Dynamical Systems Approach to Endothelial Heterogeneity

Abstract

Objective

Here we reexamine our current understanding of the molecular basis of endothelial heterogeneity. We introduce multistability as a new explanatory framework in vascular biology.

Methods

We draw on the field of non-linear dynamics to propose a dynamical systems framework for modeling multistability and its derivative properties, including robustness, memory, and plasticity.

Conclusions

Our perspective allows for both a conceptual and quantitative description of system-level features of endothelial regulation.

INTRODUCTION

Endothelial cells form the innermost lining of all blood and lymphatic vessels. The blood vasculature and its endothelial lining extend to all reaches of the vertebrate body. Far from being an inert layer of nucleated cellophane, the endothelium partakes in a wide array of physiological functions, including control of vasomotor tone, maintenance of blood fluidity, regulated transfer of water, nutrients and leukocytes across the vascular wall, innate and acquired immunity, and angiogenesis. It is also recognized that the endothelium plays an important role in a multitude of diseases, either as a primary determinant of pathophysiology or as a victim of collateral damage (reviewed in ¹). However, there exists a wide bench-to-bedside gap in endothelial biomedicine. Although searches of PubMed using the key words endothelial cells or endothelium reveal >100,000 publications, clinicians have little awareness of the endothelium in health and disease beyond its involvement in atherosclerosis.² One consideration in explaining the bench-to-bedside gap in the field relates to the elusiveness of this entity. Far from being a giant monopoly or collective of identical cells, the endothelium comprises an enormous consortium of different enterprises, each with its own identity. Indeed, endothelial cell phenotypes display remarkable heterogeneity in structure and function, in space and time, and in health and disease (reviewed in ^{3, 4}). On a molecular level, systematic mapping of endothelial cell phenotypes has revealed vascular bed-type specific expression profiles that amount to unique “vascular zip codes”.^5-7

Structural and functional heterogeneity of the endothelium reflects its role in meeting the diverse demands of underlying tissues as well as the need to adapt to and survive in distinct environments across the body. At a single point in time, endothelial phenotypes vary between different organs, between blood vessel types and even between neighboring endothelial cells (Fig. 1).^8-11 At any one location, endothelial phenotypes may change over time. As an important corollary, the endothelium is heterogeneous in its response to pathophysiological stimuli, thus contributing to the focal nature of vasculopathic disease states.

Figure 1. Examples of endothelial heterogeneity.

A) Lectin-perfused whole-mount preparation of trachea from an ephrinB2 LacZ knockin mouse showing ephrin-B2/LacZ expression in arteries (A), but not veins (V). There is some extension of expression into proximal capillaries (C). Reprinted from Developmental Biology, 230, Gale et al., Ephrin-B2 selectively marks arterial vessels and neovascularization sites in the adult, with expression in both endothelial and smooth-muscle cells, 151-160, Copyright (2001), with permission from Elsevier. B) Immunoperoxidase detection of mouse von Willebrand factor (vWF) in the endothelial lining of a cardiac vein (asterisk). There is no detectable expression in the surrounding myocardial capillaries. From Lei Yuan and William C. Aird, unpublished data (2012). C) Longitudinal hemisection of a large cortical vein doubly labeled for endothelial barrier antigen (EBA) (magenta) and occludin (yellow) showing highly heterogeneous expression of EBA (white arrows). Reprinted by permission from Macmillan Publishers Ltd: Journal of Cerebral Blood Flow & Metabolism (Saubamea et al., 32:81-92), copyright (2012). D) En face preparation of an aorta from a Robo4 LacZ knockin mouse showing Robo4/LacZ expression at the ostia of four intercostal arteries (asterisk). A similar, but non-identical figure was shown in Okada et al.¹¹ E) Human umbilical vein endothelial cells (HUVECs) stained for VE-cadherin (red), vWF (green) and nuclei (blue) reveals highly heterogeneous expression of vWF (white arrows). From Lei Yuan, Erzsébet Ravasz Regan and William C. Aird, unpublished data (2012).

Endothelial cells represent an attractive, albeit largely untapped, therapeutic target. However, from a treatment standpoint, endothelial cell heterogeneity represents a two-edge sword. On one hand, drugs may exert unwanted effects on endothelium from non-diseased locations. For example, anti-vascular endothelial growth factor (VEGF) treatment in patients with cancer has a beneficial effect at the level of tumor blood vessels, but produces side effects through its action on normal blood vessels.¹² On the other hand, therapy may be targeted to specific vascular beds that display a diseased phenotype. An evaluation of the cost-benefits of therapy and the identification of novel site-specific targets will depend on our understanding of the scope of endothelial heterogeneity and its underlying proximate mechanisms.

The goal of this review is to underscore the limitations associated with our current approaches to understanding endothelial heterogeneity and to propose a new explanatory framework that not only provides a conceptual advance, but also lends itself to mathematical modeling, quantitation and prediction. We have organized the review into six parts. In the first, we consider ways we go about thinking about endothelial cell heterogeneity. We review old concepts of the endothelial cell as an input-output device and of nature versus nurture in determining phenotypic heterogeneity. We then introduce the new paradigm of multistability as a core property of the endothelium. In the second part, we emphasize certain characteristics of multistable systems, including robustness, memory and plasticity. We show how these various properties may be represented as a landscape of states, and we reframe endothelial cell heterogeneity in terms of landscape topography. In the third section, we provide an overview of the mathematical underpinnings of multistability. To that end, we construct a layered hierarchy of signaling models from linear pathways to pathways with cross-talk and feedback. We show how mathematical methods of modeling in dynamical systems theory may be used to represent multistability and quantify landscape topography. In the fourth part, we return to the familiar nature-nurture dichotomy as a conceptual model and we point out how the principle of multistability can be incorporated into that model to improve our understanding of endothelial cell heterogeneity. In the fifth part, we discuss how modeling may be helpful to the vascular biologist. Finally, we discuss the challenges that lie ahead in modeling the endothelial regulatory system in its entirety. We propose future directions to narrow this gap, with an emphasis on a novel hierarchical modular-based strategy for modeling the dynamical regulatory network of the endothelium at multiple scales. Our aim is to bridge a gap between physicists and biologists and to encourage interdisciplinary research in endothelial cell biology.

UNDERSTANDING ENDOTHELIAL HETEROGENEITY

Current explanatory frameworks

Owing to the time-distant constraints of diffusion, microvessels and their endothelial lining are widely distributed throughout the body. The microenvironment differs broadly between tissue types. Thus, endothelial cells are exposed to a myriad of extracellular environments. In so far as the endothelial cell senses and responds to its external environment, differences in signal input across the vascular tree are enough to explain phenotypic heterogeneity. From this perspective, the endothelial cell may be viewed as a miniature input-output device (Fig. 2A) (reviewed in ¹³). In its simplest iteration, this metaphor represents the endothelium as a blank slate, marching blindly to the tune of its extracellular environment. Stated another way, endothelial cells display plasticity (the term is used loosely in this context, but will be more rigorously defined as a property of multistability). This property of the endothelium underscores the importance of studying endothelial cells in the context of their native environment. From a treatment perspective, plasticity points to the environment, rather than the cell itself, as a therapeutic target.

Figure 2. Conceptual frameworks for understanding endothelial heterogeneity.

A) Endothelial cell as an input/output device. On the input side, cell surface receptors (orange nodes) initiate the transmission of signals from the extracellular environment (thick orange arrows). These signals result in changes in protein activity and/or changes in gene expression (red nodes), which alters the phenotype and function of the endothelial cell changes (the output side; thick red arrow). B) Thought experiment demonstrating nature and nurture. Phenotypically distinct endothelial cells are removed from different sites of the vascular tree and propagated in vitro under identical culture conditions. Different cellular phenotypes are represented by different color shades. If all site-specific properties are mitotically heritable, then the cellular phenotype would be impervious to subsequent changes in the extracellular environment and remain constant over multiple passages (green lines). On the other hand, if site-specific properties are all non-heritable and reversibly coupled to the immediate extracellular milieu, then the cellular phenotype of the two cells would ultimately reach identity (orange lines). Top: Arterial and venous endothelial cells lose some but not all their in vivo characteristics, as quantified by differences in global gene expression profiles before and after isolation. Middle: Microvascular endothelial cells (MVEC) from the lung and skin are more plastic and lose virtually all of their in vivo differences when cultured.¹⁷ Bottom: In contrast, significant differences remain between MVEC from myocardial and intestinal tissues under in vitro conditions.¹⁷ The retained difference in gene expression is larger between these two groups of MVEC than between cultured arterial and venous endothelial cells, indicating that not all differences between MVEC are environmentally governed. Images of the artery (copyright Steve Gschmeissner/Photo Researcher), vein (copyright Steve Gschmeissner/Photo Researchers), lung (copyright Motta & Macchiarelli/Photo Researchers), myocardium (copyright R. Bick, B. Poindexter/Photo Researchers) and intestinal endothelium (copyright Dr. Keith Wheeler/Photo Researchers) are reprinted with permission from Photo Researchers. The image of skin endothelium is reprinted from Abraham et al,¹⁴ with permission from Wolters Kluwer Health. Copyright 2008, American Heart Association. C) Three-dimensional representation of the landscape of cellular states. All possible states are represented as positions on the x-y plane, while the z-axis accounts for their stability. Valley bottoms represent robust phenotypic states (gold marble). The sides of each valley, with a clear downward gradient, indicate unstable states (silver marble). Each valley encompasses a subset of all states, separated by boundaries below the watershed between the valleys (colored regions of the x-y plane). The least energy-demanding paths between valleys pass through saddle points of the landscape, indicated by solid arrowheads. The height of the lowest saddle point between two attractors is a crucial determinant of the barrier between phenotypes (see dotted line marking the saddle point between A and C).

