Time and length scales of autocrine signals in three dimensions

A model of autocrine signaling in cultures of suspended cells is developed on the basis of the effective medium approximation. The fraction of autocrine ligands, the mean and distribution of distances traveled by paracrine ligands before binding, as well as the mean and distribution of the ligand lifetime are derived. Interferon signaling by dendritic immune cells is considered as an illustration.Comment: 15 page

Epidermal growth factor (EGF)-like repeats of human tenascin-C as ligands for EGF receptor.

Signaling through growth factor receptors controls such diverse cell functions as proliferation, migration, and differentiation. A critical question has been how the activation of these receptors is regulated. Most, if not all, of the known ligands for these receptors are soluble factors. However, as matrix components are highly tissue-specific and change during development and pathology, it has been suggested that select growth factor receptors might be stimulated by binding to matrix components. Herein, we describe a new class of ligand for the epidermal growth factor (EGF) receptor (EGFR) found within the EGF-like repeats of tenascin-C, an antiadhesive matrix component present during organogenesis, development, and wound repair. Select EGF-like repeats of tenascin-C elicited mitogenesis and EGFR autophosphorylation in an EGFR-dependent manner. Micromolar concentrations of EGF-like repeats induced EGFR autophosphorylation and activated extracellular signal-regulated, mitogen-activated protein kinase to levels comparable to those induced by subsaturating levels of known EGFR ligands. EGFR-dependent adhesion was noted when the ligands were tethered to inert beads, simulating the physiologically relevant presentation of tenascin-C as hexabrachion, and suggesting an increase in avidity similar to that seen for integrin ligands upon surface binding. Specific binding to EGFR was further established by immunofluorescence detection of EGF-like repeats bound to cells and cross-linking of EGFR with the repeats. Both of these interactions were abolished upon competition by EGF and enhanced by dimerization of the EGF-like repeat. Such low affinity behavior would be expected for a matrix-tethered ligand; i.e., a ligand which acts from the matrix, presented continuously to cell surface EGF receptors, because it can neither diffuse away nor be internalized and degraded. These data identify a new class of insoluble growth factor ligands and a novel mode of activation for growth factor receptors

Asymptotic amplitudes and cauchy gains: A small-gain principle and an application to inhibitory biological feedback

The notions of asymptotic amplitude for signals, and Cauchy gain for input/output systems, and an associated small-gain principle, are introduced. These concepts allow the consideration of systems with multiple, and possibly feedback-dependent, steady states. A Lyapunov-like characterization allows the computation of gains for state-space systems, and the formulation of sufficient conditions insuring the lack of oscillations and chaotic behaviors in a wide variety of cascades and feedback loops. An application in biology (MAPK signaling) is worked out in detail.Comment: Updates and replaces math.OC/0112021 See http://www.math.rutgers.edu/~sontag/ for related wor

Multiscale analysis and simulation of a signalling process with surface diffusion

We present and analyze a model for cell signaling processes in biological tissues. The model includes diffusion and nonlinear reactions on the cell surfaces and both inter- and intracellular signaling. Using techniques from the theory of two-scale convergence as well the unfolding method, we show convergence of the solutions to the model to solutions of a two-scale macroscopic problem. We also present a two-scale bulk-surface finite element method for the approximation of the macroscopic model. We report on some benchmarking results as well as numerical simulations in a biologically relevant regime that illustrate the influence of cell-scale heterogeneities on macroscopic concentrations

An "All Possible Steps" Approach to the Accelerated Use of Gillespie's Algorithm

Many physical and biological processes are stochastic in nature. Computational models and simulations of such processes are a mathematical and computational challenge. The basic stochastic simulation algorithm was published by D. Gillespie about three decades ago [D.T. Gillespie, J. Phys. Chem. {\bf 81}, 2340, (1977)]. Since then, intensive work has been done to make the algorithm more efficient in terms of running time. All accelerated versions of the algorithm are aimed at minimizing the running time required to produce a stochastic trajectory in state space. In these simulations, a necessary condition for reliable statistics is averaging over a large number of simulations. In this study I present a new accelerating approach which does not alter the stochastic algorithm, but reduces the number of required runs. By analysis of collected data I demonstrate high precision levels with fewer simulations. Moreover, the suggested approach provides a good estimation of statistical error, which may serve as a tool for determining the number of required runs.Comment: Accepted for publication at the Journal of Chemical Physics. 19 pages, including 2 Tables and 4 Figure

