John R. King

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.

Auxin regulates aquaporin function to facilitate lateral root emergence.

Aquaporins are membrane channels that facilitate water movement across cell membranes. In plants, aquaporins contribute to water relations. Here, we establish a new link between aquaporin-dependent tissue hydraulics and auxin-regulated root development in Arabidopsis thaliana. We report that most aquaporin genes are repressed during lateral root formation and by exogenous auxin treatment. Auxin reduces root hydraulic conductivity both at the cell and whole-organ levels. The highly expressed aquaporin PIP2;1 is progressively excluded from the site of the auxin response maximum in lateral root primordia (LRP) whilst being maintained at their base and underlying vascular tissues. Modelling predicts that the positive and negative perturbations of PIP2;1 expression alter water flow into LRP, thereby slowing lateral root emergence (LRE). Consistent with this mechanism, pip2;1 mutants and PIP2;1-overexpressing lines exhibit delayed LRE. We conclude that auxin promotes LRE by regulating the spatial and temporal distribution of aquaporin-dependent root tissue water transport.

A Two-Phase Model of Solid Tumour Growth

Many solid tumour growth models are formulated as systems of parabolic and/or hyperbolic equations. Here an alternative, two-phase theory is developed to describe solid tumour growth. Versions of earlier models are recovered when suitable limits of the new model are taken. We contend that the multiphase approach represents a more general, and natural, modelling framework for studying solid tumour growth than existing theories.

An integrative computational model for intestinal tissue renewal.

Objectives:  The luminal surface of the gut is lined with a monolayer of epithelial cells that acts as a nutrient absorptive engine and protective barrier. To maintain its integrity and functionality, the epithelium is renewed every few days. Theoretical models are powerful tools that can be used to test hypotheses concerning the regulation of this renewal process, to investigate how its dysfunction can lead to loss of homeostasis and neoplasia, and to identify potential therapeutic interventions. Here we propose a new multiscale model for crypt dynamics that links phenomena occurring at the subcellular, cellular and tissue levels of organisation.

Systems Analysis of Auxin Transport in the Arabidopsis Root Apex

This study presents a computational model for auxin transport based on actual root cell geometries and carrier subcellular localizations and tested using the DII-VENUS auxin sensor. The model shows that nonpolar AUX1/LAX influx carriers control which tissues have high auxin levels, whereas the polar PIN carriers control the direction of auxin transport within these tissues. Auxin is a key regulator of plant growth and development. Within the root tip, auxin distribution plays a crucial role specifying developmental zones and coordinating tropic responses. Determining how the organ-scale auxin pattern is regulated at the cellular scale is essential to understanding how these processes are controlled. In this study, we developed an auxin transport model based on actual root cell geometries and carrier subcellular localizations. We tested model predictions using the DII-VENUS auxin sensor in conjunction with state-of-the-art segmentation tools. Our study revealed that auxin efflux carriers alone cannot create the pattern of auxin distribution at the root tip and that AUX1/LAX influx carriers are also required. We observed that AUX1 in lateral root cap (LRC) and elongating epidermal cells greatly enhance auxin’s shootward flux, with this flux being predominantly through the LRC, entering the epidermal cells only as they enter the elongation zone. We conclude that the nonpolar AUX1/LAX influx carriers control which tissues have high auxin levels, whereas the polar PIN carriers control the direction of auxin transport within these tissues.

Transcriptional Dynamics of Two Seed Compartments with Opposing Roles in Arabidopsis Seed Germination

Gene expression profiling in two seed compartments uncovers two transcriptional phases during seed germination that are separated by testa rupture. Seed germination is a critical stage in the plant life cycle and the first step toward successful plant establishment. Therefore, understanding germination is of important ecological and agronomical relevance. Previous research revealed that different seed compartments (testa, endosperm, and embryo) control germination, but little is known about the underlying spatial and temporal transcriptome changes that lead to seed germination. We analyzed genome-wide expression in germinating Arabidopsis (Arabidopsis thaliana) seeds with both temporal and spatial detail and provide Web-accessible visualizations of the data reported (vseed.nottingham.ac.uk). We show the potential of this high-resolution data set for the construction of meaningful coexpression networks, which provide insight into the genetic control of germination. The data set reveals two transcriptional phases during germination that are separated by testa rupture. The first phase is marked by large transcriptome changes as the seed switches from a dry, quiescent state to a hydrated and active state. At the end of this first transcriptional phase, the number of differentially expressed genes between consecutive time points drops. This increases again at testa rupture, the start of the second transcriptional phase. Transcriptome data indicate a role for mechano-induced signaling at this stage and subsequently highlight the fates of the endosperm and radicle: senescence and growth, respectively. Finally, using a phylotranscriptomic approach, we show that expression levels of evolutionarily young genes drop during the first transcriptional phase and increase during the second phase. Evolutionarily old genes show an opposite pattern, suggesting a more conserved transcriptome prior to the completion of germination.

