Alistair M. Middleton

Root gravitropism is regulated by a transient lateral auxin gradient controlled by a tipping-point mechanism

Gravity profoundly influences plant growth and development. Plants respond to changes in orientation by using gravitropic responses to modify their growth. Cholodny and Went hypothesized over 80 years ago that plants bend in response to a gravity stimulus by generating a lateral gradient of a growth regulator at an organs apex, later found to be auxin. Auxin regulates root growth by targeting Aux/IAA repressor proteins for degradation. We used an Aux/IAA-based reporter, domain II (DII)-VENUS, in conjunction with a mathematical model to quantify auxin redistribution following a gravity stimulus. Our multidisciplinary approach revealed that auxin is rapidly redistributed to the lower side of the root within minutes of a 90° gravity stimulus. Unexpectedly, auxin asymmetry was rapidly lost as bending root tips reached an angle of 40° to the horizontal. We hypothesize roots use a “tipping point” mechanism that operates to reverse the asymmetric auxin flow at the midpoint of root bending. These mechanistic insights illustrate the scientific value of developing quantitative reporters such as DII-VENUS in conjunction with parameterized mathematical models to provide high-resolution kinetics of hormone redistribution.

Mathematical modeling elucidates the role of transcriptional feedback in gibberellin signaling

The hormone gibberellin (GA) is a key regulator of plant growth. Many of the components of the gibberellin signal transduction [e.g., GIBBERELLIN INSENSITIVE DWARF 1 (GID1) and DELLA], biosynthesis [e.g., GA 20-oxidase (GA20ox) and GA3ox], and deactivation pathways have been identified. Gibberellin binds its receptor, GID1, to form a complex that mediates the degradation of DELLA proteins. In this way, gibberellin relieves DELLA-dependent growth repression. However, gibberellin regulates expression of GID1, GA20ox, and GA3ox, and there is also evidence that it regulates DELLA expression. In this paper, we use integrated mathematical modeling and experiments to understand how these feedback loops interact to control gibberellin signaling. Model simulations are in good agreement with in vitro data on the signal transduction and biosynthesis pathways and in vivo data on the expression levels of gibberellin-responsive genes. We find that GA–GID1 interactions are characterized by two timescales (because of a lid on GID1 that can open and close slowly relative to GA–GID1 binding and dissociation). Furthermore, the model accurately predicts the response to exogenous gibberellin after a number of chemical and genetic perturbations. Finally, we investigate the role of the various feedback loops in gibberellin signaling. We find that regulation of GA20ox transcription plays a significant role in both modulating the level of endogenous gibberellin and generating overshoots after the removal of exogenous gibberellin. Moreover, although the contribution of other individual feedback loops seems relatively small, GID1 and DELLA transcriptional regulation acts synergistically with GA20ox feedback.

Growth-induced hormone dilution can explain the dynamics of plant root cell elongation

In the elongation zone of the Arabidopsis thaliana plant root, cells undergo rapid elongation, increasing their length by ∼10-fold over 5 h while maintaining a constant radius. Although progress is being made in understanding how this growth is regulated, little consideration has been given as to how cell elongation affects the distribution of the key regulating hormones. Using a multiscale mathematical model and measurements of growth dynamics, we investigate the distribution of the hormone gibberellin in the root elongation zone. The model quantifies how rapid cell expansion causes gibberellin to dilute, creating a significant gradient in gibberellin levels. By incorporating the gibberellin signaling network, we simulate how gibberellin dilution affects the downstream components, including the growth-repressing DELLA proteins. We predict a gradient in DELLA that provides an explanation of the reduction in growth exhibited as cells move toward the end of the elongation zone. These results are validated at the molecular level by comparing predicted mRNA levels with transcriptomic data. To explore the dynamics further, we simulate perturbed systems in which gibberellin levels are reduced, considering both genetically modified and chemically treated roots. By modeling these cases, we predict how these perturbations affect gibberellin and DELLA levels and thereby provide insight into their altered growth dynamics.

