Bistability, bifurcations, and Waddington's epigenetic landscape

Waddington's epigenetic landscape is probably the most famous and most powerful metaphor in developmental biology. Cells, represented by balls, roll downhill through a landscape of bifurcating valleys. Each new valley represents a possible cell fate and the ridges between the valleys maintain the cell fate once it has been chosen. Here I examine models of two important developmental processes - cell-fate induction and lateral inhibition - and ask whether the landscapes for these models at least qualitatively resemble Waddington's picture. For cell-fate induction, the answer is no. The commitment of a cell to a new fate corresponds to the disappearance of a valley from the landscape, not the splitting of one valley into two, and it occurs through a type of bifurcation - a saddle-node bifurcation - that possesses an intrinsic irreversibility that is missing from Waddington's picture. Lateral inhibition, a symmetrical cell-cell competition process, corresponds better to Waddington's picture, with one valley reversibly splitting into two through a pitchfork bifurcation. I propose an alternative epigenetic landscape that has numerous valleys and ridges right from the start, with the process of cell-fate commitment corresponding to the irreversible disappearance of some of these valleys and ridges, via cell-fate induction, complemented by the creation of new valleys and ridges through processes like cell-cell competition.     

Energy Landscape Reveals That the Budding Yeast Cell Cycle Is a Robust and Adaptive Multi-stage Process

Quantitatively understanding the robustness, adaptivity and efficiency of cell cycle dynamics under the influence of noise is a fundamental but difficult question to answer for most eukaryotic organisms. Using a simplified budding yeast cell cycle model perturbed by intrinsic noise, we systematically explore these issues from an energy landscape point of view by constructing an energy landscape for the considered system based on large deviation theory. Analysis shows that the cell cycle trajectory is sharply confined by the ambient energy barrier, and the landscape along this trajectory exhibits a generally flat shape. We explain the evolution of the system on this flat path by incorporating its non-gradient nature. Furthermore, we illustrate how this global landscape changes in response to external signals, observing a nice transformation of the landscapes as the excitable system approaches a limit cycle system when nutrients are sufficient, as well as the formation of additional energy wells when the DNA replication checkpoint is activated. By taking into account the finite volume effect, we find additional pits along the flat cycle path in the landscape associated with the checkpoint mechanism of the cell cycle. The difference between the landscapes induced by intrinsic and extrinsic noise is also discussed. In our opinion, this meticulous structure of the energy landscape for our simplified model is of general interest to other cell cycle dynamics, and the proposed methods can be applied to study similar biological systems.     

From Understanding the Development Landscape of the Canonical Fate-Switch Pair to Constructing a Dynamic Landscape for Two-Step Neural Differentiation

Recent progress in stem cell biology, notably cell fate conversion, calls for novel theoretical understanding for cell differentiation. The existing qualitative concept of Waddington’s “epigenetic landscape” has attracted particular attention because it captures subsequent fate decision points, thus manifesting the hierarchical (“tree-like”) nature of cell fate diversification. Here, we generalized a recent work and explored such a developmental landscape for a two-gene fate decision circuit by integrating the underlying probability landscapes with different parameters (corresponding to distinct developmental stages). The change of entropy production rate along the parameter changes indicates which parameter changes can represent a normal developmental process while other parameters’ change can not. The transdifferentiation paths over the landscape under certain conditions reveal the possibility of a direct and reversible phenotypic conversion. As the intensity of noise increases, we found that the landscape becomes flatter and the dominant paths more straight, implying the importance of biological noise processing mechanism in development and reprogramming. We further extended the landscape of the one-step fate decision to that for two-step decisions in central nervous system (CNS) differentiation. A minimal network and dynamic model for CNS differentiation was firstly constructed where two three-gene motifs are coupled. We then implemented the SDEs (Stochastic Differentiation Equations) simulation for the validity of the network and model. By integrating the two landscapes for the two switch gene pairs, we constructed the two-step development landscape for CNS differentiation. Our work provides new insights into cellular differentiation and important clues for better reprogramming strategies.     

Molecular live cell bioimaging in stem cell research

Functional heterogeneity within stem and progenitor cells has been shown to influence cell fate decisions. Similarly, intracellular signaling activated by external stimuli is highly heterogeneous and its spatiotemporal activity is linked to future cell behavior. To quantify these heterogeneous states and link them to future cell fates, it is important to observe cell populations continuously with single cell resolution. Live cell imaging in combination with fluorescent biosensors for signaling activity serves as a powerful tool to study cellular and molecular heterogeneity and the long-term biological effects of signaling. Here, we describe these methodologies, their advantages over classical approaches, and we illustrate how they could be applied to improve our understanding of the importance of heterogeneous cellular and molecular responses to external signaling cues.     

