Multi-scale mechanisms driving root regeneration: From regeneration competence to tissue repatterning.

Plants possess an outstanding capacity to regenerate enabling them to repair damages caused by suboptimal environmental conditions, biotic attacks, or mechanical damages impacting the survival of these sessile organisms. Although the extent of regeneration varies greatly between localized cell damage and whole organ recovery, the process of regeneration can be subdivided into a similar sequence of interlinked regulatory processes. That is, competence to regenerate, cell fate reprogramming, and the repatterning of the tissue. Here, using root tip regeneration as a paradigm system to study plant regeneration, we provide a synthesis of the molecular responses that underlie both regeneration competence and the repatterning of the root stump. Regarding regeneration competence, we discuss the role of wound signaling, hormone responses and synthesis, and rapid changes in gene expression observed in the cells close to the cut. Then, we consider how this rapid response is followed by the tissue repatterning phase, where cells experience cell fate changes in a spatial and temporal order to recreate the lost stem cell niche and columella. Lastly, we argue that a multi-scale modeling approach is fundamental to uncovering the mechanisms underlying root regeneration, as it allows to integrate knowledge of cell-level gene expression, cell-to-cell transport of hormones and transcription factors, and tissue-level growth dynamics to reveal how the bi-directional feedbacks between these processes enable self-organized repatterning of the root apex.

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 .

GH3-mediated auxin inactivation attenuates multiple stages of lateral root development.

Lateral root (LR) positioning and development rely on the dynamic interplay between auxin production, transport but also inactivation. Nonetheless, how the latter affects LR organogenesis remains largely uninvestigated. Here, we systematically analyze the impact of the major auxin inactivation pathway defined by GRETCHEN HAGEN3-type (GH3) auxin conjugating enzymes and DIOXYGENASE FOR AUXIN OXIDATION1 (DAO1) in all stages of LR development using reporters, genetics and inhibitors in Arabidopsis thaliana. Our data demonstrate that the gh3.1/2/3/4/5/6 hextuple (gh3hex) mutants display a higher LR density due to increased LR initiation and faster LR developmental progression, acting epistatically over dao1-1. Grafting and local inhibitor applications reveal that root and shoot GH3 activities control LR formation. The faster LR development in gh3hex is associated with GH3 expression domains in and around developing LRs. The increase in LR initiation is associated with accelerated auxin response oscillations coinciding with increases in apical meristem size and LR cap cell death rates. Our research reveals how GH3-mediated auxin inactivation attenuates LR development. Local GH3 expression in LR primordia attenuates development and emergence, whereas GH3 effects on pre-initiation stages are indirect, by modulating meristem activities that in turn coordinate root growth with LR spacing.

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.

Complementary roles for auxin and auxin signalling revealed by reverse engineering lateral root stable prebranch site formation.

Priming is the process through which periodic elevations in auxin signalling prepattern future sites for lateral root formation, called prebranch sites. Thus far, the extent to which elevations in auxin concentration and/or auxin signalling are required for priming and prebranch site formation has remained a matter of debate. Recently, we discovered a reflux-and-growth mechanism for priming generating periodic elevations in auxin concentration that subsequently dissipate. Here, we reverse engineer a mechanism for prebranch site formation that translates these transient elevations into a persistent increase in auxin signalling, resolving the prior debate into a two-step process of auxin concentration-mediated initial signal and auxin signalling capacity-mediated memorization. A crucial aspect of the prebranch site formation mechanism is its activation in response to time-integrated rather than instantaneous auxin signalling. The proposed mechanism is demonstrated to be consistent with prebranch site auxin signalling dynamics, lateral inhibition, and symmetry-breaking mechanisms and perturbations in auxin homeostasis.

Undirected Sucrose Efflux Mitigation by the FT-Like SP6A Preferentially Enhances Tuber Resource Partitioning.

The yield of harvestable plant organs depends on overall photosynthetic output and the subsequent distribution of the produced assimilates from source leaves across different sink organs. In this study, we aimed to obtain, using a two-sink transport model, mechanistic understanding of how the interplay between sink and pathway properties together determines sink resource partitioning. As a working example, we analyzed the partitioning of resources within potato plants, investigating the determinants of tuber sink yield. Our results indicated that, contrary to earlier studies, with a spatially explicit biophysically detailed model, transport pathway properties significantly affect sink resource partitioning within the physiologically relevant domain. Additionally, we uncovered that xylem flow, through its hydraulic coupling to the phloem, and sucrose efflux along the phloem, also significantly affected resource partitioning. For tubers, it is the cumulative disadvantage compared to sink leaves (distance, xylem flow, and sucrose efflux) that enable an undirected SP6A-mediated reduction of sucrose efflux to preferentially benefit tuber resource partitioning. Combined with the SP6A-mediated sink strength increase, undirected SP6A introduction significantly enhances tuber resource partitioning.

Embodiment in distributed information processing: "Solid" plants versus "liquid" ant colonies.

Information processing is an essential part of biology, enabling coordination of intra-organismal processes such as development, environmental adaptation and inter-organismal communication. Whilst in animals with specialised brain tissue a substantial amount of information processing occurs in a centralised manner, most biological computing is distributed across multiple entities, such as cells in a tissue, roots in a root system or ants in a colony. Physical context, called embodiment, also affects the nature of biological computing. While plants and ant colonies both perform distributed computing, in plants the units occupy fixed positions while individual ants move around. This distinction, solid versus liquid brain computing, shapes the nature of computations. Here we compare information processing in plants and ant colonies, highlighting how similarities and differences originate in, as well as make use of, the differences in embodiment. We end with a discussion on how this embodiment perspective may inform the debate on plant cognition.

A reflux-and-growth mechanism explains oscillatory patterning of lateral root branching sites.

Modular, repetitive structures are a key component of complex multicellular body plans across the tree of life. Typically, these structures are prepatterned by temporal oscillations in gene expression or signaling. Although a clock-and-wavefront mechanism was identified and plant leaf phyllotaxis arises from a Turing-type patterning for vertebrate somitogenesis and arthropod segmentation, the mechanism underlying lateral root patterning has remained elusive. To resolve this enigma, we combined computational modeling with in planta experiments. Intriguingly, auxin oscillations automatically emerge in our model from the interplay between a reflux-loop-generated auxin loading zone and stem-cell-driven growth dynamics generating periodic cell-size variations. In contrast to the clock-and-wavefront mechanism and Turing patterning, the uncovered mechanism predicts both frequency and spacing of lateral-root-forming sites to positively correlate with root meristem growth. We validate this prediction experimentally. Combined, our model and experimental results support that a reflux-and-growth patterning mechanism underlies lateral root priming.

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.

Modelling the physiological relevance of sucrose export repression by an Flowering Time homolog in the long-distance phloem of potato.

Yield of harvestable plant organs depends on photosynthetic assimilate production in source leaves, long-distance sucrose transport and sink-strength. While photosynthesis optimization has received considerable interest for optimizing plant yield, the potential for improving long-distance sucrose transport has received far less attention. Interestingly, a recent potato study demonstrates that the tuberigen StSP6A binds to and reduces activity of the StSWEET11 sucrose exporter. While the study suggested that reducing phloem sucrose efflux may enhance tuber yield, the precise mechanism and physiological relevance of this effect remained an open question. Here, we develop the first mechanistic model for sucrose transport, parameterized for potato plants. The model incorporates SWEET-mediated sucrose export, SUT-mediated sucrose retrieval from the apoplast and StSP6A-StSWEET11 interactions. Using this model, we were able to substantiate the physiological relevance of the StSP6A-StSWEET11 interaction in the long-distance phloem for potato tuber yield, as well as to show the non-linear nature of this effect.

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.

What is quantitative plant biology?

Quantitative plant biology is an interdisciplinary field that builds on a long history of biomathematics and biophysics. Today, thanks to high spatiotemporal resolution tools and computational modelling, it sets a new standard in plant science. Acquired data, whether molecular, geometric or mechanical, are quantified, statistically assessed and integrated at multiple scales and across fields. They feed testable predictions that, in turn, guide further experimental tests. Quantitative features such as variability, noise, robustness, delays or feedback loops are included to account for the inner dynamics of plants and their interactions with the environment. Here, we present the main features of this ongoing revolution, through new questions around signalling networks, tissue topology, shape plasticity, biomechanics, bioenergetics, ecology and engineering. In the end, quantitative plant biology allows us to question and better understand our interactions with plants. In turn, this field opens the door to transdisciplinary projects with the society, notably through citizen science.

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.

A Self-Organized PLT/Auxin/ARR-B Network Controls the Dynamics of Root Zonation Development in Arabidopsis thaliana.

During organogenesis, coherent organ growth arises from spatiotemporally coordinated decisions of individual cells. In the root of Arabidopsis thaliana, this coordination results in the establishment of a division and a differentiation zone. Cells continuously move through these zones; thus, a major question is how the boundary between these domains, the transition zone, is formed and maintained. By combining molecular genetics with computational modeling, we reveal how an auxin/PLETHORA/ARR-B network controls these dynamic patterning processes. We show that after germination, cell division causes a drop in distal PLT2 levels that enables transition zone formation and ARR12 activation. The resulting PLT2-ARR12 antagonism controls expansion of the division zone (the meristem). The successive ARR1 activation antagonizes PLT2 through inducing the cell-cycle repressor KRP2, thus setting final meristem size. Our work indicates a key role for the interplay between cell division dynamics and regulatory networks in root zonation and transition zone patterning.

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.

Of mice and plants: Comparative developmental systems biology.

Multicellular animals and plants represent independent evolutionary experiments with complex multicellular bodyplans. Differences in their life history, a mobile versus sessile lifestyle, and predominant embryonic versus postembryonic development, have led to the evolution of highly different body plans. However, also many intriguing parallels exist. Extension of the vertebrate body axis and its segmentation into somites bears striking resemblance to plant root growth and the concomittant prepatterning of lateral root competent sites. Likewise, plant shoot phyllotaxis displays similarities with vertebrate limb and digit patterning. Additionally, both plants and animals use complex signalling systems combining systemic and local signals to fine tune and coordinate organ growth across their body. Identification of these striking examples of convergent evolution provides support for the existence of general design principles: the idea that for particular patterning demands, evolution is likely to arrive at highly similar developmental patterning mechanisms. Furthermore, focussing on these parallels may aid in identifying core mechanistic principles, often obscured by the highly complex nature of multiscale patterning processes.

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.

In Silico Roots: Room for Growth.

Computational models are invaluable tools for understanding the hormonal and genetic control of root development. Thus far, models have focused on the crucial roles that auxin transport and metabolism play in determining the auxin signaling gradient that controls the root meristem. Other hormones such as cytokinins, gibberellins, and ethylene have predominantly been considered as modulators of auxin dynamics, but their underlying patterning mechanisms are currently unresolved. In addition, the effects of cell- and tissue-level growth dynamics, which induce dilution and displacement of signaling molecules, have remained unexplored. Elucidating these additional mechanisms will be essential to unravel how root growth is patterned in a robust and self-organized manner. Models incorporating growth will thus be crucial in unraveling the underlying logic of root developmental decision making.