Physiological Indirect Response Model to Omics-Powered Quantitative Systems Pharmacology Model.

Over the past several decades, mathematical modeling has been applied to increasingly wider scopes of questions in drug development. Accordingly, the range of modeling tools has also been evolving, as showcased by contributions of Jusko and colleagues: from basic pharmacokinetics/pharmacodynamics (PK/PD) modeling to today's platform-based approach of quantitative systems pharmacology (QSP) modeling. Aimed at understanding the mechanism of action of investigational drugs, QSP models characterize systemic effects by incorporating information about cellular signaling networks, which is often represented by omics data. In this perspective, we share a few examples illustrating approaches for the integration of omics into mechanistic QSP modeling. We briefly overview how the evolution of PK/PD modeling into QSP has been accompanied by an increase in available data and the complexity of mathematical methods that integrate it. We discuss current gaps and challenges of integrating omics data into QSP models and propose several potential areas where integrated QSP and omics modeling may benefit drug development.

Persistent non-homeostatic remodeling of aortic collagen following a brief episode of hypertension: A computational study.

The healthy adult aorta exhibits a remarkable homeostatic ability to respond to sustained changes in hemodynamic loads under many circumstances, but this mechanical homeostasis can be compromised or lost in natural aging and diverse pathological processes. Herein, we investigate persistent non-homeostatic changes in the composition and mechanical properties of the thoracic aorta in adult wild-type mice following 14 days of angiotensin II-induced hypertension. We employ a multiscale computational model of arterial growth and remodeling driven by mechanosensitive and angiotensin II-related cell signaling pathways. We find that experimentally observed findings can only be recapitulated computationally if the collagen deposited during the transient period of hypertension has altered properties (deposition stretch, fiber angle, crosslinking) compared with the collagen produced in the original homeostatic state. Some of these changes are predicted to persist for at least six months after blood pressure is restored to normal levels, consistent with the experimental findings.

Intracellular signaling control of mechanical homeostasis in the aorta.

Mature arteries exhibit a preferred biomechanical state in health evidenced by a narrow range of intramural and wall shear stresses. When stresses are perturbed by changes in blood pressure or flow, homeostatic mechanisms tend to restore target values via altered contractility and/or cell and matrix turnover. In contrast, vascular disease associates with compromised homeostasis, hence we must understand mechanisms underlying mechanical homeostasis and its robustness. Here, we use a multiscale computational model wherein mechanosensitive intracellular signaling pathways drive arterial growth and remodeling. First, we identify an ensemble of cell-level parameterizations where tissue-level responses are well-regulated and adaptive to hemodynamic perturbations. The responsible mechanism is persistent multiscale negative feedback whereby mechanosensitive signaling drives mass turnover until homeostatic target stresses are reached. This demonstrates how robustness emerges despite inevitable cell and individual heterogeneity. Second, we investigate tissue-level effects of signaling node knockdowns (ATIR, ROCK, TGF[Formula: see text]RII, PDGFR, ERK1/2) and find general agreement with experimental reports of fault tolerance. Robustness against structural changes manifests via low engagement of the node under baseline stresses or compensatory multiscale feedback via upregulation of additional pathways. Third, we show how knockdowns affect collagen and smooth muscle turnover at baseline and with perturbed stresses. In several cases, basal production is not remarkably affected, but sensitivities to stress deviations, which influence feedback strength, are reduced. Such reductions can impair adaptive responses, consistent with previously reported aortic vulnerability despite grossly normal appearances. Reduced stress sensitivities thus form a candidate mechanism for how robustness is lost, enabling transitions from health towards disease.

Roles of mTOR in thoracic aortopathy understood by complex intracellular signaling interactions.

Thoracic aortopathy-aneurysm, dissection, and rupture-is increasingly responsible for significant morbidity and mortality. Advances in medical genetics and imaging have improved diagnosis and thus enabled earlier prophylactic surgical intervention in many cases. There remains a pressing need, however, to understand better the underlying molecular and cellular mechanisms with the hope of finding robust pharmacotherapies. Diverse studies in patients and mouse models of aortopathy have revealed critical changes in multiple smooth muscle cell signaling pathways that associate with disease, yet integrating information across studies and models has remained challenging. We present a new quantitative network model that includes many of the key smooth muscle cell signaling pathways and validate the model using a detailed data set that focuses on hyperactivation of the mechanistic target of rapamycin (mTOR) pathway and its inhibition using rapamycin. We show that the model can be parameterized to capture the primary experimental findings both qualitatively and quantitatively. We further show that simulating a population of cells by varying receptor reaction weights leads to distinct proteomic clusters within the population, and that these clusters emerge due to a bistable switch driven by positive feedback in the PI3K/AKT/mTOR signaling pathway.

