Cell signaling model for arterial mechanobiology

Abstract

Arterial growth and remodeling at the tissue level is driven by mechanobiological processes at cellular and sub-cellular levels. Although it is widely accepted that cells seek to promote tissue homeostasis in response to biochemical and biomechanical cues-such as increased wall stress in hypertension-the ways by which these cues translate into tissue maintenance, adaptation, or maladaptation are far from understood. In this paper, we present a logic-based computational model for cell signaling within the arterial wall, aiming to predict changes in extracellular matrix turnover and cell phenotype in response to pressure-induced wall stress, flow-induced wall shear stress, and exogenous sources of angiotensin II, with particular interest in mouse models of hypertension. We simulate a number of experiments from the literature at both the cell and tissue level, involving single or combined inputs, and achieve high qualitative agreement in most cases. Additionally, we demonstrate the utility of this modeling approach for simulating alterations (in this case knockdowns) of individual nodes within the signaling network. Continued modeling of cellular signaling will enable improved mechanistic understanding of arterial growth and remodeling in health and disease, and will be crucial when considering potential pharmacological interventions.

Fig 1. Arterial wall signaling network constructed from the literature.

The network structure corresponds to rule-based statements, derived from the literature and shown (along with abbreviations) in S1 Appendix, containing 50 species and 82 reactions. Black solid lines denote activation and red dotted lines inhibition. For clarity, inhibition is shown to affect a node directly; however, to implement this, an ‘AND NOT’ logic operation is used with all incoming reactions to the node (see S1 Appendix). EC represents endothelial cells (the signaling for which is not considered in detail—see text) and SMC/FB refers to a homogenized approach to modeling contributions by the intramural smooth muscle cells and fibroblasts. Given our interest in AngII-induced hypertension, we focus on collagen production leading to fibrosis as revealed by murine experiments. Network visualization was achieved using Cytoscape [19] and Netflux (https://github.com/saucermanlab/Netflux).

Fig 2. Comparison of qualitative experimental input–output relations and model predictions.

A. Experimental input–output relations from the literature ([–60]) used for qualitative model validation. Increases and decreases of an output in response to each of three inputs are represented by upward and downward arrows respectively. In cases of conflicting results, both are depicted. Cases with no observed changes are shown by horizontal lines, and unknown relationships by empty boxes. For the supporting references, orange indicates upregulation, black indicates no observed change, and blue indicates downregulation. B. Model predicted absolute differences in steady state species activity when the inputs (intramural stress, wall shear stress (Wss), and AngII) are perturbed relative to baseline: orange denotes an increase and blue a decrease relative to the original steady state (white). These simulations correspond directly to the experimental findings, with model parameters tuned to achieve the best qualitative agreement (see S2 Appendix). We denote agreement and disagreement between model and experiments by check marks and crosses, respectively. Default uniform model parameters are n = 1.25, EC₅₀ = 0.55, b = 0.2 and p = 0.3 (Eqs 1–4), with weights w = 1 (see Methods). TGFB: transforming growth factor-β, MMP: matrix metalloproteinase, TSP1: thrombospondin-1, TIMP: tissue inhibitor of MMPs, NO: nitric oxide, and ET1: endothelin-1.

Fig 3. Network sensitivity analysis as each node is perturbed.

For a separate individual partial knockdown of each of the 45 interior nodes (Y_max = 1 to Y_max = 0.1), we calculate absolute differences (knockdown–reference) in steady state activity of every other species (y–axis). The marked cases (1)–(4) are discussed in the main text. In both the reference and knockdown cases, uniform initial conditions, y₀ = 0.2, are used for four of the inputs: Stress, AngIIin, SACs, and Integrins, whereas Wss = 0.5.

Fig 4. Species responses to exogenous AngII under three levels of baseline stress.

We show model outputs (relative to the baseline case, Stress = AngII = b) for four species of interest in response to three levels of stress, σ: low (b), intermediate (b + p), and high (b + 2p), as well as low (b) and high (b + 2p) AngII inputs. Arrows show general trends, with the MMPs exhibiting three different qualitative behaviors, the first two of which were similar to those observed in Figs 1–3 in [39].

Fig 5. Model dose-response surfaces to Stress and AngII and consequences of non-monotonicity.

A. Output steady states of 6 species of interest as a function of Stress and AngII inputs, yielding dose-response surfaces. B. Cross-section of the MMP9 surface showing how MMP activity can first increase and then decrease in response to Stress, here with AngII = 0. C. Cross-section of the MMP9 surface showing that intermediate and high baseline Stress can lead to either initial increases or decreases in MMP activity as AngII is applied.

Fig 6. Model-predicted collagen mRNA expression for control, AngII, and p38 MAPK knockdowns as wall stress increases.

We show fold-change expressions of collagen type I and collagen type III mRNA with three levels of stress (y_Stress = σ = {0.2, 0.3, 0.4}), with and without AngII (y_AngIIin = {0, 0.2}). Bars are model outputs, and filled circles correspond to data from [52]. In the absence of AngII, we also simulate a p38 MAPK inhibitor (via a knockdown to 10% maximal activity), which corresponds to findings in Fig 5D,E in [52]. Note that the default Hill parameters were not refined to achieve quantitative agreement, which was considerable nonetheless.