Sequential induction of auxin efflux and influx carriers regulates lateral root emergence

In Arabidopsis, lateral roots originate from pericycle cells deep within the primary root. New lateral root primordia (LRP) have to emerge through several overlaying tissues. Here, we report that auxin produced in new LRP is transported towards the outer tissues where it triggers cell separation by inducing both the auxin influx carrier LAX3 and cell‐wall enzymes. LAX3 is expressed in just two cell files overlaying new LRP. To understand how this striking pattern of LAX3 expression is regulated, we developed a mathematical model that captures the network regulating its expression and auxin transport within realistic three‐dimensional cell and tissue geometries. Our model revealed that, for the LAX3 spatial expression to be robust to natural variations in root tissue geometry, an efflux carrier is required—later identified to be PIN3. To prevent LAX3 from being transiently expressed in multiple cell files, PIN3 and LAX3 must be induced consecutively, which we later demonstrated to be the case. Our study exemplifies how mathematical models can be used to direct experiments to elucidate complex developmental processes.

Mathematical Modelling of the Aux/IAA Negative Feedback Loop

The hormone auxin is implicated in regulating a diverse range of developmental processes in plants. Auxin acts in part by inducing the Aux/IAA genes. The associated pathway comprises multiple negative feedback loops (whereby Aux/IAA proteins can repress Aux/IAA genes) that are disrupted by auxin mediating the turnover of Aux/IAA protein. In this paper, we develop a mathematical model of a single Aux/IAA negative feedback loop in a population of identical cells. The model has a single steady-state. We explore parameter space to uncover a number of dynamical regimes. In particular, we identify the ratio between the Aux/IAA protein and mRNA turnover rates as a key parameter in the model. When this ratio is sufficiently small, the system can evolve to a stable limit cycle, corresponding to an oscillation in Aux/IAA expression levels. Otherwise, the steady-state is either a stable-node or a stable-spiral. These observations may shed light on recent experimental results.

Modeling Regulatory Networks to Understand Plant Development: Small Is Beautiful

We now have unprecedented capability to generate large data sets on the myriad genes and molecular players that regulate plant development. Networks of interactions between systems components can be derived from that data in various ways and can be used to develop mathematical models of various degrees of sophistication. Here, we discuss why, in many cases, it is productive to focus on small networks. We provide a brief and accessible introduction to relevant mathematical and computational approaches to model regulatory networks and discuss examples of small network models that have helped generate new insights into plant biology (where small is beautiful), such as in circadian rhythms, hormone signaling, and tissue patterning. We conclude by outlining some of the key technical and modeling challenges for the future.

Bistability in a model of mesoderm and anterior mesendoderm specification in Xenopus laevis

In this paper we develop a model of mesendoderm specification in Xenopus laevis based on an existing gene regulation network. The mesendoderm is a population of cells that may contribute to either the mesoderm or endoderm. The model that we develop encompasses the time evolution of transcription factor concentrations in a single cell and is shown to have stable steady states that correspond to mesoderm and anterior mesendodermal cell types, but not endoderm (except in cells where Goosecoid expression is inhibited). Both in vitro and in vivo versions of the model are developed and analysed, the former indicating how cell fate is determined in large part by the concentration of Activin administered to a cell, with the model results comparing favourably with current quantitative experimental data. A numerical investigation of the in vivo model suggests that cell fate is determined largely by a VegT and beta-Catenin pre-pattern, subsequently being reinforced by Nodal. We argue that this sensitivity of the model to a VegT and beta-Catenin pre-pattern indicates that a key VegT self-limiting mechanism (for which there is experimental evidence) is absent from the model. Furthermore, we find that the lack of a steady state corresponding to endoderm is entirely consistent with current in vivo data, and that the in vivo model corresponds to mesendoderm specification on the dorsal, but not the ventral, side of the embryo.

Concomitant expression of far upstream element (FUSE) binding protein (FBP) interacting repressor (FIR) and its splice variants induce migration and invasion of non‐small cell lung cancer (NSCLC) cells