生态学系统的空间异质性

空间异质性是生态学系统的一个普遍牧场生,生态学家对它在生态学中的重要性已取得了比以往更深刻的认识。试图从空间异质性的含义,空间异质性与尺度和等级的关系,空间异质性的定量描述,空间异质性对生物和非生物过程的影响,以及空间异质性的动态等5个方面综述了有关空间异质性的生态学研究的新进展。     

To lyse or not to lyse: transient-mediated stochastic fate determination in cells infected by bacteriophages

Cell fate determination is usually described as the result of the stochastic dynamics of gene regulatory networks (GRNs) reaching one of multiple steady-states each of which corresponds to a specific decision. However, the fate of a cell is determined in finite time suggesting the importance of transient dynamics in cellular decision making. Here we consider cellular decision making as resulting from first passage processes of regulatory proteins and examine the effect of transient dynamics within the initial lysis-lysogeny switch of phage λ. Importantly, the fate of an infected cell depends, in part, on the number of coinfecting phages. Using a quantitative model of the phage λ GRN, we find that changes in the likelihood of lysis and lysogeny can be driven by changes in phage co-infection number regardless of whether or not there exists steady-state bistability within the GRN. Furthermore, two GRNs which yield qualitatively distinct steady state behaviors as a function of phage infection number can show similar transient responses, sufficient for alternative cell fate determination. We compare our model results to a recent experimental study of cell fate determination in single cell assays of multiply infected bacteria. Whereas the experimental study proposed a "quasi-independent" hypothesis for cell fate determination consistent with an observed data collapse, we demonstrate that observed cell fate results are compatible with an alternative form of data collapse consistent with a partial gene dosage compensation mechanism. We show that including partial gene dosage compensation at the mRNA level in our stochastic model of fate determination leads to the same data collapse observed in the single cell study. Our findings elucidate the importance of transient gene regulatory dynamics in fate determination, and present a novel alternative hypothesis to explain single-cell level heterogeneity within the phage λ lysis-lysogeny decision switch.     

Temporal variability of aphid biological control in contrasting landscape contexts

Landscape complexity may provide ecosystem services to agriculture through the provision of natural enemies of agricultural pests. Strong positive effect of adjacent semi-natural habitats on natural enemies in croplands has been evidenced, but the resulting impact on biological control remains unclear. Taking into account the temporal dynamics of pest and natural enemies in agricultural landscapes provides better resolution to the studies and better understanding of the biological control service.In this study, the population dynamics of aphids and two groups of predators (coccinellid and carabid beetles) were examined. Insects were sampled in 20 wheat fields, surrounded by structurally simple and complex landscapes in Chilean central valley. Considering the whole sampling period, the diversity of aphids and natural enemies were similar in wheat crops surrounded by both types of landscapes, and the abundance of ladybirds was higher in crops in the complex landscapes. The dynamics of predators was more advanced in complex landscapes than in the simple ones, whereas the dynamics of aphids were similar in both types of landscape. Negative correlation between abundance of predators and aphid population growth rate in both landscape contexts were observed suggesting a control of the pest population by the predators. Different temporal patterns were observed in these correlations in the two landscape contexts, which suggests differences in the biological control related to the landscape composition.The present study shows that colonization of crops by natural enemies occurs sooner in structurally complex landscapes and suggests that this early colonization may facilitate an early and efficient control of aphid populations, nevertheless the biological control efficiency seems to be higher in structurally simple landscapes later in the season.     

Single‐cell dynamics of chromatin activity during cell lineage differentiation in Caenorhabditis elegans embryos

Elucidating the chromatin dynamics that orchestrate embryogenesis is a fundamental question in developmental biology. Here, we exploit position effects on expression as an indicator of chromatin activity and infer the chromatin activity landscape in every lineaged cell during Caenorhabditis elegans early embryogenesis. Systems‐level analyses reveal that chromatin activity distinguishes cellular states and correlates with fate patterning in the early embryos. As cell lineage unfolds, chromatin activity diversifies in a lineage‐dependent manner, with switch‐like changes accompanying anterior–posterior fate asymmetry and characteristic landscapes being established in different cell lineages. Upon tissue differentiation, cellular chromatin from distinct lineages converges according to tissue types but retains stable memories of lineage history, contributing to intra‐tissue cell heterogeneity. However, the chromatin landscapes of cells organized in a left–right symmetric pattern are predetermined to be analogous in early progenitors so as to pre‐set equivalent states. Finally, genome‐wide analysis identifies many regions exhibiting concordant chromatin activity changes that mediate the co‐regulation of functionally related genes during differentiation. Collectively, our study reveals the developmental and genomic dynamics of chromatin activity at the single‐cell level.     