From Transcript to Tissue: Multiscale Modeling from Cell Signaling to Matrix Remodeling.

Tissue-level biomechanical properties and function derive from underlying cell signaling, which regulates mass deposition, organization, and removal. Here, we couple two existing modeling frameworks to capture associated multiscale interactions-one for vessel-level growth and remodeling and one for cell-level signaling-and illustrate utility by simulating aortic remodeling. At the vessel level, we employ a constrained mixture model describing turnover of individual wall constituents (elastin, intramural cells, and collagen), which has proven useful in predicting diverse adaptations as well as disease progression using phenomenological constitutive relations. Nevertheless, we now seek an improved mechanistic understanding of these processes; we replace phenomenological relations in the mixture model with a logic-based signaling model, which yields a system of ordinary differential equations predicting changes in collagen synthesis, matrix metalloproteinases, and cell proliferation in response to altered intramural stress, wall shear stress, and exogenous angiotensin II. This coupled approach promises improved understanding of the role of cell signaling in achieving tissue homeostasis and allows us to model feedback between vessel mechanics and cell signaling. We verify our model predictions against data from the hypertensive murine infrarenal abdominal aorta as well as results from validated phenomenological models, and consider effects of noisy signaling and heterogeneous cell populations.

Cell signaling model for arterial mechanobiology.

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.

Switching behaviour in vascular smooth muscle cell-matrix adhesion during oscillatory loading.

Integrins regulate mechanotransduction between smooth muscle cells (SMCs) and the extracellular matrix (ECM). SMCs resident in the walls of airways or blood vessels are continuously exposed to dynamic mechanical forces due to breathing or pulsatile blood flow. However, the resulting effects of these forces on integrin dynamics and associated cell-matrix adhesion are not well understood. Here we present experimental results from atomic force microscopy (AFM) experiments, designed to study the integrin response to external oscillatory loading of varying amplitudes applied to live aortic SMCs, together with theoretical results from a mathematical model. In the AFM experiments, a fibronectin-coated probe was used cyclically to indent and retract from the surface of the cell. We observed a transition between states of firm adhesion and of complete detachment as the amplitude of oscillatory loading increased, revealed by qualitative changes in the force timecourses. Interestingly, for some of the SMCs in the experiments, switching behaviour between the two adhesion states is observed during single timecourses at intermediate amplitudes. We obtain two qualitatively similar adhesion states in the mathematical model, where we simulate the cell, integrins and ECM as an evolving system of springs, incorporating local integrin binding dynamics. In the mathematical model, we observe a region of bistability where both the firm adhesion and detachment states can occur depending on the initial adhesion state. The differences are seen to be a result of mechanical cooperativity of integrins and cell deformation. Switching behaviour is a phenomenon associated with bistability in a stochastic system, and bistability in our deterministic mathematical model provides a potential physical explanation for the experimental results. Physiologically, bistability provides a means for transient mechanical stimuli to induce long-term changes in adhesion dynamics-and thereby the cells' ability to transmit force-and we propose further experiments for testing this hypothesis.

Effect of Loading History on Airway Smooth Muscle Cell-Matrix Adhesions.

Integrin-mediated adhesions between airway smooth muscle (ASM) cells and the extracellular matrix (ECM) regulate how contractile forces generated within the cell are transmitted to its external environment. Environmental cues are known to influence the formation, size, and survival of cell-matrix adhesions, but it is not yet known how they are affected by dynamic fluctuations associated with tidal breathing in the intact airway. Here, we develop two closely related theoretical models to study adhesion dynamics in response to oscillatory loading of the ECM, representing the dynamic environment of ASM cells in vivo. Using a discrete stochastic-elastic model, we simulate individual integrin binding and rupture events and observe two stable regimes in which either bond formation or bond rupture dominate, depending on the amplitude of the oscillatory loading. These regimes have either a high or low fraction of persistent adhesions, which could affect the level of strain transmission between contracted ASM cells and the airway tissue. For intermediate loading, we observe a region of bistability and hysteresis due to shared loading between existing bonds; the level of adhesion depends on the loading history. These findings are replicated in a related continuum model, which we use to investigate the effect of perturbations mimicking deep inspirations (DIs). Because of the bistability, a DI applied to the high adhesion state could either induce a permanent switch to a lower adhesion state or allow a return of the system to the high adhesion state. Transitions between states are further influenced by the frequency of oscillations, cytoskeletal or ECM stiffnesses, and binding affinities, which modify the magnitudes of the stable adhesion states as well as the region of bistability. These findings could explain (in part) the transient bronchodilatory effect of a DI observed in asthmatics compared to a more sustained effect in normal subjects.