GPS for QSP: A Summary of the ACoP6 Symposium on Quantitative Systems Pharmacology and a Stage for Near-Term Efforts in the Field.

Quantitative Systems Pharmacology (QSP) is experiencing increased application in the drug discovery and development process. Like its older sibling, systems biology, the QSP field is comprised of a mix of established disciplines and methods, from molecular biology to engineering to pharmacometrics. As a result, there exist critical segments of the discipline that differ dramatically in approach and a need to bring these groups together toward a common goal.

Systematic Analysis of Quantitative Logic Model Ensembles Predicts Drug Combination Effects on Cell Signaling Networks.

A major challenge in developing anticancer therapies is determining the efficacies of drugs and their combinations in physiologically relevant microenvironments. We describe here our application of "constrained fuzzy logic" (CFL) ensemble modeling of the intracellular signaling network for predicting inhibitor treatments that reduce the phospho-levels of key transcription factors downstream of growth factors and inflammatory cytokines representative of hepatocellular carcinoma (HCC) microenvironments. We observed that the CFL models successfully predicted the effects of several kinase inhibitor combinations. Furthermore, the ensemble predictions revealed ambiguous predictions that could be traced to a specific structural feature of these models, which we resolved with dedicated experiments, finding that IL-1α activates downstream signals through TAK1 and not MEKK1 in HepG2 cells. We conclude that CFL-Q2LM (Querying Quantitative Logic Models) is a promising approach for predicting effective anticancer drug combinations in cancer-relevant microenvironments.

Distinct genital tract HIV-specific antibody profiles associated with tenofovir gel.

The impact of topical antiretrovirals for pre-exposure prophylaxis on humoral responses following HIV infection is unknown. Using a binding antibody multiplex assay, we investigated HIV-specific IgG and IgA responses to envelope glycoproteins, p24 Gag and p66, in the genital tract (GT) and plasma following HIV acquisition in women assigned to tenofovir gel (n=24) and placebo gel (n=24) in the CAPRISA 004 microbicide trial to assess if this topical antiretroviral had an impact on mucosal and systemic antibody responses. Linear mixed effect modeling and partial least squares discriminant analysis was used to identify multivariate antibody signatures associated with tenofovir use. There were significantly higher response rates to gp120 Env (P=0.03), p24 (P=0.002), and p66 (P=0.009) in plasma and GT in women assigned to tenofovir than placebo gel at multiple time points post infection. Notably, p66 IgA titers in the GT and plasma were significantly higher in the tenofovir compared with the placebo arm (P<0.05). Plasma titers for 9 of the 10 HIV-IgG specificities predicted GT levels. Taken together, these data suggest that humoral immune responses are increased in blood and GT of individuals who acquire HIV infection in the presence of tenofovir gel.

Physiome-on-a-Chip: The Challenge of "Scaling" in Design, Operation, and Translation of Microphysiological Systems.

Scaling of a microphysiological system (MPS) or physiome-on-a-chip is arguably two interrelated, modeling-based activities: on-platform scaling and in vitro-in vivo translation. This dual approach reduces the need to perfectly rescale and mimic in vivo physiology, an aspiration that is both extremely challenging and not substantively meaningful because of uncertain relevance of any specific physiological condition. Accordingly, this perspective offers a tractable approach for designing interacting MPSs and relating in vitro results to analogous context in vivo.

Quantitative Systems Pharmacology Approaches Applied to Microphysiological Systems (MPS): Data Interpretation and Multi-MPS Integration.

Our goal in developing Microphysiological Systems (MPS) technology is to provide an improved approach for more predictive preclinical drug discovery via a highly integrated experimental/computational paradigm. Success will require quantitative characterization of MPSs and mechanistic analysis of experimental findings sufficient to translate resulting insights from in vitro to in vivo. We describe herein a systems pharmacology approach to MPS development and utilization that incorporates more mechanistic detail than traditional pharmacokinetic/pharmacodynamic (PK/PD) models. A series of studies illustrates diverse facets of our approach. First, we demonstrate two case studies: a PK data analysis and an inflammation response--focused on a single MPS, the liver/immune MPS. Building on the single MPS modeling, a theoretical investigation of a four-MPS interactome then provides a quantitative way to consider several pharmacological concepts such as absorption, distribution, metabolism, and excretion in the design of multi-MPS interactome operation and experiments.

Direct Lyapunov exponent analysis enables parametric study of transient signalling governing cell behaviour.