In addition to the cell’s microenvironment, endothelial cells from different sites of the vasculature have different epigenetic footprints (e.g., DNA methylation and histone modification of genes) that render certain site-specific phenotypes stable even when the cell is placed into a new environment. One way to conceptualize the relative roles of the microenvironment and epigenetics in mediating phenotypic heterogeneity is to draw on the time honored distinction in the behavioral biosciences between nature and nurture. Consider the following thought experiment: remove two phenotypically distinct endothelial cells from any two organs (say the liver and the heart) or from an artery and a vein, and culture them under identical conditions for multiple passages (Fig. 2B).¹⁴ On the nurture side of the equation, differences in phenotype that are critically dependent on differences in the tissue environment will drift in vitro and ultimately disappear. If, however, the site-specific differences in phenotype are impervious to the extracellular milieu, they will be mitotically stable and retained in vitro. This is the nature side of the ledger. We often think of the nurture mechanism as one that involves environmentally responsive signaling pathways, with nature reflecting epigenetically fixed site-specific properties. The more the phenotypes of the two cells converge in vitro, the more plastic the endothelial cells are in their native environment. Conversely, the more divergent the cells remain in culture, the more robust their phenotypes are in vivo. According to this model, plasticity and robustness (or phenotypic stability) may be quantified as the ratio of differentially expressed genes or proteins that drift or are retained in vitro.

In fact, previous studies have shown that both nature and nurture are important in determining site-specific properties of the endothelium.^15-17 For example, a study of endothelial cells from human tonsils revealed that approximately 50% of the vascular bed-specific genes were “washed out” when cultured in vitro, implicating a role for both the tissue environment and epigenetics in mediating differential gene expression.¹⁵ This conclusion is further supported by a DNA microarray study in which the transcriptome of endothelial cells harvested from the porcine coronary artery were compared with those from the iliac artery. The data revealed that most, but not all, differences observed in vivo were lost in multiply passaged cells.¹⁶

A major limitation of the nature-nurture concept, as it currently stands, is that for any one property, it portrays plasticity and robustness as being mutually exclusive. For example, if endothelial cells are removed from an artery and grown in standard culture conditions, the expression of some, but not all artery-specific genes will be lost. Although the overall pattern of change embodies both nurture (those site-specific genes that drift) and nature (those site-specific genes that are retained), the behavior of each gene (or phenotype) is designated as either a nature or nurture effect. However, if we look hard enough, we are likely to find a new culture condition (e.g., the addition of naturally occurring extracellular factor(s), chemicals and/or drugs; or the knockdown or overexpression of gene(s)) that reassigns any one “nature gene” to the nurture category. In fact, few, if any, properties of the endothelium are truly immutable, and the line between nature and nurture is heavily blurred.

The limited explanatory power of nature-nurture is further illustrated when considering phenotypic differences between cells that are exposed to identical or very similar microenvironments. For example, expression of endothelial barrier antigen (EBA) in venules and capillaries of the brain follows a mosaic pattern (Fig. 1C).⁹ Do neighboring expressing and non-expressing cells experience significant differences in their microenvironment? Even if such micro-gradients of extracellular cues exist, why is the expression of neighboring cells so “black and white”? In keeping with the nature and nurture dichotomy, the alternative explanation is that the EBA gene is epigenetically modified in ways that differ between in expressing and non-expressing cells. It is difficult to imagine the selective advantage of “locking in” such a pattern. Moreover, even if we were to accept that the EBA gene is differentially modified at the level of DNA methylation or the histone code, we must acknowledge that these differences were triggered at some point in the past by the microenvironment, thus bringing us back full circle to the nurture side of the equation. A second illustrative example is the patchy nature of von Willebrand factor (vWF) gene expression in cultured human primary endothelial cells (Fig. 1). In this case, it is even more difficult to envision biologically relevant spatial differences in the microenvironment of neighboring cultured endothelial cells, let alone the existence of distinct clonal populations of vWF expressing and non-expressing cells.

In summary, the notion that some properties of the endothelial cell are dependent upon persistent environmental signals, while others are epigenetically “fixed” is a heuristically valuable, though decidedly flawed, conceptual framework for approaching mechanisms of endothelial cell heterogeneity. We believe that the right question to ask is not whether a given property of an endothelial is malleable (nature) or fixed (nurture), but rather what is the nature-and-nurture potential of that property?

Multistability of endothelial cells: a novel explanatory framework

The ability of a single endothelial cell to assume two or more distinct phenotypes under identical extracellular conditions is termed multistability. Discrete phenotypes may be thought of as minima or valleys in a landscape and the internal state of a single endothelial cell may be represented as a marble on the landscape surface (Fig. 2C; Online Fig. I). Stable phenotypes lie at the lowest points of each valley, while high points on the landscape represent unstable states poised to change in time, as dictated by the cell’s internal dynamics. Barriers between phenotypes are visualized as ridges between the valleys. Beyond providing a useful metaphor for endothelial cell heterogeneity, the landscape surface lends itself to mathematical modeling. Quantitative definition of this landscape is derived from the full regulatory system of the cell. The regulatory system, which for a given genome is identical in all cell types of the body, comprises the full repertoire of genes and proteins together with their potential interactions. In dynamical systems theory, the collection of all possible states of a system is referred to as the phase space.^18-20 The phase space of a cell is represented by the collection of all points on the landscape surface. The topography of the landscape (e.g., the valleys and ridges) is rigidly defined by the combined effect of all interactions (links and synergies/antagonisms) between the cell’s regulatory molecules.²¹ To understand global properties of the endothelium, we should consider all possible states of the endothelial cell, including the unlikeliest of scenarios (e.g., that it differentiates into a neuron or a liver cell). In other words, we must assume that every single state is (at least in theory) accessible to the endothelial cell.

The rest of the review will focus on multistability as an organizing principle for approaching endothelial cell heterogeneity. Our goal is to guide the reader from employing the landscape surface as a conceptual model to recognizing its potential value as a quantitative tool for modeling and predicting the behavior of endothelial cells. The principles of multistability and landscape surfaces are of course applicable to any cell type in the body. Indeed, landscape topography is defined by the genome, not by the cell type (Online Supplement V.A).²² What makes the concept particularly attractive for understanding endothelial biology is that endothelial cells cut a far wider swath of landscape than most other cell types. Whereas liver and skin cells probably spend their lives clustered in a few neighboring valleys, endothelial cells tend to wander the hills and valleys of the landscape. Multistability captures the broad array of spatial and temporal states available to the endothelial cell.

PROPERTIES OF MULTISTABILITY AND THE LANDSCAPE OF STATES

Before introducing the mathematical basis of multistability, we wish to emphasize key derivative properties of multistable cells that, while intuitive, nonetheless set the stage for more in-depth modeling. These properties include homeostasis, robustness, memory and plasticity. It is important to recognize that in dynamical systems theory, these terms are rigorously defined and quantified in terms of the landscape of states (Online Fig. I). Thus, a consideration of multistability and its core principles takes us one step closer from metaphorical realm to reality.

Robustness and homeostasis

Multistability requires that the cell be robustly maintained within each state. Robustness in this context is defined by the capacity of a cell to remain in a single stable state when faced with random perturbations. These perturbations (termed biological noise) affect all cells, and have multiple sources (reviewed in ^23-26). For example, the normal kinetics of molecular processes has a significant degree of randomness, causing natural fluctuations in the rates of protein activation, transcription, translation and degradation. Concentration fluctuations (and hence noise) may also result from slightly asymmetric partitioning during cell divisions.²⁷ A robust state will typically maintain itself in a range of non-identical environments (“nature”). The term cellular homeostasis is used to refer to the robustness of one stable state of the cell subject to constant subtle intracellular noise and small variations in the extracellular environment.^{28, 29} For example, consider arterial and venous endothelial cells. These are bistable states of the endothelium since a difference between them is retained in many environments (Fig. 3A). In the presence of noise, arterial-cell “marbles” or venous-cell “marbles” wander about the slope of their respective valleys, without jumping to the other valley. The constant noise-driven movement of the cell’s state on the slopes of the same valley manifests as minor fluctuations in phenotype (microheterogeneity).²⁶ Such changes occur at the level of a single cell over time and at the level of a cell population over time and in space. For example, a FACS analysis of a cell surface protein that is expressed in venous cells but not in arterial cells (e.g., EphB4) on a ‘pure’ population of venous cells would typically yield a simple-peaked Bell-curve with a well-defined average. This type of distribution is a signature of a natural spread around a homeostatically controlled expression value.

Figure 3. Dynamical systems perspective of endothelial cell heterogeneity in a bistable system.

For purposes of illustration, valleys represent arterial and venous endothelial cells. A) Microheterogeneity is shown as noise-driven fluctuations around one equilibrium state (shown as minor variants of the venous state). Top: The landscape is projected onto three dimensions, one of which is a marker for the global state of the system (in this case, the venous marker EphB4). Bottom: The expression histogram of EphB4 comprises a single peak with a natural spread around its average. B) Macroheterogeneity describes a population of cells occupying two different equilibrium states (shown as arterial and venous states). Top: The landscape is projected onto three dimensions, one of which is a marker for the global state of the system (in this case, EphB4). Bottom: The expression histogram of EphB4 is bimodal, with high EphB4 representing a venous phenotype, and low EphB4 representing an arterial phenotype.

Cellular memory

Homeostasis coupled with multistability reflects the ability of cells to “remember” their input history (e.g., arterial differentiation). This memory determines which steady state they manifest at any point in time, and results in stable phenotypic heterogeneity. A mixed population of arterial and venous endothelial cells in culture exemplifies this. Their internal states are mutually exclusive: a cell can be an arterial cell or a venous cell, but not both (Fig. 3B). Rather than reflecting transient, non-functional drift within a single valley, each state is associated with differences in gene expression and protein activity that separate the cell population into different valleys (for example, Notch 4 and Hey 2 in arterial endothelial cells, and EphB4 and Smoothened in venous endothelial cells ¹⁷), each of which confers unique structural and/or functional properties. Within a population of cells, these valleys are manifested as macroheterogeneity.²⁶ Single-cell measurements on a mixed population of arterial and venous cells would likely yield double-peaked expression histograms for each of these genes.

Plasticity

The existence of more than one stable state endows the system not only with memory, but also with plasticity. In multistable systems, there will always be signals (apparent or not) that can switch the cell from one steady state to another. In some cases, the new state is retained when the signals are withdrawn (“nature”). In other cases, signal withdrawal causes the state to switch back (“nurture”). Plasticity with respect to these signals does not require the absence of robustness (i.e., barriers between states). On the contrary, it typically relies on the existence of multiple, mutually exclusive states. For example, in the angiogenic sprout, stalk and tip cells represent robust biological phenotypes that reliably appear under appropriate environmental conditions.³⁰ However, in response to specific signals (e.g., merging of two tip cells), transitions do occur between the two states. Using the landscape representation, such specific stimuli trigger changes in cell state (and thus the position of the “marble”) that place the cell into a different valley. The accompanying phenotype changes are abrupt and switch-like. Genes that mediate such specific, phenotype-changing perturbations are powerful regulators of cellular function. Cell surface receptors often orchestrate such switches, accompanied by large changes in global expression pattern and, consequently, in cellular phenotype. For example, VEGF receptors in endothelial cells orchestrate changes in migration, proliferation, cell-cell adhesion, vasomotor tone, and hemostatic balance, and govern the selection of tip cells vs. stalk cells, along with the significant differences between their phenotype.

