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.

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.

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.

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.

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.

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.

Organization of ventricular fibrillation in the human heart.

Sudden cardiac death is a major cause of death in the industrialized world, claiming approximately 300,000 victims annually in the United States alone. In most cases, sudden cardiac death is caused by ventricular fibrillation (VF). Experimental studies in large animal hearts have shown that the uncoordinated contractions during VF are caused by large numbers of chaotically wandering reentrant waves of electrical activity. However, recent clinical data on VF in the human heart seem to suggest that human VF may have a markedly different organization. Here, we use a detailed model of the human ventricles, including a detailed description of cell electrophysiology, ventricular anatomy, and fiber direction anisotropy, to study the organization of human VF. We show that characteristics of our simulated VF are qualitatively similar to the clinical data. Furthermore, we find that human VF is driven by only approximately 10 reentrant sources and thus is much more organized than VF in animal hearts of comparable size, where VF is driven by approximately 50 sources. We investigate the influence of anisotropy ratio, tissue excitability, and restitution properties on the number of reentrant sources driving VF. We find that the number of rotors depends strongest on minimum action potential duration, a property that differs significantly between human and large animal hearts. Based on these findings, we suggest that the simpler spatial organization of human VF relative to VF in large animal hearts may be caused by differences in minimum action potential duration. Both the simpler spatial organization of human VF and its suggested cause may have important implications for treating and preventing this dangerous arrhythmia in humans.

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.

Comparison of electrophysiological models for human ventricular cells and tissues.

In this paper we briefly review currently published models for human ventricular cells and tissues. We discuss the Priebe-Beuckelmann (PB) model and the reduced version of this model constructed by Bernus et al. (redPB), the Ten Tusscher-Noble-Noble-Panfilov (TNNP) model and the Iyer-Mazhari-Winslow (IMW) model. We compare several characteristics of these models such as: sources of experimental data the models are based on, action potential morphology, action potential duration (APD) and conduction velocity (CV) restitution and computational efficiency. Finally, we discuss the application of a subset of these models-the redPB and the TNNP model-to study simulated spiral wave dynamics in 2D tissue sheets and in the human ventricles. We discuss the suitability of the different models for particular research questions and their limitations.

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.

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.

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.