Exploring the Mechanisms of Differentiation,Dedifferentiation, Reprogramming and Transdifferentiation

We explored the underlying mechanisms of differentiation, dedifferentiation, reprogramming and transdifferentiation (cell type switchings) from landscape and flux perspectives. Lineage reprogramming is a new regenerative method to convert a matured cell into another cell including direct transdifferentiation without undergoing a pluripotent cell state and indirect transdifferentiation with an initial dedifferentiation-reversion (reprogramming) to a pluripotent cell state. Each cell type is quantified by a distinct valley on the potential landscape with higher probability. We investigated three driving forces for cell fate decision making: stochastic fluctuations, gene regulation and induction, which can lead to cell type switchings. We showed that under the driving forces the direct transdifferentiation process proceeds from a differentiated cell valley to another differentiated cell valley through either a distinct stable intermediate state or a certain series of unstable indeterminate states. The dedifferentiation process proceeds through a pluripotent cell state. Barrier height and the corresponding escape time from the valley on the landscape can be used to quantify the stability and efficiency of cell type switchings. We also uncovered the mechanisms of the underlying processes by quantifying the dominant biological paths of cell type switchings on the potential landscape. The dynamics of cell type switchings are determined by both landscape gradient and flux. The flux can lead to the deviations of the dominant biological paths for cell type switchings from the naively expected landscape gradient path. As a result, the corresponding dominant paths of cell type switchings are irreversible. We also classified the mechanisms of cell fate development from our landscape theory: super-critical pitchfork bifurcation, sub-critical pitchfork bifurcation, sub-critical pitchfork with two saddle-node bifurcation, and saddle-node bifurcation. Our model showed good agreements with the experiments. It provides a general framework to explore the mechanisms of differentiation, dedifferentiation, reprogramming and transdifferentiation.     

Macrofaunal Responses to Edges Are Independent of Habitat-Heterogeneity in Experimental Landscapes

Despite edges being common features of many natural habitats, there is little general understanding of the ways assemblages respond to them. Every edge between two contrasting habitats has characteristics governed by the composition of adjoining habitats and/or by the nature of any transitions between them. To develop better explanatory theory, we examined the extent to which edges act independently of the composition of the surrounding landscape and to which transitions between different types of habitats affect assemblages. Using experimental landscapes, we measured the responses of assemblages of marine molluscs colonising different experimental landscapes constructed with different compositions (i.e. different types of habitats within the landscape) and different types of transitions between habitats (i.e. sharp vs gradual). Edge effects (i.e. proximity to the edge of the landscape) were independent of the internal composition of experimental landscape; fewer species were found near the edges of landscapes. These reductions may be explained by differences in differential larval settlement between edges and interiors of experimental landscapes. We also found that the sharpness of transitions influenced the magnitude of interactions in the different types of habitats in experimental landscapes, most probably due to the increased number of species in areas of transition between two habitats. Our experiments allowed the effects of composition and transitions between habitats to be disentangled from those of proximity to edges of landscapes. Understanding and making predictions about the responses by species to edges depends on understanding not only the nature of transitions across boundaries, but also the landscape in which the edges are embedded.     

Ubiquitin-dependent control of development in Saccharomyces cerevisiae

In response to external environmental stimuli and intrinsic developmental cues, yeast cells reset their gene expression programs and change phenotype. These switches in cellular state require the dismantling of an initial regulatory program, in addition to the induction of different sets of genes to specify the new cell phenotype. Recent experiments examining the role of protein degradation in these transitions have highlighted the importance of inactivating previously utilized regulators and have led to advances in our understanding of how cells change from one phenotypic state to another.     

Critical threshold effects of benthiscape structure on stream herbivore movement

In landscape ecology, substantial theoretical progress has been made in understanding how critical threshold levels of habitat loss may result in sudden changes in landscape connectivity to animal movement. Empirical evidence for such thresholds in real systems, however, remains scarce. Streambed landscapes provide a strong testing ground for studying critical thresholds because organisms are faced with substantial environmental heterogeneity while attempting to overcome the physical force of water. In this study, I report on the results from a series of experiments investigating the influence of habitat abundance and current velocity on the movement dynamics of two stream herbivores (caddisfly larva Agapetus boulderensis and snail Physa sp.) that differ substantially in how they perceive landscape structure. Specifically, I ask whether critical thresholds to herbivore movement exist in streambed landscapes. By exploiting the pattern recognition capabilities of artificial neural networks, I found that the rate, sinuosity and directionality of movement by Agapetus and Physa varied nonlinearly according to the abundance of habitat patches, current velocity and habitat-current interaction. Both the study organisms exhibited threshold responses to habitat abundance, yet the location and slope of these thresholds differed between species and with respect to different current velocities. These results suggest that a critical threshold in functional connectivity (i.e. the connection of habitat patches by dispersal) is not an inherent property of the landscape, but in fact emerges from the interplay of species' interactions with landscape structure. Moreover, current velocity interacted with habitat abundance to elicit strong upstream-oriented movement for both the species. This suggests that dispersing individuals may be polarized in the upstream direction and therefore functional connectivity is not equal in all directions. Such results highlight the need for future research addressing the sources of variability of critical threshold effects in ecological phenomena.     

Riverine landscapes: an introduction

1. This paper is an introduction to a special issue of Freshwater Biology containing selected papers from the First International Symposium on Riverine Landscapes held in March 2001 in Switzerland.
2. The primary goal of the symposium was to synthesise present understanding of riverine landscapes from the perspectives of different disciplines. A landscape approach was used to address interactions between patterns and processes, in the context of spatial heterogeneity, across scales in physical and biological systems.
3. The three main themes were: (i) hydrogeomorphic processes, (ii) biological dynamics and (iii) human influences in riverine landscapes.