A guide to ERK dynamics, part 1: mechanisms and models

Extracellular signal-regulated kinase (ERK) has long been studied as a key driver of both essential cellular processes and disease. A persistent question has been how this single pathway is able to direct multiple cell behaviors, including growth, proliferation, and death. Modern biosensor studies have revealed that the temporal pattern of ERK activity is highly variable and heterogeneous, and critically, that these dynamic differences modulate cell fate. This two-part review discusses the current understanding of dynamic activity in the ERK pathway, how it regulates cellular decisions, and how these cell fates lead to tissue regulation and pathology. In part 1, we cover the optogenetic and live-cell imaging technologies that first revealed the dynamic nature of ERK, as well as current challenges in biosensor data analysis. We also discuss advances in mathematical models for the mechanisms of ERK dynamics, including receptor-level regulation, negative feedback, cooperativity, and paracrine signaling. While hurdles still remain, it is clear that higher temporal and spatial resolution provide mechanistic insights into pathway circuitry. Exciting new algorithms and advanced computational tools enable quantitative measurements of single-cell ERK activation, which in turn inform better models of pathway behavior. However, the fact that current models still cannot fully recapitulate the diversity of ERK responses calls for a deeper understanding of network structure and signal transduction in general.

A narrative review on the biology of piezo1 with platelet-rich plasma in cardiac cell regeneration

Cardiomyocyte regeneration following cardiac damage is challenging to study because of the inflammatory process, the multiplication of cells in the stroma, and the creation of scar tissue. In addition to the initial damage, the subsequent decrease in cardiac myocytes adds to heart failure. Piezo1 is remarkably understudied in the heart, which may be related to its recent discovery. Despite this, Piezo1 is expressed in a variety of cardiovascular cell populations, notably epithelial cells (EC), cardiac fibroblasts (CF), and cardiac myocytes (CM), in both animal and human samples, with fibroblasts expressing more than myocytes. Researchers have recently shown that disrupting Piezo1 signaling causes defects in zebrafish developing the outflow tract (OFT) and aortic valves. Platelet plasma membranes may provide lipid substrates, such as phosphatidylinositol bisphosphate, that aid in activating the piezo 1 ion channel in the cardiovascular system. In addition, CXC chemokine ligand 8/CXC chemokine receptor 1/2 (CXCL8-CXCR1/2) signaling was identified to establish the proliferation of coronary endothelial cells during cardiac regeneration. Notably, all these pathways are calcium-dependent, and cell proliferation and angiogenesis were necessary to recover myocardial cells. This review will examine the most current findings to understand further how platelet-rich plasma (PRP) and the piezo 1 channel might aid in cardiomyocyte regeneration.

Ligand-receptor promiscuity enables cellular addressing

In multicellular organisms, secreted ligands selectively activate, or "address," specific target cell populations to control cell fate decision-making and other processes. Key cell-cell communication pathways use multiple promiscuously interacting ligands and receptors, provoking the question of how addressing specificity can emerge from molecular promiscuity. To investigate this issue, we developed a general mathematical modeling framework based on the bone morphogenetic protein (BMP) pathway architecture. We find that promiscuously interacting ligand-receptor systems allow a small number of ligands, acting in combinations, to address a larger number of individual cell types, defined by their receptor expression profiles. Promiscuous systems outperform seemingly more specific one-to-one signaling architectures in addressing capability. Combinatorial addressing extends to groups of cell types, is robust to receptor expression noise, grows more powerful with increases in the number of receptor variants, and is maximized by specific biochemical parameter relationships. Together, these results identify design principles governing cellular addressing by ligand combinations.

CPPs to the Test: Effects on Binding, Uptake and Biodistribution of a Tumor Targeting Nanobody

Nanobodies are well-established targeting ligands for molecular imaging and therapy. Their short circulation time enables early imaging and reduces systemic radiation exposure. However, shorter circulation time leads to lower tracer accumulation in the target tissue. Cell-penetrating peptides (CPPs) improve cellular uptake of various cargoes, including nanobodies. CPPs could enhance tissue retention without compromising rapid clearance. However, systematic investigations on how the functionalities of nanobody and CPP combine with each other at the level of 2D and 3D cell cultures and in vivo are lacking. Here, we demonstrate that conjugates of the epidermal growth factor receptor (EGFR)-binding nanobody 7D12 with different CPPs (nonaarginine, penetratin, Tat and hLF) differ with respect to cell binding and induction of endocytosis. For nonaarginine and penetratin we compared the competition of EGF binding and performance of L- and D-peptide stereoisomers, and tested the D-peptide conjugates in tumor cell spheroids and in vivo. The D-peptide conjugates showed better penetration into spheroids than the unconjugated 7D12. Both in vivo and in vitro, the behavior of the agent reflects the combination of both functionalities. Although CPPs cause promising increases in in vitro uptake and 3D penetration, the dominant effect of the CPP in the control of biodistribution warrants further investigation.

Estimating drug potency in the competitive target mediated drug disposition (TMDD) system when the endogenous ligand is included

Predictions for target engagement are often used to guide drug development. In particular, when selecting the recommended phase 2 dose of a drug that is very safe, and where good biomarkers for response may not exist (e.g. in immuno-oncology), a receptor occupancy prediction could even be the main determinant in justifying the approved dose, as was the case for atezolizumab. The underlying assumption in these models is that when the drug binds its target, it disrupts the interaction between the target and its endogenous ligand, thereby disrupting downstream signaling. However, the interaction between the target and its endogenous binding partner is almost never included in the model. In this work, we take a deeper look at the in vivo system where a drug binds to its target and disrupts the target's interaction with an endogenous ligand. We derive two simple steady state inhibition metrics (SSIMs) for the system, which provides intuition for when the competition between drug and endogenous ligand should be taken into account for guiding drug development.