Transcription factors integrate a variety of oncogenic input information, facilitate tumour growth and cell dissemination, and therefore represent promising therapeutic target structures. Because over‐expression of DNA‐interacting far upstream element binding protein (FBP) supports non‐small cell lung cancer (NSCLC) migration, we asked whether its repressor, FBP‐interacting repressor (FIR) is functionally inactivated and how FIR might affect NSCLC cell biology. Different FIR splice variants were highly expressed in the majority of NSCLCs, with the highest levels in tumours carrying genomic gains of chromosome 8q24.3, which contained the FIR gene locus. Nuclear FIR expression was significantly enriched at the invasion front of primary NSCLCs, but this did not correlate with tumour cell proliferation. FIR accumulation was associated with worse patient survival and tumour recurrence; in addition, FIR over‐expression significantly correlated with lymph node metastasis in squamous cell carcinomas (SCCs). In vitro, we applied newly developed methods and modelling approaches for the quantitative and time‐resolved description of the pro‐migratory and pro‐invasive capacities of SCC cells. siRNA‐mediated silencing of all FIR variants significantly reduced the speed and directional movement of tumour cells in all phases of migration. Furthermore, sprouting efficiency and single cell invasiveness were diminished following FIR inhibition. Interestingly, the silencing of FIR isoforms lacking exon 2 (FIRΔexon2) alone was sufficient to reduce lateral migration and invasion. In summary, by using scale‐spanning data derived from primary human tissues, quantitative cellular analyses and mathematical modelling, we have demonstrated that concomitant over‐expression of FIR and its splice variants drives NSCLC migration and dissemination. Copyright

An individual-based model for collective cancer cell migration explains speed dynamics and phenotype variability in response to growth factors

Collective cell migration is a common phenotype in epithelial cancers, which is associated with tumor cell metastasis and poor patient survival. However, the interplay between physiologically relevant pro-migratory stimuli and the underlying mechanical cell–cell interactions are poorly understood. We investigated the migratory behavior of different collectively migrating non-small cell lung cancer cell lines in response to motogenic growth factors (e.g. epidermal growth factor) or clinically relevant small compound inhibitors. Depending on the treatment, we observed distinct behaviors in a classical lateral migration assay involving traveling fronts, finger-shapes or the development of cellular bridges. Particle image velocimetry analysis revealed characteristic speed dynamics (evolution of the average speed of all cells in a frame) in all experiments exhibiting initial acceleration and subsequent deceleration of the cell populations. To better understand the mechanical properties of individual cells leading to the observed speed dynamics and the phenotypic differences we developed a mathematical model based on a Langevin approach. This model describes intercellular forces, random motility, and stimulation of active migration by mechanical interaction between cells. Simulations show that the model is able to reproduce the characteristic spatio-temporal speed distributions as well as most migratory phenotypes of the studied cell lines. A specific strength of the proposed model is that it identifies a small set of mechanical features necessary to explain all phenotypic and dynamical features of the migratory response of non-small cell lung cancer cells to chemical stimulation/inhibition. Furthermore, all processes included in the model can be associated with potential molecular components, and are therefore amenable to experimental validation. Thus, the presented mathematical model may help to predict which mechanical aspects involved in non-small cell lung cancer cell migration are affected by the respective therapeutic treatment.Cancer research: Mathematical model describes mechanics of cell coordinationIn many cancers, spreading and the formation of metastasis involve the coordinated migration of many cells. An interdisciplinary team of researchers from Heidelberg and Frankfurt studied the collective movement of cultured lung cancer cells subject to chemical stimulation. Based on extensive data analysis a mathematical model was developed to explain the variety of migration behaviors observed under different treatments. The model describes the mechanics of compression, stretch, cell elasticity and force-regulated active motion—which in sum lead to coordination within large cell groups. Simulations demonstrate how these mechanical features affect cell coordination and collective behavior. In tests of potential medical treatment strategies, the model can be used to predict the effects of the drug on specific mechanical properties of single cells.

Data-Driven Modeling of Intracellular Auxin Fluxes Indicates a Dominant Role of the ER in Controlling Nuclear Auxin Uptake

In plants, the phytohormone auxin acts as a master regulator of developmental processes and environmental responses. The best characterized process in the auxin regulatory network occurs at the subcellular scale, wherein auxin mediates signal transduction into transcriptional programs by triggering the degradation of Aux/IAA transcriptional repressor proteins in the nucleus. However, whether and how auxin movement between the nucleus and the surrounding compartments is regulated remain elusive. Using a fluorescent auxin analog, we show that its diffusion into the nucleus is restricted. By combining mathematical modeling with time course assays on auxin-mediated nuclear signaling and quantitative phenotyping in single plant cell systems, we show that ER-to-nucleus auxin flux represents a major subcellular pathway to directly control nuclear auxin levels. Our findings propose that the homeostatically regulated auxin pool in the ER and ER-to-nucleus auxin fluxes underpin auxin-mediated downstream responses in plant cells.