Landscape topography

The phase space of all cell states is naturally partitioned into distinct valley basins. At any point in time, a single cell occupies one position in that space. At equilibrium, this will correspond to the bottom of a valley. Phenotypically distinct cells occupy different valleys. That is true whether the cells are from different lineages (e.g., an endothelial cell and a smooth muscle cell) or from the same lineage (e.g., an arterial endothelial cell versus a venous endothelial cell, or a stalk cell versus a tip cell). What sets apart the degree of phenotypic heterogeneity is the depth of the valleys with respect to the barriers between them. Every stable phenotype of a multistable cell is simultaneously robust to certain environmental changes and plastic with respect to a select set of influences. This framework requires us to ask not whether a property is plastic or robust, but how plastic and robust it is to particular environmental changes.

Landscape of states and endothelial cell heterogeneity

The landscape of cell states helps us to reframe questions about endothelial cell heterogeneity. For example, in the case of arterial and venous endothelial cells, what is the nature of the bistable switch that maintains them in one state or another? What extracellular cues and signals brought about the specification of an arterial or venous fate in the first place? Can we use that information to flip mature venous and arterial endothelial cells to the opposite state? Understanding this bistable circuit may point to functional differences between endothelial cells of a vein graft and the arterial endothelial cells nearby, and may prove relevant for coronary bypass surgery. At the other end of the spectrum, application of the landscape model to mosaic-type heterogeneity in single vessels raises the question of how high the barrier is between the states. Is the vessel frozen into a mosaic pattern, or does it ‘blink’ ON and OFF during the lifetime of a cell? Is the change driven by biologically relevant signals or by extracellular and/or intracellular noise? Perhaps the most intriguing question is whether the mosaic pattern itself is functional. In other words, can there be a biological function at the level of the vessel that can be optimally performed by an endothelium expressing an ON/OFF mosaic, but not by a vessel with the same total protein, evenly distributed?

FROM PATHWAYS TO COMPLEX DYNAMICAL REGULATORY SYSTEMS

Our next goal is to move beyond the language of metaphors and establish a mathematical theory that models multistability as a mechanism of endothelial cell heterogeneity. The majority of studies aimed towards delineating intracellular signaling pathways employ a highly reductionist approach in which causal links are framed in simplistic, linear terms. The aim here is to expose the limiting assumptions hidden in linear representations of regulation, and gradually introduce methods that can provide a more realistic picture of the endothelial regulatory system. We will illustrate how increasingly complex layers of regulation may be modeled, including crosstalk and feedback. We will then apply these principles to understanding the endothelial regulatory system in landscape terms.

For purposes of clarity, we have chosen to focus on only a small number of exemplars in the text. The reader is referred to the Online Supplement for additional examples, including detailed linear, cross-talk and feedback features of the caspase pathway for which there is sufficient published data. Definitions of the major concepts discussed are shown in Supplemental Table 1.

Linear pathways and signal transduction

The cellular regulatory system functions to detect environmental signals and to transduce that information into specific cellular responses. In its simplest version, a regulatory system comprises a linear, unidirectional chain of molecular changes from an extracellular ligand to phenotype-determining biomolecules. The conceptual appeal of linear pathways that connect concrete causes to concrete effects lies in the clear, unambiguous narrative they provide. For example, consider the endothelial-restricted transcription factor, GATA-2, which has been shown to mediate inflammation in endothelial cells.^{31, 32} In a simple linear interaction, PKC-Ζ activates GATA-2 (Figs. 4A-C). In this scheme, PKC-Ζ represents the input and GATA-2 the output. The interaction between the two elements may be depicted in one of three ways. First, an arrow may be used to represent a causal link between input and output (Fig. 4A). Several such interactions may be linked together to from a signal transduction cascade. This simple conceptual representation may be modeled by making certain assumptions about the nature of the interaction (e.g., is it cooperative?), and by choosing the level of detail expected from the model (e.g., continuous versus Boolean approximations). In continuous terms, the molecular dynamics of a biochemical interaction may be captured by mathematical models describing enzyme kinetics and cooperative or antagonistic ligand binding (e.g., the Michaelis–Menten equation ^{33, 34} or Hill equation ³⁵). When the concentration of active GATA-2 is plotted as a function of PKC-Ζ, the result is a nonlinear, sigmoid-shaped curve (Fig. 4B, left). The curve represents the dose-response of GATA-2 under equilibrium conditions. Equilibrium is achieved whenever active GATA-2 levels stabilize in the wake of a transient increase or decrease, triggered by a change in PKC-Ζ activity. Thus, if the output (GATA-2) at time 0 is above or below the equilibrium value for a given PKC-Ζ, the system will follow an energy gradient towards that equilibrium (Fig. 4B, right). The square area of all possible PKC-Ζ and GATA-2 expression levels represents the phase space of this two-dimensional system.

Figure 4. Linear and crosstalking GATA-2 signaling pathways.

A) Signal transduction cascade showing GATA-2 activation by PKC-Ζ. Major assumptions of the simple model are shown on the right. In this scheme, active GATA-2 levels are dictated by PKC-Ζ alone. B) Continuous model of the PKC-Ζ → GATA-2 interaction using Hill reaction kinetics. Left, equilibrium concentration of active GATA-2 as a function of PKC-Ζ. Response curves for GATA-2 are colored according to increasing levels of PKC-Ζ cooperativity (h, Hill coefficients). The large green dot with black border represents one equilibrium state. Right, direction (arrows) and velocity (V, colors) of variable changes when the system is placed into different out-of-equilibrium states. Velocity color scale: green, close to equilibrium and slow to change; purple, far from equilibrium and fast to change. Shown are two representative time courses from initial active GATA-2 concentrations (at a fixed PKC-Ζ level) above and below equilibrium (green dots and black arrows). All points lead to equilibrium (black-bordered green dot). C) Boolean model of the PKC-Ζ → GATA-2 interaction. A Boolean model requires discretization of GATA-2 and PKC-Ζ concentrations, such that they are either ON (high, represented as 1) or OFF (low, represented as 0). The cutoff between concentration values considered ON or OFF is dictated by reaction kinetics. The Boolean gate describes the fact that GATA-2 is ON when PKC-Ζ is ON, and GATA-2 is OFF when PKC-Ζ is OFF (GATA-2 = PKC-Ζ). Highly cooperative interactions have steep, step-like responses to their inputs, and are well approximated by Boolean gates. The Boolean model has 4 possible states (depicted as nodes), of which two ({0,0} and {1,1}) represent equilibrium states (shown in red). Black arrows show all state changes dictated by the Boolean gate. D) Signal transduction cascade showing GATA-2 regulation by PKC-Ζ and TFII-I. Major assumptions of the simple model are shown on the right. Active PKC-Ζ activates GATA-2, while TFII-I inhibits the transcriptional activity of active GATA-2 by competitive binding to its DNA target sites. In this scheme, active GATA-2 levels are dictated exclusively by PKC-Ζ and TFII-I levels; both inputs are independent of each other and remain constant. E) Continuous model of the cooperative regulation of GATA-2 by PKC-Ζ and TFII-I using Hill reaction kinetics. Since TFII-I inhibits the active GATA-2 transcription factor, its absence is required for full GATA-2-mediated activation of transcription. This antagonism is formally described as the product of the two Hill functions. Left, equilibrium concentration of GATA-2 as a function of PKC-Ζ and TFII-I are shown as a surface. Each TFII-I - PKC-Ζ concentration pair (each point on the horizontal plane) corresponds to one equilibrium GATA-2 level (vertical axis), forming a hill-shaped surface. Color scale: Red, high GATA-2 levels; blue, low GATA-2 levels. Right, direction (arrowheads) and velocity (V, colors) of variable changes when the system is placed into different out-of-equilibrium states. Velocity color scale: green, closer to equilibrium and slower to change; purple, further from equilibrium and faster to change. F) Boolean model of the cooperative regulation of GATA-2 by PKC-Ζ and TFII-I. The Boolean gate controlling GATA-2 activity is a Negated AND gate (NAND), where GATA-2 is ON only if PKC-Ζ is ON and TFII-I is OFF. The model has 8 possible states, of which four (000, 100, 110 and 011) represent equilibrium states (shown in red). Black arrows depict all state changes dictated by the regulatory rules.

A coarser approximation for characterizing the interaction between PKC-Ζ and GATA-2 is to employ a non-continuous binary ON/OFF function, where ON = 1, OFF = 0 (Fig. 4C). This so-called Boolean model is the simplest mathematical representation of a cooperative interaction.^36-38 In our example, GATA-2 is OFF when PKC-Ζ is OFF (represented as {0,0}); GATA-2 is ON when PKC-Ζ is ON (represented as {1,1}). When displayed graphically, the result is a step-wise curve, whereby the stable states ({0,0} and {1,1}) represent the equilibrium. In Boolean terms, the phase space of the system consists of four states (Fig. 4C). A major assumption common to both continuous and Boolean models of a unidirectional cascade is that its output is dictated solely by the input (in this example, the level of active GATA-2 is determined only by levels of PKC-Ζ).