Computational models aid in the quantitative understanding of cell signalling networks. One important goal is to ascertain how multiple network components work together to govern cellular responses, that is, to determine cell 'signal-response' relationships. Several methods exist to study steady-state signals in the context of differential equation-based models. However, many biological networks influence cell behaviour through time-varying signals operating during a transient activated state that ultimately returns to a basal steady-state. A computational approach adapted from dynamical systems analysis to discern how diverse transient signals relate to alternative cell fates is described. Direct finite-time Lyapunov exponents (DLEs) are employed to identify phase-space domains of high sensitivity to initial conditions. These domains delineate regions exhibiting qualitatively different transient activities that would be indistinguishable using steady-state analysis but which correspond to different outcomes. These methods are applied to a physicochemical model of molecular interactions among caspase-3, caspase-8 and X-linked inhibitor of apoptosis--proteins whose transient activation determines cell death against survival fates. DLE analysis enabled identification of a separatrix that quantitatively characterises network behaviour by defining initial conditions leading to apoptotic cell death. It is anticipated that DLE analysis will facilitate theoretical investigation of phenotypic outcomes in larger models of signalling networks.

Computational modelling of ErbB family phosphorylation dynamics in response to transforming growth factor alpha and heregulin indicates spatial compartmentation of phosphatase activity.

Members of the ErbB receptor family are associated with several cancers and appear to be providing useful targets for pharmacological therapeutics for tumours of the lung and breast. Further improvements of these therapies may be guided by a quantitative, dynamic integrative systems understanding of the complexities of ErbB dimerisation, trafficking and activation, for it is these complexities that render difficult intuiting how perturbations such as drug intervention will affect ErbB signalling activities. Towards this goal, we have developed a computational model implementing commonly accepted principles governing ErbB receptor interaction, trafficking, phosphorylation and dephosphorylation. Using this model, we are able to investigate several hypotheses regarding the compartmental localisation of dephosphorylation. Model results applied to experimental data on ErbB 1, ErbB2 and ErbB3 phosphorylation in H292 human lung carcinoma cells support a hypothesis that key dephosphorylation activity for these receptors occurs largely in an intracellular, endosomal compartment rather than at the cell surface plasma membrane. Thus, the endocytic trafficking-related compartmentalisation of dephosphorylation may define a critical aspect of the ErbB signalling response to ligand.

Quantitative comparison of polyethylenimine formulations and adenoviral vectors in terms of intracellular gene delivery processes.

An objective of designing molecular vehicles exhibiting virus-like transgene delivery capabilities but with low toxicity and immunogenicity continues to drive synthetic vector development. As no single step within the gene delivery pathway represents the critical limiting barrier for all vector types under all circumstances, improvements in synthetic vehicle design may be aided by quantitative analysis of the contributions of each step to the overall delivery process. To our knowledge, however, synthetic and viral gene delivery methods have not yet been explicitly compared in terms of these delivery pathway steps in a quantitative manner. As a first address of this challenge, we compare here quantitative parameters characterizing intracellular gene delivery steps for an E1/E3-deleted adenoviral vector and three polyethylenimine (PEI)-based vector formulations, as well as the liposomal transfection reagent Lipofectamine and naked DNA; the cargo is a plasmid encoding the beta-galactosidase gene under a CMV promoter, and the cell host is the C3A human hepatocellular carcinoma line. The parameters were determined by applying a previously validated mathematical model to transient time-course measurements of plasmid uptake and trafficking (from whole-cell and isolated nuclei lysates, by real-time quantitative PCR), and gene expression levels, enabling discovery of those for which the adenoviral vector manifested superiority. Parameter-sensitivity analysis permitted identification of processes most critically rate-limiting for each vector. We find that the adenoviral vector advantage in delivery appears to reside partially in its import to the nuclear compartment, but that its vast superiority in transgene expression arises predominantly in our situation from postdelivery events: on the basis of per-nuclear plasmid, expression efficiency from adenovirus is superior by orders of magnitude over the PEI vectors. We find that a chemical modification of a PEI-based vector, which substantially improves its performance, appears to do so by enhancing certain trafficking rate parameters, such as binding and uptake, endosomal escape, and binding to nuclear import machinery, but leaves endosomal escape as a barrier over which transgene delivery could be most sensitively increased further for this polymer.

Motile chondrocytes from newborn calf: migration properties and synthesis of collagen II.

OBJECTIVE: To determine whether differentiated chondrocytes are motile. DESIGN: Calf articular chondrocytes isolated from six animals were cultured in spinner flasks and removed on days 3 and 7. Boyden chamber assays and time-lapse videomicroscopy were performed to monitor and quantify cell migration. A novel method for selectively harvesting and metabolically labeling the migrated cells was developed, based on cell movement to the underside of the Boyden chamber membranes. The 3H-collagen synthesized by these cells was purified and analyzed by SDS-PAGE and autoradiography either before or after cyanogen bromide cleavage. RESULTS: In Boyden chambers, locomotion of day 3 chondrocytes on fibronectin-coated membranes was approximately 3-fold higher than on bovine serum albumin-coated controls (39+/-15 vs 12+/-8 cells/mm(2), respectively (P=0.005)). Insulin-like growth factor-I (IGF-I, 10 ng/ml) was chemotactic, increasing motility to 87+/-16 cells/mm(-) (difference from fibronectin alone: P=0.0003). A similar response was observed for day 7 cells, but IGF-I activation was not as pronounced (P=0.055). The collagen patterns produced by the migrated cells closely resembled those of standard collagen type II, without any evidence of collagen I production. In videotracking experiments, motile cells attached on fibronectin exhibited typical lamellipodia and filopodia, and approximately 30% of attached cells were motile (speed >1 micro m/h and directional persistence >1h). Typical cell path lengths were 30-50 micro m, substantially greater than a full cell length displacement. CONCLUSION: A population of well-differentiated chondrocytes capable of matrix (COL II) synthesis are motile in vitro. This original finding opens new avenues to study the potential of motile cells for cartilage repair.