Mathematical modelling of drug transport in tumour multicell spheroids and monolayer cultures.

In this paper we adapt an avascular tumour growth model to compare the effects of drug application on multicell spheroids and on monolayer cultures. The model for the tumour is based on nutrient driven growth of a continuum of live cells, whose birth and death generates volume changes described by a velocity field. The drug is modelled as an externally applied, diffusible material capable of killing cells, both linear and Michaelis-Menten kinetics for drug action on cells being studied. Numerical solutions of the resulting system of partial differential equations for the multicell spheroid case are compared with closed form solutions of the monolayer case, particularly with respect to the effects on the cell kill of the drug dosage and of the duration of its application. The results show an enhanced survival rate in multicell spheroids compared to monolayer cultures, consistent with experimental observations, and indicate that the key factor determining this is drug penetration. An analysis of the large time tumour spheroid response to a continuously applied drug at fixed concentration reveals up to three stable large time solutions, namely the trivial solution (i.e. a dead tumour), a travelling wave (continuously growing tumour) and a sublinear growth case in which cells reach a pseudo-steady-state in the core. Each of these possibilities is formulated and studied, with the bifurcations between them being discussed. Numerical solutions reveal that the pseudo-steady-state solutions persist to a significantly higher drug dose than travelling wave solutions.

Crypt dynamics and colorectal cancer: advances in mathematical modelling

Abstract.   Mathematical modelling forms a key component of systems biology, offering insights that complement and stimulate experimental studies. In this review, we illustrate the role of theoretical models in elucidating the mechanisms involved in normal intestinal crypt dynamics and colorectal cancer. We discuss a range of modelling approaches, including models that describe cell proliferation, migration, differentiation, crypt fission, genetic instability, APC inactivation and tumour heterogeneity. We focus on the model assumptions, limitations and applications, rather than on the technical details. We also present a new stochastic model for stem‐cell dynamics, which predicts that, on average, APC inactivation occurs more quickly in the stem‐cell pool in the absence of symmetric cell division. This suggests that natural niche succession may protect stem cells against malignant transformation in the gut. Finally, we explain how we aim to gain further understanding of the crypt system and of colorectal carcinogenesis with the aid of multiscale models that cover all levels of organization from the molecular to the whole organ.

13C nuclear magnetic resonance detection of interactions of serine hydroxymethyltransferase with C1-tetrahydrofolate synthase and glycine decarboxylase complex activities in Arabidopsis.

In C3 plants, serine synthesis is associated with photorespiratory glycine metabolism involving the tetrahydrofolate (THF)-dependent activities of the glycine decarboxylase complex (GDC) and serine hydroxymethyl transferase (SHMT). Alternatively, THF-dependent serine synthesis can occur via the C1-THF synthase/SHMT pathway. We used 13C nuclear magnetic resonance to examine serine biosynthesis by these two pathways in Arabidopsis thaliana (L.) Heynh. Columbia wild type. We confirmed the tight coupling of the GDC/SHMT system and observed directly in a higher plant the flux of formate through the C1-THF synthase/SHMT system. The accumulation of 13C-enriched serine over 24 h from the GDC/SHMT activities was 4-fold greater than that from C1-THF synthase/SHMT activities. Our experiments strongly suggest that the two pathways operate independently in Arabidopsis. Plants exposed to methotrexate and sulfanilamide, powerful inhibitors of THF biosynthesis, reduced serine synthesis by both pathways. The results suggest that continuous supply of THF is essential to maintain high rates of serine metabolism. Nuclear magnetic resonance is a powerful tool for the examination of THF-mediated metabolism in its natural cellular environment.

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.