In small systems such as this two-variable PKC-Ζ-GATA-2 network, continuous modeling can provide a detailed quantitative description of the biochemical interactions. However, detailed kinetic information is usually lacking for larger systems (e.g., those with 20-100 regulatory components). Thus, Boolean or discrete-state modeling may be the only viable option. Boolean models track the sequence, but not the precise timing or concentration dependence of regulatory events. They can nevertheless discern the qualitative behaviors (i.e., phenotypes) of large regulatory systems. Previous studies have demonstrated the advantages of Boolean over continuous modeling (reviewed in ^39-42), and have validated the use of Boolean logic in modeling signal transduction pathways.^43-61

Unidirectional linear pathways admit two sources of phenotypic heterogeneity. First, as stand-alone causal chains, they connect every input from the extracellular environment to a distinct output (input_n → output_n). Thus, if one or more inputs differ between endothelial cells, heterogeneity will, by definition, arise (so long as the cell type-specific outputs are manifest as distinguishable phenotypes). Importantly, linear systems lack long-term memory. For example, if a signal A activates B, then removal of A will result in deactivation of B. The system’s response is transient, as it is reflected in the half-life of the elements, which in the case of posttranslational modification, protein and mRNA is typically on the order of minutes to hours. Consequently, the endothelial cell is at the complete mercy of its environment, coupling spatial and temporal changes in the extracellular milieu to unfiltered outputs. A second source of phenotypic heterogeneity is biological noise. A feature of linear pathways is that they lack the capacity to dampen such noise. On the contrary, theoretical and experimental work shows that multi-step linear cascades typically amplify noise by compounding fluctuations along the interactions.^{62, 63}

If we return to our metaphors, we will find that the input-output device and the nurture side of the nature-nurture equation are theoretically explained by linear cascades. However, if all pathways were linear, the behavior of endothelial cells would be completely plastic; given enough time, all heterogeneity imposed by the microenvironment would be lost when cells are placed in identical environments (e.g., arterial and venous endothelial cells would acquire an identical phenotype in culture). Indeed, a limitation of linear signaling is that it precludes the generation of multiple mitotically stable phenotypes (which defines “nature”). Importantly, as we strive for a more rigorous model of the cell’s regulatory system, we find that linear models do not capture two of the most basic properties of biological regulation and endothelial behavior, namely multistability and robustness. Stated another way, linear cascades lack memory and homeostatic control over their outputs. For that, we must turn to crosstalk and feedback.

Crosstalk and signal processing: introducing robustness

In reality, most signaling pathways are not strictly linear, but are rife with crosstalk. Crosstalk refers to the convergence of upstream signals from different sources. To return to our GATA-2 example, consider now that while PKC-Ζ activates GATA-2, TFII-I (GTF2I) inhibits its transcriptional activity (Fig. 4D).⁶⁴ In this case, both PKC-Ζ and TFII-I converge on GATA-2. Since there are three variables in the system, the inter-dependence of their concentrations may be depicted in three dimensions (Fig. 1E, left). The horizontal plane comprises the two inputs (PKC-Ζ and TFII-I). Any point on this plane (i.e., a given concentration of PKC-Ζ and TFII-I) defines the output (GATA-2) on the vertical axis. In continuous terms, the equilibrium state is shaped like a hill with the peak corresponding to high PKC-Ζ and low TFII-I (Fig. 4E). Although the hill-shaped surface that is drawn in color represents the states in equilibrium, the phase space extends far beyond the hill. It occupies a three-dimensional space that is confined only by the natural limits of each of the three variables (e.g., their maximum concentration). Note that by adding just one additional element to the signaling cascade, the kinetic equations become more complicated. Moreover, each subsequent variable creates a new dimension, which hinders graphical representation. One way of simplifying the model is to employ Boolean logic to describe the combined effect of inputs. As introduced in the previous section, Boolean logic approximates both input and output variables as either ON or OFF. Interactions in the system are defined by Boolean gates. In our example, GATA2 is ON if TFII-I is OFF and PKC-Ζ is ON. This may be written: GATA2 = (NOT PKC-Ζ) AND PKC-Ζ. According to the rules of Boolean logic, only 4 of the 8 possible states are stable ({0,1,1}, {0,0,0}, {1,1,0} and {1,0,0}; Fig. 4E). If the input and output at time 0 do not conform to one of these stable states, the system will move towards equilibrium. In Boolean terms, the phase space of the system consists of eight states.

The behavior of regulatory networks that do not contain any type of feedback (i.e., those with linear pathways and cross-talk) is dictated solely by inputs received from the outside. Once the state of the inputs is set, their influence propagates downstream until the whole network settles into a steady state pattern of gene expression and protein activity. To illustrate this, we assembled a cross-talking VEGF and tumor necrosis factor (TNF) signaling network (Fig. 5A) while excluding known feedback.^{65, 66} The system comprises 37 variables (which are also termed elements or network nodes), each of which may be ON or OFF. Thus in Boolean terms, there are 2³⁷, or ~10¹¹ possible states of the system. However, in crosstalking systems such as this, the number of input combinations sets the upper limit of the number of stable states (or phenotypic outputs). There are 4 (2²) possible inputs depending on the ON/OFF state of VEGF and TNF signals (they may be represented as {0,0}, {1,0}, {0,1} and {1,1}). Thus, of the ~10¹¹ possible states, there can be no more than 4 distinct, stable expression profiles of the entire system, no matter how complicated the layered hierarchy and no matter what the starting concentration of the 37 variables. In fact, in this particular example, the network settles into one of only two possible output states. These output states are reflected by the combined ON/OFF pattern of the end-nodes: p27^kip1, vascular cell adhesion molecule (VCAM)-1, Down syndrome critical region-1, E-selectin (SELE), intercellular adhesion molecule (ICAM)-1, Bcl-X_L, and Caspase 3 ({0,1,1,1,1,1,0} if VEGF or TNF are ON, or {1,0,0,0,0,0,1} if both are OFF). Thus, depending on the nature of the inputs, the system inevitably settles into one of these two stable states.

Figure 5. Agonist-mediated signaling pathways with crosstalk.

A) Crosstalk between a subset of VEGF- and TNF-induced signaling interactions. Arrows with orange shadows highlight the convergence of multiple inputs on single nodes. Node color denotes different types of macromolecules: orange, extracellular signaling molecules; dark blue, signal receptors; blue, signaling proteins or metabolites; and red, transcription factors. Genes associated with inflammation and apoptosis are outlined in gray boxes. Arrow colors denote interaction types: purple, ligand-receptor binding; green, post-translational modification; cyan, cytoplasmic-nuclear localization; black, degradation; and red, transcriptional control. Indirect links are shown as dashed lines. B) Crosstalk between VEGF, thrombin and TNF signaling in inflammation. The VEGF- and TNF-induced pathways are a subset of the signaling network shown in (A). Outputs are represented by three inflammatory genes: VCAM-1, E-selectin (SELE) and ICAM-1. All possible ON (red)/OFF (black) combinations of the three extracellular inputs lead to one of only two outputs: No inflammation (000) and Inflammation (111). Color code for arrows and nodes is the same as in (A). Indirect links are shown as dashed lines. C) Crosstalk between the pathways that control VCAM-1 expression. In this scheme, VCAM-1 activation occurs only in the presence of simultaneous signal from three distinct pathways: AKT1, Ca²⁺ and NF-κB signaling. The ligands shown in (B) activate all three signal intermediates. Other extracellular stimuli, however, may activate a subset of the three without triggering a corresponding increase in VCAM-1. Color code for arrows and nodes is the same as in (A).

Pathways with crosstalk provide the cell with the capacity not only to transduce but also to process information. Instead of performing simple one-to-one mapping of each input to a distinct output (a property of linear pathways), signal processing in crosstalking pathways enables the regulatory system to map groups of inputs to a single output and thus distill relevant aspects of the environment. For example, consider that VEGF, TNF and thrombin can each activate VCAM-1, SELE and ICAM-1 (Fig. 5B). In Boolean logic, the input of VEGF, TNF and thrombin are expressed in binary terms (ON = 1 and OFF = 0), and their interactions are defined by an “OR” gate (i.e., VCAM-1 = VEGF OR TNF OR Thrombin). Of all 8 (2³) possible input patterns, 7 of them induce VCAM-1, SELE and ICAM-1 (4 are shown in Fig. 5B), while only one of them {0,0,0} does not. In this example, crosstalk allows the cell to filter information and thus discriminate between an all-OFF pattern and all other permutations. In this way, the cell functions as a sensor of inflammation. (Recall that in linear pathways each of these inputs [VEGF, TNF and thrombin] would, by definition, yield a distinct non-overlapping inflammatory output.)

Another simple logic operation is at work in the transcriptional control of VCAM-1 in an endothelial cell. Previous studies have shown that in response to an inflammatory stimulus, GATA-2, NFAT1 and NF-κB are all required to activate VCAM-1 expression.^{31, 67} Thus, VCAM-1 transcription is governed by an “AND” gate (Fig. 5C). As a result, VCAM-1 is always OFF unless all three inputs are ON ({1,1,1}). Here again, the pathway maps one set of input patterns (7 of all 2³ possible inputs) to one output, and another set of input patterns (1 of all 2³ possible inputs) to another output. In this case the system discriminates between an all-ON pattern and all other permutations. It can be said to behave as a gatekeeper or checkpoint where a critical threshold of signals must converge before it moves forward.

Crosstalking pathways may manifest other properties, including canalyzation ^{68, 69} and signal filtering through feedforward loops,^{70, 71} each of which endows the cell with additional layers of signal processing. These are discussed in detail in the Online Supplement III.⁷²

A consideration of crosstalk further advances our understanding of endothelial cell heterogeneity. For one, a regulatory system of this type is no longer completely beholden to the environment. Plasticity is now complemented by robustness. The endothelial cell can use logic operations to respond to biologically relevant combinations of signal inputs, filter out signals that are not relevant in a given context, and buffer (to some extent) the effect of biological noise. These properties explain why environmentally responsive vascular bed-specific properties (i.e., those on the nurture side) are nonetheless robust. For example, liver sinusoidal cells from two individuals display a common phenotype, despite differences in the genetic makeup and lifestyle of the host. Moreover, a sinusoidal endothelial cell retains its identity after being exposed to a bolus of orally ingested nutrients or drugs. That is, classes of similar environments (between or within individuals) engender a single phenotype with noise-generated fluctuations around it.

The most important limitation of crosstalking regulatory networks is that, no matter how sophisticated their wiring and computing power may be, they do not have any lasting memory of their past states. Their equilibrium behavior is dictated solely by inputs received from the outside. Thus, they cannot generate multistability, or explain the existence of multiple mitotically stable endothelial phenotypes under identical conditions (i.e., within the same environment). There are two ways for a cell to acquire memory and thus multistability. One is through positive feedback. The other is through epigenetic modification of DNA or histones. Each of these will be discussed in turn.

Feedback and memory: introducing multistability

As a general rule, the response of cellular networks is not specified by extracellular signal inputs alone. Rather, signaling pathways receive additional regulatory input from inside the cell. These internal signals may strengthen or attenuate the ligand-triggered response in the form of feedback (reviewed in ^{73, 74}).

Negative feedback is essential for maintaining cellular homeostasis.⁷⁵ For example, NF-κB leads to immediate early response of target genes (e.g., A20, I-κB), which in turn inactivate the transcription factor (reviewed in ^{76, 77}). Self-repressing feedback creates a fast self-limiting response circuit, as over-activation of the transcription factor is limited by a concurrent production of its inhibitors.^{78, 79} While allowing for rapid and full induction of NF-κB in response to inflammatory mediators, this feedback moderates NF-κB activation once equilibrium is reached (Online Fig. VIIA).⁸⁰ Another property of negative feedback loops is that they filter out basal noise-related fluctuations in activity (Online Fig. VIIB).⁸⁰

Positive feedback establishes the necessary conditions for multistability, and by extension the interplay between plasticity and robustness.^81-83 An example of positive feedback is an activated transcription factor that feeds back to induce it’s own expression (other examples of negative and positive feedback are detailed in the Online Supplement IV). As we discussed above, PKC-Ζ activates the transcription factor, GATA-2 (Figs. 6A-C). Once activated, GATA-2 feeds back to induce its own expression.^{84, 85} As shown in the continuous and Boolean models, this self-amplifying loop creates a bistable ON/OFF switch (in Boolean terms, {0,1} and {0,0}) (Figs. 6B-C). Importantly, the persistence of the original input signal (PKC-Ζ) is not necessary for sustained expression of the output (GATA-2) (the model predicts that the cell will “remember” that GATA-2 expression is ON even when PKC-Ζ is turned OFF). Thus, this example demonstrates the potential role of positive feedback in generating multistability, as defined by the persistence of more than one state (GATA-2 ON [1] and GATA-2 OFF [0]) under identical conditions (PKC-Ζ OFF [0]). The ability of simple engineered circuits to maintain multistability in live eukaryotic cells, explicitly designed through mathematical modeling to perform as a toggle switch, has been demonstrated experimentally (reviewed in ^{86, 87}).

Figure 6. Bistability due to positive feedback.

A) Signal transduction cascade showing GATA-2 regulation by PKC-Ζ and GATA-2. PKC-Ζ activates GATA-2, which then feeds back to upregulate its own expression. B) Continuous model of the positive feedback loop. Active GATA-2 concentration is increased not only by PKC-Ζ (modeled using Hill enzyme kinetics), but also by the presence of active GATA-2 itself. The two effects are additive, as reflected by the GATA-2 rate equation. PKC-Ζ levels are assumed to be constant. Left, equilibrium concentration of GATA-2 as a function of PKC-Ζ. At low levels of PKC-Ζ there are three GATA-2 concentrations where the rate of GATA-2 change is 0 (points 1, 2, 3). Two of these concentrations are stable states (represented by the green dots) and one is unstable (point 2; the smallest deviation from this precise value leads the system away from this GATA-2 concentration and towards one of the stable states). Consequently, this system is bistable. At intermediate-high levels of PKC-Ζ there is only one stable equilibrium concentration of GATA-2 (point 4). Right, direction (arrowheads) and velocity (V, colors) of variable changes when the system is placed into different out-of-equilibrium states. Velocity color scale: green, closer to equilibrium and slower to change; purple, further from equilibrium and faster to change. C) Boolean model of the positive feedback loop. The regulatory rule controlling GATA-2 activity is an OR gate, where GATA-2 serves as one of its own inputs. Discretization of PKC-Ζ and GATA-2 concentrations is shown on the right. The Boolean model has 4 possible states, of which three (00, 01 and 11) are equilibrium states (red). Black arrows depict state changes dictated by the Boolean gate. D) Partitioning noise with low partition error magnitude (symmetric division). Partitioning noise is the result of an uneven division of a dividing cell’s contents to its daughters. When the contents of a bistable system such as the PKC-Ζ - GATA-2 system are symmetrically divided, errors are small enough that the GATA-2-deficient daughter cell (light pink) has sufficient transcription factor to auto-induce its own expression (production > degradation), whereas in the daughter cell with a slight excess of GATA-2, degradation outstrips production. Consequently, the daughter cells ultimately assume the same stable phenotype as the original cell (red). E) Partitioning noise with large partition error magnitude (asymmetric division). Here, errors are large enough to leave the GATA-2-deficient daughter cell in a state where degradation outpaces auto-induction (orange, unstable state), ultimately leading to a loss of GATA-2 (green, stable state). The daughter cell with an excess of GATA-2 (dark red) stabilizes at the same GATA-2 concentration as the original cell (dark red to red). F) Boolean model of DNA methylation control of the eNOS promoter. Methyltransferases (Y) can inhibit the eNOS promoter (P_eNOS) by methylating CpG sequences, while demethylases (X) can remove repressive DNA methylation marks, leading to promoter activation. In this scheme, it is assumed that X and Y have equal and opposing activities such that when both X and y are ON their activities cancel each other out (and thus have no effect on P_eNOS). Whenever one type of enzyme alone is present, it dictates the methylation state of the promoter (presence of Y alone leads to P_eNOS OFF; presence of X alone leads to P_eNOS ON). In the absence of both enzymes, P_eNOS sustains its methylated or demethylated state indefinitely (the value of P_eNOS depends on the current state of P_eNOS itself). This may be modeled as a self-feedback loop. The Boolean rule controlling the state of P_eNOS is a complex three-input gate. The model has 8 possible states, of which 6 represent equilibrium states (shown in red). Black arrows depict all state changes dictated by the regulatory rules.

As we have seen, acyclic systems are designed such that their input alone dictates the output. Thus, knowledge of the input alone allows us to predict the output. With feedback however, we need to know the initial state of the regulatory system at the time the signal or perturbation arrives, and we must follow the dynamical rules that lead the system towards one of its final states. To return to the example shown in Fig. 6A, consider that the input, PKC-Ζ is turned OFF. Knowing that there is a positive link between PKC-Ζ and GATA-2, we may ask what happens to GATA-2 activity. The answer depends on the state of GATA-2 when PKC-Ζ was turned OFF. If GATA-2 was ON, it will stay on (owing to memory), while if GATA-2 was OFF, it will remain OFF. Thus, in this simple example, it is necessary to know the initial state of the node (GATA-2) before predicting the outcome. The implications of this phenomenon reach into the experimental world. For example, the use of a siRNA against PKC-Ζ in endothelial cells may fail to inhibit its downstream target (GATA-2) despite an abundance of the transcription factor in the cell.

Differences in the history of signal input can result in two endothelial populations with different internal states, stably maintained under identical environmental conditions. The existence of multiple states is not always associated with readily distinguishable phenotypes. These subtleties are illustrated by a previous study in which human umbilical vein endothelial cells were preconditioned in the absence (control) or presence of small concentrations of TNF for 14 h followed by a 24 h washout period in fresh control (TNF-deficient) medium.⁸⁸ The cells were then incubated with the activation agonist, thrombin. In TNF-preconditioned cells, thrombin failed to promote nuclear translocation of p65 NF-κB, despite a normalization of I-κB phosphorylation, I-κB protein levels, nuclear-cytoplasmic ratios of p65 NF-κB, and NF-κB target gene expression following the 24 h washout. These experiments reveal the existence of two cell populations (those that have or have not been exposed to TNF), each with different initial states or “set-points” (at the time thrombin is added). This bistability within the endothelial regulatory system manifests as a persistent change (the inability of NF-κB to respond to thrombin) triggered by a transient signal (presence, then absence of TNF). In this particular case, we do not know the full identity of the phenotype switched by TNF (we do not have a name for it as we do for, say, apoptosis versus survival), mainly because additional molecular markers have yet to be identified to distinguish the two stable states (or set-points).

From the standpoint of endothelial heterogeneity, feedback contributes to the plasticity, robustness and multistability of endothelial phenotypes. In the context of a single phenotype, negative feedback can ensure homeostasis by dampening the effects of small changes in extracellular and intracellular forces, resulting in robust maintenance of the phenotype. At the same time, positive feedback provides cells with the capacity to display different stable phenotypes within a single environment. When cells undergo symmetrical division, the regulatory components are more or less evenly distributed between daughter cells. As long as the partition errors are compensated for by homeostasis, positive feedback constitutes a mechanism for mitotic trait stability that does not rely on epigenetic modifications (Fig. 6D). If the partitioning errors exceed the corrective capacity of homeostasis, the two daughter cells can occasionally diverge and stably acquire distinct phenotypes (Fig. 6E). In this manner, mitotic stability is not foolproof. Traits may persist anywhere from a few cell decisions to the lifetime of an organism.

As important and ubiquitous as feedback is, it presents a conceptual hurdle. In contrast to linear pathways and pathways with crosstalk, the input cannot be used to predict the output. Rather, as we discussed in the GATA-2 and TNF preconditioning examples, one must have knowledge of the state of all nodes at the moment the external signal arrives. In other words, the correspondence between signal and outcome is no longer straightforward, but rather depends on knowledge of the initial internal state of the system. This is a tall order, as the number of potential initial states grows exponentially with the number of regulatory nodes. This hurdle emphasizes the need for interdisciplinary interactions with the goal of building predictive models of the regulatory network.

Epigenetics: a special case of feedback

With feedback, memory and multistability are encoded by the links or “wiring” of the system. The nodes themselves need not have memory. A second mechanism for generating multistability is epigenetic modification of DNA or histones. In this case, it is the element itself (i.e., the DNA or histone template) that possesses the memory; the node has two robust states that can be maintained without any active signaling. Linear signaling and signaling with crosstalk may trigger epigenetic changes. However from a modeling perspective, such epigenetic switches may be viewed as a form of feedback in which the element feeds back on itself. It can maintain its own state due to the stability of covalent modifications (Fig. 6F). A Boolean description of an endothelial promoter controlled by DNA methylation illustrates this. Transcription of the endothelial cell-restricted gene endothelial nitric oxide synthase (eNOS) is mediated not only by extracellular signals (e.g., shear stress ^{89, 90} or VEGF ^{91, 92}) but also by the methylation state of its promoter.⁹³ Methyltransferases (X in Fig. 6F) and demethylases (Y) control the methylation status (hence activity) of the eNOS promoter P_eNOS. If only X or Y is present (i.e., ON), the available enzyme will dictate the state of P_eNOS (methyltransferase X will methylate and silence the promoter; demethylase Y will demethylate and activate the promoter). If both enzymes are ON, the net effect will depend on their relative concentration and/or activity (e.g., their binding affinity to DNA). However, if both enzymes are absent, P_eNOS may exist and persist in any of its two states (i.e., ON or OFF), depending on its last modification. In this manner, DNA methylation acts as a bistable switch.

Consequently, knowledge of the present state of X and Y alone does not always predict the state of P_eNOS. In order to correctly represent the regulatory rule (or gate) that controls the promoter, P_eNOS itself is needed as an input for its own Boolean gate (Fig. 6F). The bistability of the methylation state plays a similar role to positive self-feedback in GATA-2 regulation. As a result, eNOS mRNA expression can be modeled using a combination of Boolean gates: eNOS_mRNA = P_eNOS AND (shear stress OR VEGF), where P_eNOS = [X AND (NOT Y)] OR [(NOT Y) AND P_eNOS] OR [X AND P_eNOS] represents the methylation state of the promoter. The eNOS promoter is methylated (OFF) in most cell types and remains off in the presence of most environmental signals. For example, smooth muscle cells or fibroblasts do not express eNOS in the absence or the presence of shear stress.⁹⁴ In endothelial cells, however, the eNOS promoter is maintained in a permissive methylation state and is responsive to extracellular signals such as laminar flow.

Mitotically stable differences in endothelial phenotypes are almost always ascribed to epigenetic DNA modifications. However, as discussed in the previous section, memory and multistability are also properties of networks with positive feedback. Thus, by framing epigenetics as a special form of feedback, we are emphasizing positive feedback as the primary determinant of these two key properties.

DNA modifications are not the only examples of memory elements in endothelial cells. Stable structures such as Weibel-Palade bodies can preserve their contents until they are released by the endothelial cell. For example, a previous study showed that simulation of endothelial cells with inflammatory mediators results in an accumulation of interleukin (IL)-8 in Weibel-Palade bodies, where it colocalizes with vWF.⁹⁵ IL-8 was retained in these storage organelles for several days after the removal of the stimulus. Subsequent stimulation of the endothelial cells with secretagogues resulted in the release of the storage pool. Thus, the storage of IL-8 in Weibel-Palade bodies represents a form of memory of a previous inflammatory insult, which then allows the cell to respond quickly to another inflammatory stimulus. This is another example that demonstrates the importance of the input history of the cell in determining its subsequent behavior.

Modeling phase space, attractors, attractor basins and barriers

So far, we have described regulatory systems according to the nature of the links in the pathway. Conceptually, such systems may be linear, they may have crosstalk, and/or they may manifest feedback. Epigenetics may be considered to be a special form of feedback in which the memory is encoded by the node (DNA) itself. In reality, most regulatory pathways consist of many nodes and links with multiple levels of crosstalk and feedback. An important challenge is to represent or model this complexity in ways that are at the same time understandable and testable. Dynamical systems theory provides one such approach. It establishes multistability as a core property of the endothelial cell and it allows us to organize the collection of cellular states into multiple valleys within a landscape and mathematically model its topography. Its methodology revolves around describing a system’s phase space, a concept that was introduced earlier (see “Multistability of endothelial cells: a novel explanatory framework”).

Phase space refers to the space of all possible states that a dynamical system may occupy at any time.^18-20 A “dynamical system” is defined as any system in which one or more variables can change, such as the regulatory components of a cell. In systems with a single variable, the space is represented by a line. The phase space of two variables comprises a flat plane (see Figs. 4A-C). Three-variable systems occupy three-dimensional space (see Figs. 4D-F). Larger networks give rise to phase spaces with ever-increasing dimensions. For example, consider the bistable 6-node apoptotic cascade network shown in Fig. 7A, which we assembled based on data from previously published studies ^{48, 53, 55, 58}. Using a Boolean approximation, this network has a phase space of 2⁶ (or 64) “points” (Fig. 7C). An entire cell can have 2ⁿ possible states where n represents the number of nodes in its full regulatory network. Thus, the phase space of endothelial cell, whose genome consists of some 30,000 genes, is ~2^30,000 (not counting non-coding RNA, multiple splice forms and posttranslational modifications). While all of these states are theoretically possible, are they actually represented in any living cell?

Figure 7. Boolean model of a caspase-mediated survival-apoptosis switch.

A) Signal transduction cascade showing interactions based on published Boolean models of mammalian caspase-mediated apoptosis. Shown is a core network of 6 nodes (anti-apoptotic: Bcl-X_L, IAPs; pro-apoptotic: Caspase 3, Caspase 8, Caspase 9 and BAX) whose links are simplified according to their net positive or negative effects (see Supplemental Table 3). The Caspase 3 self-loop captures the fact that when both Caspase 3 and Caspase 9 are high at the same time, they are sufficient to sustain Caspase 3 activation even in the presence of IAPs. Caspase 9 alone can cleave Caspase 3 to its active form, but the presence of IAPs keeps the active Caspase 3 enzyme in check. Once Caspase 3 activity is turned on (e.g., through transient inhibition of IAPs), the two caspases sustain each other’s activity. B) Boolean gates that control the dynamics of the model. It is assumed that IAPs and Bcl-X_L actively accumulate when not inhibited (i.e., they are ON by default independent of any extraneous intracellular or extracellular signals). C) State transition graph of the Boolean model. All 2⁶ possible system states are shown as nodes in a state transition graph spanning three attractors. Solid black lines indicate state transitions that occur when the Boolean rules in (B) are applied synchronously (all nodes are updated at the same time in each time step). Noise is modeled as a set of independent, random gate output errors (error probability p = 0.000335) at each time step. Gray transition links represent changes in the state of the system whenever one of its 6 node outputs has been flipped by noise (the most probable noise-induced transitions are single gate flips in a given time step). The attractor basin that each state belongs to is indicated by node border color. The energy of states, calculated in the presence of noise, is mapped onto node the size as well as fill color (large green nodes have low energy and thus high probability, while small red states have high energy and are rarely visited via noise-driven state changes). The expression patterns corresponding to each attractor are shown as heat maps (green, ON; red, OFF). The expression patterns representing the two fixed-points are overlaid on the regulatory network (circles with gray background). These two patterns correspond to survival ({0,0,0,1,1,0}) and apoptotic ({1,1,1,0,0,1}) cellular phenotypes. The limit cycle shown in the middle represents a shallow attractor basin with few states. It is extremely sensitive to noise-induced transitions that place the system into one of the two stable states, and it does not correspond to a robust biological phenotype (see Supplemental Table 3). Large red and blue stars mark two possible initial conditions with trajectories in different attractor basins.

The answer to this question is no.^96-99 Any change in the intracellular or extracellular environment may alter one or more of the 30,000 nodes (i.e., genes) and thus shift the regulatory system’s state in phase space. However, the system will typically respond by further changing its state along discrete trajectories (as dictated by its regulatory links) and settle into the same or a different steady state (equilibrium). The dynamics of the system (its change in time) is equivalent to the movement of its global state within phase space. In a stable state, all Boolean rules that reflect combinatorial gene regulation are satisfied. Occasionally, trajectories in phase space may settle into a periodic “orbit” or pattern that repeats ad infinitum (termed limit cycle). In biological systems these represent rhythmic behaviors such as cell cycle or circadian clocks.^{74, 100} Trajectories of certain dynamical systems can wander around in phase space forever, never quite repeating the same path (chaos; e.g., turbulent blood flow).^18-20

To return to our apoptosis/survival model, of all possible 64 initial states, the vast majority (n = 59) settle into one of the two stable states: apoptosis or survival (Fig. 7C). Rarely (5 of the 64 possible starting states), the system enters a small limit cycle (Fig. 7C). The collection of all trajectories shown in Fig. 7C is referred to as a state transition graph. Consider a situation in which all 6 nodes except BCL-X_L and Bax are OFF. In Boolean terms, this may be written as {0,0,0,1,0,1} (Fig. 7C, red star). Regardless of the cause that brought about these initial conditions (e.g., an extracellular signal or intracellular noise), the regulatory system will subsequently change. It will follow a trajectory in the large phase space, as dictated by the Boolean logic gates shown in Fig. 7B. Adhering to these rules, a cascade of events may be followed in time (red arrows), ending in the stable (survival) state {0,0,0,1,1,0}. Alternatively, if the network begins with Caspase 3 ON and the other 5 nodes off (blue star), the system can be traced to stable (apoptosis) state {1,1,1,0,0,1} (red arrows). The full repertoire of the system’s natural dynamics is reflected by the collection of all state-changes, or trajectories in phase space (Fig. 7C, black arrows).

In the general theory of dynamical systems, stable states and rhythms are referred to as the attractors of a system (e.g., stable states {1,1,1,0,0,1} and {0,0,0,1,1,0} in Fig. 7C). All other states are by definition unstable. The regulatory rules of the system define the dynamics as trajectories within phase space. The collection of cellular states that lead to a given attractor forms its attractor basin (for example all the red bordered nodes in Fig. 7C leading to the stable survival attractor {0,0,0,1,1,0}). The three attractor basins in Fig. 7C collect all possible dynamical behavior this small model can reproduce.

The attractor basins of a dynamical system may be represented as a landscape of valleys in phase space. Attractor states lie at valley bottoms, while the ridges between valleys separate the attractor basins. The entire topography of the landscape, including the height of each state, is dictated by rigorous mathematical formulation (see Online Supplement V.B).^{45, 101-103} In the complete absence of noise, the regulatory system, no matter what its starting conditions, ultimately settles into a single attractor. In Fig. 7C, the two stable states are {0,0,0,1,1,0} [survival] and {1,1,1,0,0,1} [apoptosis]. There are only two ways to deviate from the stable state and change the system from one attractor to another. One is to expose the cell to an extracellular signal such as a ligand, which alters the system’s state. An extreme example would be a hypothetical extracellular factor that directly flips 2 of the 6 nodes in the regulatory network shown in Fig. 7A (from {0,0,0,1,1,0} to {1,0,0,1,0,0}), thus inducing apoptosis. The second way of inducing a change in stable states is by chance through biological noise. Noise-related perturbations can trigger a transient burst of protein or gene activation/de-activation, which can potentially propagate through parts of the regulatory system. These perturbations typically leave the regulatory system within the same attractor basin. The same set of internal regulatory rules (i.e., the ‘wiring’ of the system) that give rise to the attractor basin itself drive the system back to it. The greater its resistance to change, the more robust an attractor is. As noise results in a random change in the state of the system, states that have very similar expression/activation profiles to the attractor will be visited often. These states lie close to the attractors, at the side of their valleys. States that are very different (far from) the attractor will be visited only rarely. For example, consider that we begin with cells in the survival state ({0,0,0,1,1,0}). Noise might induce a transient increase in Caspase 8, causing a change to {0,1,0,1,1,0} (Fig. 7C). Additional noise experienced in an out-of-equilibrium state could push the system even further up the hill (e.g., to {1,1,0,1,1,0}). In theory, if we waited long enough, noise alone would eventually drive the system from the survival basin to the apoptosis basin. The probability of crossing from one attractor basin to the next (e.g., from survival to apoptosis) defines the barrier between the two attractors. In other words, barriers between attractor valleys are dictated by the ability of biological noise to switch a cell from one valley to another. Conversely, the robustness or stability of an attractor is defined by the overall probability of the system being in that basin (for details regarding the interpretation of attractor landscape topography, see Online Supplement V.B and Online Fig. I).

In the absence of noise, then, the barrier, by definition, is infinite and can only be crossed by a targeted change in the environment (for example, a ligand whose receptor is connected to the regulatory system, or experimental overexpression or knockdown of a gene). In the presence of noise, barriers may be large or small, depending on the regulatory system. Large barriers are typical between attractors that represent distinct cell lineages (e.g., an endothelial cell and a cardiomyocyte). These barriers can preserve distinct lineage differences across a wide range of external environments. Intermediate barriers are found between relatively stable attractors, but may be crossed when exposed to distinct environmental signals (e.g., flow-dependent differences in arterial vs. capillary endothelial cell properties). With low barriers, biological noise itself is sufficient to cause shifting from one attractor to another. In this case, the property within one cell will slowly drift back and forth across the barrier resulting in transient heterogeneity.^{23, 24, 104} However, when viewed from a cell-population perspective, the heterogeneity is stable, since a population from a single cell, regardless of its initial state, will eventually reconstitute a mixture of the two distinct states.^104-107

REFRAMING NATURE vs. NURTURE IN DYNAMICAL SYSTEMS TERMS

Operational definitions

As discussed in the Introduction and shown in Fig. 2B, the operative definition of nature and nurture is based on a conceptually straightforward experiment in which two phenotypically distinct endothelial cells are cultured and passaged under identical conditions in vitro. Nurture describes those phenotypic differences that are washed out; they disappear along with the environment that created them. Thus, these differences are environmentally imposed or imprinted onto the endothelial cell. We consider these innate to the environment. By contrast, nature is defined as those differences in traits that are retained in vitro even when cells are allowed to divide. These properties are mitotically stable and are preserved when the cellular environment changes. They are considered innate to the cell. All cells in the human body share an identical genome. Thus, by definition, mitotically stable differences between cells of different lineages and between subpopulations of the same lineage are dictated by mechanisms that are not encoded in the DNA sequence. Viewed from this perspective, the nature-nurture distinction separates those properties of endothelial cells that are environmentally dependent from those that are epigenetically fixed and impervious to changes in the tissue environment. A systems level approach to endothelial cell heterogeneity helps to reframe the nature-nurture dichotomy in far more nuanced terms.

A dynamical systems view of ‘nature’

In dynamical systems terms, ‘nature’ equates with multistability. When two phenotypically distinct endothelial cells are removed from their native tissue and cultured under identical conditions, they may settle into a new steady state (depending on how different their new environment is), but the two final states are likely to be different nonetheless.¹⁷ In other words, the endothelial cell will display multistability, or the ability to manifest more than one phenotype in the same environment. Multistability requires that the cell have memory of its phenotype and thus of past signal inputs. We have discussed three ways in which memory is achieved: positive feedback; heritable methylation of DNA and/or posttranslational modification of histones (i.e., epigenetics); or intracellular structures with long half-lives (e.g., Weibel-Palade bodies). In each case, cellular memory is manifest when an extracellular stimulus drives the state of a cell from attractor A to B, and the cell remains in its new state even when the original signal is withdrawn.

While the epigenetic DNA template is symmetrically partitioned during mitosis, there are inevitable differences in the partitioning (concentration and localization) of coding and non-coding mRNA and proteins, including those involved in DNA and histone modification and positive feedback loops and those sequestered in intracellular organelles. For the daughter cells to maintain memory of its state, any effects of asymmetrical partitioning must be corrected by homeostatic mechanisms (Fig. 6C). In landscape terms, the fidelity of the partitioning process is necessary to land the daughter cells in the same global attractor as the parent cell. Homeostatic mechanisms (i.e., the regulatory interactions which define the attractor landscape and basins) can then maintain the cells in the attractor basin. Thus, in dynamical systems theory, the nature side of the nature-nurture equation includes a combination of positive feedback, DNA methylation and histone modification, stable storage organelles, symmetric partitioning of all RNA and protein in the cell, and homeostatic processes for correcting and maintaining the system-level attractor state of a cell (i.e., its location in phase space).

The probability of the daughter cell landing and staying in the same attractor as the mother cell depends on the robustness of the attractor, which in turn is a function of barrier heights between neighboring attractors (see Online Fig. I). Attractors with high barriers (e.g., between an endothelial cell and a skin cell), which are more commonly controlled by epigenetic mechanisms (DNA methylation and histone modification), withstand higher partitioning errors and a wider range of environmental influences. For example, spontaneous differentiation of an endothelial cells to a keratinocyte rarely if ever occurs in the timescale of our observations. Medium barriers (e.g., between a capillary and venule endothelial cell within the same tissue) are sufficient for mitotic maintenance of traits in limited sets of similar environments, while lower barriers endow only transient mitotic stability of a trait (Online Supplement V.F).

A dynamical systems view of ‘nurture’

Whereas nature focuses our attention on the internal wiring of the cell, specifically the memory of the system (hence its mitotic stability), nurture points to the extracellular environment of the cell. The microenvironment is integrally linked to the cellular regulatory system, primarily through ligand-receptor interactions. No cell is immune to its environment (though cancer cells are more autonomous than their normal counterparts). Changes in the extracellular environment may result in altered expression/activation of one or more nodes in the regulatory system. From a dynamical systems perspective, the outcome will depend on whether the new trajectory in phase space is sufficient to push the system out of its current attractor basin into a new one. There are three possible scenarios. First, the cell may show a transient response and relax back to its previous phenotype. Second, the change in environment may activate memory-inducing pathways (e.g., positive feedback, DNA methylation, histone modification) that shift the cell to a new attractor basin that is stable even when the signal is removed. Finally, the environment may promote a change in attractors, but only as long as the new signals persist. In this way, the environment restricts the system-level state of a cell to a subspace of its entire phase space.

The native (or constitutive) environment of endothelial cells in a tissue contains dominant cues that establish the range of robust attractors accessible to them, and thereby set the upper limits of phenotypic heterogeneity compatible with the tissue. In some cases, the signal input “locks in” the expression of certain genes. For example, at some point during embryonic development, before the onset of blood flow, yet unidentified extracellular signals induce mitotically stable differences in arterial and venous endothelial cells.¹⁰⁸ As evidenced by studies in which veins are grafted into the arterial circulation, or where arterial and venous endothelial cells are cultured under identical conditions, these differences persist even when the cells are placed in a new environment (Fig. 8A).^{17, 109, 110} Thus, while the exposure of a venous endothelial cell to arterial flow may result in a change in attractor that is distinct from the native venous phenotype, it will not be identical to that of an arterial cell (owing to its site-specific memory). In contrast to these relatively fixed site-specific properties (which were nonetheless triggered at some point in the past by an extracellular cue), other differences in venous and arterial endothelial phenotypes are dependent upon persistent differences in the extracellular environment. For example, high laminar flow in large arteries places the endothelial regulatory system in an attractor basin that renders the cell relatively insensitive to inflammatory stimuli (Fig. 8B). In other words, exposure of the arterial endothelial cell to activation agonists tends to leave the cell in the same “quiescent” attractor. By contrast, endothelial cells in regions of non-laminar flow (e.g., branch points of arteries) and low flow (e.g., postcapillary venules) occupy a different attractor (owing both to differences in flow and vein-specific epigenetic changes). The attractor is sensitive to inflammation such that the cell shifts to a new “activation” basin. Thus, blood flow serves as one environmental factor able to restrict the range of phenotypic response of endothelial cells (Fig. 8B).

Figure 8. A dynamical systems view of nature and nurture.

A) Endothelial phenotype drift in culture (reinterpretation of experimental results from Chi et al. ¹⁷). Left, Under in vivo conditions, functional differences between microvascular endothelial cells (MVEC) in different organs (lung, skin and intestine) and between arterial and venous endothelial cells are illustrated as distinct attractor basins. Right, When the endothelial cells are removed from the body and cultured in vitro, arterial and venous identity is retained, but the three types of microvascular cells drift close to each other (as defined by their transcriptome). B) Endothelial attractors compatible with different environmental cues. Left and middle, Endothelial cells in the presence of high flow (e.g., arterial endothelial cells in vivo) occupy the same attractor state regardless of the presence or absence of physiological levels of TNF-α. The region of phase space to which endothelial cells are constrained to in the presence of flow is shown as a purple circle. Similarly, constraints due to low shear flow / TNF-α / absence of TNF-α are shown as blue rectangle / black contour / gray contour, respectively. In the absence of high shear stress (e.g., low or disturbed flow in venules and arterial branch points, respectively), a cell can assume two different phenotypes and thus occupy different attractors, depending on levels of TNF-α in its microenvironment. Thus, in response to the same TNF-α signal, endothelial cells in venules and at arterial branch points assume an activated phenotype. Right, Endothelial activation in vitro (in the absence of flow). Endothelial cells cultured on a plate retain certain characteristics of their vessel of origin. Thus, endothelial cells isolated from arteries and venules occupy two distinct attractor basins. However, in the absence of flow (and other inputs inherent in their native environments), both arterial and venous endothelial cells may acquire an activation phenotype in response to TNF-α. At the same time, the distinction between their arterial and venous properties is not lost. They assume an inflamed arterial and an inflamed venous cell phenotype, respectively.

In summary, a combination of epigenetic and environmental properties restricts the attractors accessible to endothelial cells. Stated another way, the sensitivity of any regulated trait to environmental change strongly depends on the particulars of the cell’s environment before the change occurs. Consequently, plasticity with respect to an environmental influence is tightly linked to the robustness of homeostatically maintained phenotypes.

Nature versus nurture revisited

If all possible states of the endothelial regulatory system are considered, the nature-nurture boundary begins to blur. Every site-specific phenotype is either initiated by changes and/or maintained by differences in the environment. Moreover, since endothelial cells share the same dynamical regulatory system and phase space with each other and with all other cells in the body, all lineage-specific and vascular bed-specific phenotypes (whether or not they are mitotically stable) are theoretically alterable in a new environment. At the extreme, this is exemplified by cellular reprogramming experiments (reviewed in ^{99, 111}).^112-116 Thus, a dynamical systems view of endothelial heterogeneity emphasizes the central role of ‘nurture’.

Under normal conditions, endothelial cells do not wander aimlessly about their phase space. Rather, they occupy certain stable states, and thus demonstrate stable site-specific phenotypes. These states, whether or not they meet our operative definition of nature or nurture, are resistant to small noisy fluctuations in external conditions by virtue of the cell’s regulatory network. In this sense, the ability to maintain phenotypic heterogeneity is innate to the cell (and ultimately explained by ‘nature’). In dynamical systems theory, what matters when approaching mechanisms of endothelial heterogeneity is not whether a site-specific phenotype is retained in cultured passage cells, but rather how high or low the barriers are between phenotypes, and what type (and magnitude) of perturbation can shift the cell from one state to another. It is not possible to separate a living cell from its environment. The properties intrinsic to a regulatory system are connected to the environment this system monitors. Every functional phenotype is at the same time innate to the regulatory system and sensitive to some aspects of the environment.

PRACTICAL RELEVANCE OF PREDICTIVE REGULATORY MODELING

Thus far, our discussion has focused on how to build mathematical and computational models of cellular regulatory networks. Simply building accurate models, however, is not the end goal of the type of research outlined here. The ultimate goal is a thorough understanding of how endothelial phenotypes are generated, maintained, and otherwise regulated in physiological and pathophysiological states, and how they may be manipulated therapeutically. Theoretical models and dynamical systems theory serve as precision tools, capable of revealing a wide range of phenotypes and responses potentially generated by the cellular regulatory system. In this section, we address the question of how models complement and inform research at the bench (for a discussion of the principles of theoretical modeling, please see Online Supplement I.).

A dynamical systems model allows for high-throughput in silico experimentation. For example, it may be used to screen for and predict external signals that will force the regulatory system into a single phenotypic state. (These signals are external to the model itself, but influence it through one or more of its nodes.) Such signals may be characteristic of certain tissue environments. Dynamical models can also be used to predict transient signals that can switch the regulatory system from one phenotype to another in a single pulse. These predictions may provide a mechanistic explanation for phenotypic heterogeneity observed in neighboring endothelial cells. In addition to predicting environmental signals that may lead endothelial cells to acquire one or another state, dynamical systems modeling also permits in silico testing of the effect of predetermined extracellular cues on endothelial phenotypes. This is especially helpful when considering a complex mixture of signals, as occurs in tissue environments, and when using large regulatory models with multiple levels of feedback. Another use of the model is to predict the effect of silencing or overexpressing one or more gene, or otherwise altering regulatory links between genes.

Dynamical systems models may be further used to study disease. For example, diseases associated with gain or loss of function may be represented by locking in the state of the relevant intracellular nodes in the circuit (i.e., render it impervious to regulatory influences). Alternatively, diseases that are driven by the microenvironment may be modeled by incorporating the effects of persistent environmental signals on the regulatory circuit. Once these models have been modified to reflect the disease, investigating the influences of the cellular environment can suggest therapeutic interventions that target the extracellular or intracellular microenvironment, which is unique to each vascular bed. Thus, the computational model of the disease can provide a first screen of experiments before they reach the bench, much the same way as in silico screening of chemical libraries can point to pharmacological proteins.

One way to “visualize” the results of in silico manipulations is to consider the attractor landscape of the dynamical regulatory model. For example, the bistable survival/ apoptosis switch (Fig. 7) in endothelial cells has an attractor landscape with two deep valleys (survival and apoptosis). Treating these cells with a high dose of TNF while blocking protein synthesis leads to apoptosis.¹¹⁷ In modeling terms, this translates into Caspase 8 activation that no longer requires the presence of active Caspase 3. With Caspase 8 unable to turn OFF, the survival attractor is no longer stable. The landscape of the model in the presence of TNF has only one deep valley. The region of phase space corresponding to the original survival attractor turns into a steep slope, leading cells from survival towards apoptosis. Addition of TNF alone, however, has a different effect. In this case, activation of Caspase 8 is blocked or reduced by c-FLIP (the maintenance of which requires de novo protein synthesis).¹¹⁸ TNF-induced NF-κB activation also helps to protect the stability of the survival state. As a consequence, the attractor landscape following TNF activation in the presence of growth factors preserves the bistability of this regulatory switch. It may nevertheless change the size of its attractor basins and alter the barrier between them. As a result, cells may become susceptible to transient pro-apoptotic influences.

An appreciation of the landscape surface underscores the importance of maintaining the capacity for multistability when developing new therapies. Indeed, the desired goal in therapy may be to restore the natural barriers between states (and thus maintain both robustness and plasticity), rather than forcing a cell into one phenotype or valley. For example, the task of restoring a chronically inflamed endothelium to health is often equated with rendering the endothelium quiescent. However, by driving the cell into a non-activated attractor, one deprives endothelial cells of the capacity to react to transient inflammatory stimuli in a healthy manner. This is especially problematic if the intervention targets all endothelial cells, including those not affected by chronic inflammation. A more attractive goal is to specifically target the unhealthy microenvironment, while leaving the regulatory circuit responsive to signals it evolved to respond to (e.g., local infection). Naturally, there are situations in which the goal is indeed to force a state of our choosing onto the endothelium. For example, in targeting tumor endothelial cells our aim is to guarantee the lack of stable survival state, at least within the tumor environment. Here too, however, it is critical to find an intervention that strikes an optimal balance between altering the landscape of tumor endothelial cells while leaving the rest of the vasculature in a protected survival attractor.

To summarize, dynamical modeling of a regulatory circuit, coupled with in silico experimentation, can delineate the extensive ramifications and the boundaries of our current knowledge of regulatory interactions, far beyond what is possible using human memory, unaided by computation. Thus it can serve as a valuable complement to experimental work and lead us in directions we could not otherwise anticipate.

CONCLUSIONS AND FUTURE DIRECTIONS

In this review, we have tried to build a case for approaching endothelial heterogeneity using dynamical systems theory. Dynamical systems modeling provides both a metaphorical and a quantitative platform for describing and predicting the nature, scope and mechanisms of phenotypic heterogeneity. These predictions may be tested using wet-bench experimentation and the results then used in an iterative process to fine-tune the model. To date, regulatory modeling in biology has been limited to small circuits that contain a limited number of nodes (e.g., the caspase pathway). Despite advances in the use of discrete-state modeling to study an ever-increasing number of regulatory interactions, such approaches fall well short of capturing the full regulatory network of a mammalian cell. An important challenge for the future is to develop computational strategies for modeling the complete regulatory system of a cell such as the endothelial cell. This will require top-down approaches in which ever expanding system-level regulatory interaction databases (e.g., protein-protein interactions,^119-123 DNA-protein interactions,¹¹⁹ signal transducing interactions ^{124, 125}) are used to build dynamical models. Together with enhanced modeling techniques and advances in visualizing attractor landscapes, these databases may eventually lead to a full-scale endothelial regulatory network model. An alternative, and perhaps complementary approach is to piece together the behavior of the full regulatory network by combining studies of its isolated subparts (e.g., the apoptotic model in Fig. 7). Indeed, recent studies on the structural properties of large cellular networks suggest that such an approach might just work, provided that the system is cut at the right ‘joints’.^{126, 127} Specifically, there appear to exist within biological interaction networks certain dense subgraphs, with high-link density among their components and sparser connections to the rest of the network.^{128, 129} However, these modules are structurally defined and the extent to which they may be used in isolation to predict the dynamics observed in the cell, orchestrated by the entire regulatory system, remains to be seen.

We hypothesize that in addition to structural hierarchy, the full-scale regulatory network of mammalian cells also comprises a hierarchy of dynamical modules. These regulatory modules are characterized by robust attractors that correspond to mutually exclusive functional phenotypes (e.g., cell crawling vs. firm adhesion vs. floating; apoptosis vs. survival). The attractors, or phenotypes, are manifest both at the sub-graph and full-scale level and therefore can be studied in isolation. Full-scale attractors correspond to different combinations of the module attractors (e.g., firmly adherent and surviving cells; or crawling and surviving cells). These attractor combinations are dictated by interactions between modules, which determine the system-level stability of each module attractor combination (e.g., floating and survival do not form a stable combination in endothelial cells). Module-level phenotypes result of the interplay between all nodes of each dynamical module. The dynamical module as a whole, on the other hand, acts as robust building block for the higher scales of biological organization. A goal of future studies is to demonstrate dynamical, hierarchically modular organization in endothelial cells and to determine whether such a property may be exploited to bridge the gap between molecular pathways and system-level phenotypes in the endothelium.

Non-standard Abbreviations and Acronyms

A20 (TNFAIP3)

tumor necrosis factor, alpha-induced protein 3

BAX

BCL2-associated X protein

Bcl-X_L

BCL2-like 1

c-FLIP (CFLAR)

CASP8 and FADD-like apoptosis regulator

DSCR-1

Down syndrome critical region-1

Caspase 3

apoptosis-related cysteine peptidase

Caspase 8

apoptosis-related cysteine peptidase

Caspase 9

caspase recruitment domain family, member 9

EBA

endothelial barrier antigen

eNOS

endothelial nitric oxide synthase

EphB4

EPH receptor B4

GATA-2

GATA binding protein 2

Hey2

hairy/enhancer-of-split related with YRPW motif 2

IAPs

inhibitor of apoptosis proteins

ICAM-1

intercellular adhesion molecule-1

I-κB

nuclear factor of kappa light polypeptide gene enhancer in B-cells inhibitor

NFAT1 (NFATC2)

nuclear factor of activated T-cells

cytoplasmic

calcineurin-dependent 2

NF-κB

nuclear factor of kappa light polypeptide gene enhancer in B cells

p27^kip1 (CDKN1B)

cyclin-dependent kinase inhibitor 1B (p27, Kip1)

PKC-Ζ

protein kinase C, zeta

SELE

E-selectin

Smoothened

frizzled family receptor

TFII-I (GTF2I)

general transcription factor IIi

TNF

tumor necrosis factor

VCAM-1

vascular cell adhesion molecule-1

VEGF

vascular endothelial growth factor

vWF

von Willebrand factor