A passivity-based stability criterion for a class of interconnected systems and applications to biochemical reaction networks

This paper presents a stability test for a class of interconnected nonlinear systems motivated by biochemical reaction networks. One of the main results determines global asymptotic stability of the network from the diagonal stability of a "dissipativity matrix" which incorporates information about the passivity properties of the subsystems, the interconnection structure of the network, and the signs of the interconnection terms. This stability test encompasses the "secant criterion" for cyclic networks presented in our previous paper, and extends it to a general interconnection structure represented by a graph. A second main result allows one to accommodate state products. This extension makes the new stability criterion applicable to a broader class of models, even in the case of cyclic systems. The new stability test is illustrated on a mitogen activated protein kinase (MAPK) cascade model, and on a branched interconnection structure motivated by metabolic networks. Finally, another result addresses the robustness of stability in the presence of diffusion terms in a compartmental system made out of identical systems.Comment: See http://www.math.rutgers.edu/~sontag/PUBDIR/index.html for related (p)reprint

Compensatory effects in the PI3K/PTEN/AKT signaling network following receptor tyrosine kinase inhibition

Overcoming de novo and acquired resistance to anticancer drugs that target signaling networks is a formidable challenge for drug design and effective cancer therapy. Understanding the mechanisms by which this resistance arises may offer a route to addressing the insensitivity of signaling networks to drug intervention and restore the efficacy of anticancer therapy. Extending our recent work identifying PTEN as a key regulator of Herceptin sensitivity, we present an integrated theoretical and experimental approach to study the compensatory mechanisms within the PI3K/PTEN/AKT signaling network that afford resistance to receptor tyrosine kinase (RTK) inhibition by anti-HER2 monoclonal antibodies. In a computational model representing the dynamics of the signaling network, we define a single control parameter that encapsulates the balance of activities of the enzymes involved in the PI3K/PTEN/AKT cycle. By varying this control parameter we are able to demonstrate both distinct dynamic regimes of behavior of the signaling network and the transitions between those regimes. We demonstrate resistance, sensitivity, and suppression of RTK signals by the signaling network. Through model analysis we link the sensitivity-to-resistance transition to specific compensatory mechanisms within the signaling network. We study this transition in detail theoretically by variation of activities of PTEN, PI3K, AKT enzymes, and use the results to inform experiments that perturb the signaling network using combinatorial inhibition of RTK, PTEN, and PI3K enzymes in human ovarian carcinoma cell lines. We find good alignment between theoretical predictions and experimental results. We discuss the application of the results to the challenges of hypersensitivity of the signaling network to RTK signals, suppression of drug resistance, and efficacy of drug combinations in anticancer therapy

Autocrine epidermal growth factor signaling stimulates directionally persistent mammary epithelial cell migration

Cell responses to soluble regulatory factors may be strongly influenced by the mode of presentation of the factor, as in matrix-bound versus diffusible modes. The possibly diverse effect of presenting a growth factor in autocrine as opposed to exogenous (or paracrine) mode is an especially important issue in cell biology. We demonstrate here that migration behavior of human mammary epithelial cells in response to stimulation by epidermal growth factor (EGF) is qualitatively different for EGF presented in exogenous (paracrine), autocrine, and intracrine modes. When EGF is added as an exogenous factor to the medium of cells that express EGF receptor (EGFR) but not EGF, cell migration speed increases while directional persistence decreases. When these EGFR-expressing cells are made to also express via retroviral transfection EGF in protease-cleaveable transmembrane form on the plasma membrane, migration speed similarly increases, but directional persistence increases as well. Addition of exogenous EGF to these cells abrogates their enhanced directional persistence, reducing their directionality to a level similar to wild-type cells. If the EGFR-expressing cells are instead transduced with a gene encoding EGF in a soluble form, migration speed and directional persistence were unaffected. Thus, autocrine presentation of EGF at the plasma membrane in a protease-cleavable form provides these cells with an enhanced ability to migrate persistently in a given direction, consistent with their increased capability for organizing into gland-like structures. In contrast, an exogenous/paracrine mode of EGF presentation generates a “scattering” response by the cells. These findings emphasize the functional importance of spatial restriction of EGFR signaling, and suggest critical implications for growth factor–based therapeutic treatments