Autocrine loops with positive feedback enable context-dependent cell signaling.

We describe a mechanism for context-dependent cell signaling mediated by autocrine loops with positive feedback. We demonstrate that the composition of the extracellular medium can critically influence the intracellular signaling dynamics induced by extracellular stimuli. Specifically, in the epidermal growth factor receptor (EGFR) system, amplitude and duration of mitogen-activated protein kinase (MAPK) activation are modulated by the positive-feedback loop formed by the EGFR, the Ras-MAPK signaling pathway, and a ligand-releasing protease. The signaling response to a transient input is short-lived when most of the released ligand is lost to the cellular microenvironment by diffusion and/or interaction with an extracellular ligand-binding component. In contrast, the response is prolonged or persistent in a cell that is efficient in recapturing the endogenous ligand. To study functional capabilities of autocrine loops, we have developed a mathematical model that accounts for ligand release, transport, binding, and intracellular signaling. We find that context-dependent signaling arises as a result of dynamic interaction between the parts of an autocrine loop. Using the model, we can directly interpret experimental observations on context-dependent responses of autocrine cells to ionizing radiation. In human carcinoma cells, MAPK signaling patterns induced by a short pulse of ionizing radiation can be transient or sustained, depending on cell type and composition of the extracellular medium. On the basis of our model, we propose that autocrine loops in this, and potentially other, growth factor and cytokine systems may serve as modules for context-dependent cell signaling.

Quantitative analysis of synthetic gene delivery vector design properties.

As intracellular gene delivery pathways are highly complex combinations of multiple potentially rate-limiting cellular and molecular processes, approaches to the design of synthetic delivery vectors focusing on any single barrier individually will likely be suboptimal. We offer here an "integrative systems" approach to vector characterization and design, combining quantitative experiment and computational modeling studies of vector uptake and trafficking kinetics. This model is validated using data for delivery of a green fluorescent protein (GFP)-encoding plasmid by means of Lipofectamine, permitting specification of model parameter values. The model is then used to make a priori predictions on the effect of polymer length in polyplex vectors, with additional parameter values determined from previous independent experimental studies of plasmid release. Comparison with data on GFP expression via these polyplex vectors shows that the model successfully predicts an experimentally observed biphasic dependence of expression efficiency on polymer length and quantifies the contributions of competing effects yielding the optimal intermediate polymer length. Finally, we use the model to predict potential effects of incorporating nuclear localization sequences in these kinds of synthetic vectors, and find that the degree of benefit from these will depend on the values of other key system properties including the vector unpackaging rate constant. Thus, we demonstrate the usefulness of a bioengineering, integrative-systems modeling approach to improved vector design and analysis.

A mathematical model for chemoattractant gradient sensing based on receptor-regulated membrane phospholipid signaling dynamics.

The crawling movement of cells in response to a chemoattractant gradient is a complex process requiring the coordination of various subcellular activities. Although a complete description of the mechanisms underlying cell movement remains elusive, the very first step of directional sensing, enabling the cell to perceive the imposed gradient, is becoming more transparent. A fundamental problem of directional sensing is its exquisite sensitivity. Even in the presence of relatively shallow chemoattractant gradients, cell projections are extended precisely in the region exposed to the highest chemoattractant concentration. This reflects the existence of a mechanism for amplifying the external signal. Recent experiments have identified a potential candidate for the seat of this amplification-membrane phosphoinositides such as PI4,5P2 and PI3,4,5P3 appear to be the first components of the signal transduction pathway to be amplified. Perturbing the cell with various chemoattractant gradients reveals a rich spectrum of phosphoinositide dynamics (Parent, C. A., and P. N. Devreotes. Science 284:765, 1999). The goal of this work is to develop a mathematical model of these phosphoinositide dynamics. Specifically, we address the following questions: (a) Which signaling pathway could lead to the localized accumulation of membrane phosphoinositides? (b) Why is this accumulation independent of the slope and mean value of the chemoattractant gradient? The model is based on the phosphoinositide cycle that transfers phosphoinositides between the plasma membrane and endoplasmic reticulum. We show that a mathematical model taking due account of receptor desensitization and the reaction-diffusion processes of the phosphoinositide cycle captures many of the experimentally observed dynamics. Having shown the plausibility of the model with respect to directional sensing, we discuss its implications for lamellipod extension, the process that follows directional sensing.

Methylation of episomal plasmids as a barrier to transient gene expression via a synthetic delivery vector.

Efficient and sustained transgene expression are desirable features for many envisioned gene therapy applications, yet synthetic vectors tested to date are rarely successful in achieving these properties. Substantial research efforts have focused on protection of plasmid DNA from nuclease attack as well as increasing nuclear transport of plasmids, resulting in significant but still limited gains. We show here that a further barrier to efficient and sustained expression exists for synthetic vectors: plasmid DNA methylation. We have investigated this barrier for transient expression of a green fluorescent protein (GFP) transgene delivered via Lipofectamine, by testing the effects of culturing C3A human hepatoblastoma cells with 5-Azacytidine (AzaC), an irreversible inhibitor of DNA methyltransferase. To control for loss of plasmids by dilution during mitosis, transfected cells were growth-arrested for 1 week and their subsequent GFP expression quantified by FACS. In the presence of AzaC, a significantly greater fraction of transfected cells remained GFP-positive and possessed higher levels of GFP production relative to AzaC-untreated cells. Additionally, we have applied a Methyl-Assisted PCR (MAP) assay to quantify a subset of methylated CpG sites in the GFP gene. When MAP was performed on plasmids isolated from transfected cells, the extent of methylation was found to be inversely related to the level of GFP expression.

Spatial range of autocrine signaling: modeling and computational analysis.

Autocrine loops formed by growth factors and their receptors have been identified in a large number of developmental, physiological, and pathological contexts. In general, the spatially distributed and recursive nature of autocrine signaling systems makes their experimental analysis, and often even their detection, very difficult. Here, we combine Brownian motion theory, Monte Carlo simulations, and reaction-diffusion models to analyze the spatial operation of autocrine loops. Within this modeling framework, the ability of autocrine cells to recapture the endogenous ligand and the distances traveled by autocrine ligands are explicitly related to ligand diffusion coefficients, density of surface receptors, ligand secretion rate, and rate constants of ligand binding and endocytic internalization. Applying our models to study autocrine loops in the epidermal growth factor receptor system, we find that autocrine loops can be highly localized--even at the level of a single cell. We demonstrate how the variations in molecular and cellular parameters may "tune" the spatial range of autocrine signals over several orders of magnitude: from microns to millimeters. We argue that this versatile regulation of the spatial range of autocrine signaling enables autocrine cells to perceive a broad spectrum of environmental information.

Quantitative analysis of the EGF receptor autocrine system reveals cryptic regulation of cell response by ligand capture.

Autocrine signaling is important in normal tissue physiology as well as pathological conditions. It is difficult to analyze these systems, however, because they are both self-contained and recursive. To understand how parameters such as ligand production and receptor expression influence autocrine activity, we investigated a human epidermal growth factor/epidermal growth factor receptor (EGF/EGFR) loop engineered into mouse B82 fibroblasts. We varied the level of ligand production using the tet-off expression system and used metalloprotease inhibitors to modulate ligand release. Receptor expression was varied using antagonistic blocking antibodies. We compared autocrine ligand release with receptor activation using a microphysiometer-based assay and analyzed our data using a quantitative model of ligand release and receptor dynamics. We found that the activity of our autocrine system could be described in terms of a simple ratio between the rate of ligand production (V(LT)) and the rate of receptor production (V(R)). At a V(LT)/V(R) ratio of <0.3, essentially no ligand was found in the extracellular medium, but a significant number of cell receptors (30-40%) were occupied. As the V(LT)/V(R) ratio increased from 0.3 towards unity, receptor occupancy increased and significant amounts of ligand appeared in the medium. Above a V(LT)/V(R) ratio of 1.0, receptor occupancy approached saturation and most of the released ligand was lost into the medium. Analysis of human mammary epithelial cells showed that a V(LT)/V(R) ratio of < 5 x 10(-4)was sufficient to evoke >20% of a maximal proliferative response. This demonstrates that natural autocrine systems can be active even when no ligand appears in the extracellular medium.

Molecular properties in cell adhesion: a physical and engineering perspective.

The past several years have seen accelerating growth in research directed towards the understanding and control of cell adhesion processes, from a spectrum of disciplinary approaches including molecular cell biology, biochemistry, biophysics and bioengineering. Consequently, our understanding of the mechanisms involved in cell adhesion has increased substantially. Corresponding quantitative analysis and modeling of the key molecular properties governing their action in regulating dynamic cell attachment and detachment events is crucial for advancing conceptual insight along with technological applications.