Systems-Level Properties of EGFR-RAS-ERK Signaling Amplify Local Signals to Generate Dynamic Gene Expression Heterogeneity

Intratumoral heterogeneity is associated with aggressive tumor behavior, therapy resistance, and poor patient outcomes. Such heterogeneity is thought to be dynamic, shifting over periods of minutes to hours in response to signaling inputs from the tumor microenvironment. However, models of this process have been inferred from indirect or post-hoc measurements of cell state, leaving the temporal details of signaling-driven heterogeneity undefined. Here, we developed a live-cell model system in which microenvironment-driven signaling dynamics can be directly observed and linked to variation in gene expression. Our analysis reveals that paracrine signaling between two cell types is sufficient to drive continual diversification of gene expression programs. This diversification emerges from systems-level properties of the EGFR-RAS-ERK signaling cascade, including intracellular amplification of amphiregulin-mediated paracrine signals and differential kinetic filtering by target genes including Fra-1, c-Myc, and Egr1. Our data enable more precise modeling of paracrine-driven transcriptional variation as a generator of gene expression heterogeneity. A record of this paper's transparent peer review process is included in the Supplemental Information.

A systems perspective of heterocellular signaling

Signal exchange between different cell types is essential for development and function of multicellular organisms, and its dysregulation is causal in many diseases. Unfortunately, most cell-signaling work has employed single cell types grown under conditions unrelated to their native context. Recent technical developments have started to provide the tools needed to follow signaling between multiple cell types, but gaps in the information they provide have limited their usefulness in building realistic models of heterocellular signaling. Currently, only targeted assays have the necessary sensitivity, selectivity, and spatial resolution to usefully probe heterocellular signaling processes, but these are best used to test specific, mechanistic models. Decades of systems biology research with monocultures has provided a solid foundation for building models of heterocellular signaling, but current models lack a realistic description of regulated proteolysis and the feedback processes triggered within and between cells. Identification and understanding of key regulatory processes in the extracellular environment and of recursive signaling patterns between cells will be essential to building predictive models of heterocellular systems.

3-Econsystems: MicroRNAs, Receptors, and Latent Viruses; Some Insights Biology Can Gain from Economic Theory

This mini-review describes three biological systems. All three include competing molecules and a limiting molecule that binds the competing molecules. Such systems are extensively researched by economists. In fact, the issue of limited resources is the defining feature of economic systems. Therefore, we call these systems "econsystems." In an econsystem, the allocation of the limiting molecule between the competing molecules determines the behavior of the system. A cell is an example of an econsystem. Therefore, a change in the allocation of a limiting molecule as a result of, for instance, an abnormal change in the concentration of one of the competing molecules, may result in abnormal cellular behavior, and disease. The first econsystem described in this mini-review includes a long non-coding RNA and a messenger RNA (lncRNA and mRNA). The limiting molecule is a microRNA (miRNA). The lncRNA and mRNA are known as competing endogenous RNAs (ceRNAs). The second econsystem includes two receptors, and the limiting molecule is a ligand. The third econsystem includes a cis-regulatory element of a latent virus and that of a human gene. The limiting molecule is a transcription complex that binds both cis-elements.

Targeting autocrine HB-EGF signaling with specific ADAM12 inhibition using recombinant ADAM12 prodomain

Dysregulation of ErbB-family signaling underlies numerous pathologies and has been therapeutically targeted through inhibiting ErbB-receptors themselves or their cognate ligands. For the latter, “decoy” antibodies have been developed to sequester ligands including heparin-binding epidermal growth factor (HB-EGF); however, demonstrating sufficient efficacy has been difficult. Here, we hypothesized that this strategy depends on properties such as ligand-receptor binding affinity, which varies widely across the known ErbB-family ligands. Guided by computational modeling, we found that high-affinity ligands such as HB-EGF are more difficult to target with decoy antibodies compared to low-affinity ligands such as amphiregulin (AREG). To address this issue, we developed an alternative method for inhibiting HB-EGF activity by targeting its cleavage from the cell surface. In a model of the invasive disease endometriosis, we identified A Disintegrin and Metalloproteinase 12 (ADAM12) as a protease implicated in HB-EGF shedding. We designed a specific inhibitor of ADAM12 based on its recombinant prodomain (PA12), which selectively inhibits ADAM12 but not ADAM10 or ADAM17. In endometriotic cells, PA12 significantly reduced HB-EGF shedding and resultant cellular migration. Overall, specific inhibition of ligand shedding represents a possible alternative to decoy antibodies, especially for ligands such as HB-EGF that exhibit high binding affinity and localized signaling.

Equilibrium and dynamic design principles for binding molecules engineered for reagentless biosensors

Reagentless biosensors rely on the interaction of a binding partner and its target to generate a change in fluorescent signal using an environment-sensitive fluorophore or Förster resonance energy transfer. Binding affinity can exert a significant influence on both the equilibrium and the dynamic response characteristics of such a biosensor. We here develop a kinetic model for the dynamic performance of a reagentless biosensor. Using a sinusoidal signal for ligand concentration, our findings suggest that it is optimal to use a binding moiety whose equilibrium dissociation constant matches that of the average predicted input signal, while maximizing both the association rate constant and the dissociation rate constant at the necessary ratio to create the desired equilibrium constant. