Dynamical systems approach to endothelial heterogeneity

Abstract

Endothelial cells display remarkable phenotypic heterogeneity. An important goal is to elucidate the scope and mechanisms of endothelial heterogeneity and to use this information to develop vascular bed-specific therapies. We reexamine our current understanding of the molecular basis of endothelial heterogeneity. We introduce multistability as a new explanatory framework in vascular biology. We draw on the field of nonlinear dynamics to propose a dynamical systems framework for modeling multistability and its derivative properties, including robustness, memory, and plasticity. Our perspective allows for both a conceptual and quantitative description of system-level features of endothelial regulation.

Figures

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 From Lei Yuan and William C. Aird, unpublished data (2012).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.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 From Lei Yuan, Erzsébet Ravasz Regan and William C. Aird, unpublished data (2012).

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.Bottom: In contrast, significant differences remain between MVEC from myocardial and intestinal tissues under in vitro conditions. 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, 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).

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.

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.

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).

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 (PeNOS) 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 PeNOS). Whenever one type of enzyme alone is present, it dictates the methylation state of the promoter (presence of Y alone leads to PeNOS OFF; presence of X alone leads to PeNOS ON). In the absence of both enzymes, PeNOS sustains its methylated or demethylated state indefinitely (the value of PeNOS depends on the current state of PeNOS itself). This may be modeled as a self-feedback loop. The Boolean rule controlling the state of PeNOS 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.

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-XL, 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-XL 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.

Figure 8. A dynamical systems view of nature and nurture

A) Endothelial phenotype drift in culture (reinterpretation of experimental results from Chi et al. ). 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.