand how multicellular body plans of increasing complexity have evolved, and how the corresponding developmental programs are genetically encoded. It has been repeatedly argued that key to the evolution of increased body plan complexity is the modularity of the underlying developmental gene regulatory networks (GRNs). This modularity is considered essential for network robustness and evolvability. In our opinion, these ideas, appealing as they may sound, have not been sufficiently tested. Here we use computer simulations to study the evolution of GRNs' underlying body plan patterning. We select for body plan segmentation and differentiation, as these are considered to be major innovations in metazoan evolution. To allow modular networks to evolve, we independently select for segmentation and differentiation. We study both the occurrence and relation of robustness, evolvability and modularity of evolved networks. Interestingly, we observed two distinct evolutionary strategies to evolve a segmented, differentiated body plan. In the first strategy, first segments and then differentiation domains evolve (SF strategy). In the second scenario segments and domains evolve simultaneously (SS strategy). We demonstrate that under indirect selection for robustness the SF strategy becomes dominant. In addition, as a byproduct of this larger robustness, the SF strategy is also more evolvable. Finally, using a combined functional and architectural approach, we determine network modularity. We find that while SS networks generate segments and domains in an integrated manner, SF networks use largely independent modules to produce segments and domains. Surprisingly, we find that widely used, purely architectural methods for determining network modularity completely fail to establish this higher modularity of SF networks. Finally, we observe that, as a free side effect of evolving segmentation and differentiation in combination, we obtained in-silico developmental mechanisms resembling mechanisms used in vertebrate development.

The role of genome and gene regulatory network canalization in the evolution of multi-trait polymorphisms and sympatric speciation.

BACKGROUND: Sexual reproduction has classically been considered as a barrier to the buildup of discrete phenotypic differentiation. This notion has been confirmed by models of sympatric speciation in which a fixed genetic architecture and a linear genotype phenotype mapping were assumed. In this paper we study the influence of a flexible genetic architecture and non-linear genotype phenotype map on differentiation under sexual reproduction.We use an individual based model in which organisms have a genome containing genes and transcription factor binding sites. Mutations involve single genes or binding sites or stretches of genome. The genome codes for a regulatory network that determines the gene expression pattern and hence the phenotype of the organism, resulting in a non-linear genotype phenotype map. The organisms compete in a multi-niche environment, imposing selection for phenotypic differentiation. RESULTS: We find as a generic outcome the evolution of discrete clusters of organisms adapted to different niches, despite random mating. Organisms from different clusters are distinct on the genotypic, the network and the phenotypic level. However, the genome and network differences are constrained to a subset of the genome locations, a process we call genotypic canalization. We demonstrate how this canalization leads to an increased robustness to recombination and increasing hybrid fitness. Finally, in case of assortative mating, we explain how this canalization increases the effectiveness of assortativeness. CONCLUSION: We conclude that in case of a flexible genetic architecture and a non-linear genotype phenotype mapping, sexual reproduction does not constrain phenotypic differentiation, but instead constrains the genotypic differences underlying it. We hypothesize that, as genotypic canalization enables differentiation despite random mating and increases the effectiveness of assortative mating, sympatric speciation is more likely than is commonly suggested.

Influence of diffuse fibrosis on wave propagation in human ventricular tissue.

AIMS: During ageing, after infarction, in cardiomyopathies and other cardiac diseases, the percentage of fibrotic (connective) tissue may increase from 6% up to 10-35%. The presence of increased amounts of connective tissue is strongly correlated with the occurrence of arrhythmias and sudden cardiac death. METHODS AND RESULTS: In this article, we investigate the role of diffuse fibrosis on wave propagation, arrhythmogenesis, and arrhythmia mechanism in human ventricular tissue using computer modelling. We show that diffuse fibrosis slows down wave propagation and increases tissue vulnerability to wave break and spiral wave formation. We also demonstrate that diffuse fibrosis increases the period of re-entrant arrhythmias and can suppress the restitution-induced transition from tachycardia to fibrillation. CONCLUSION: The latter suggests that mechanisms different from restitution-induced spiral break-up might be more likely to account for the onset of fibrillation in the presence of large amounts of diffuse fibrotic tissue.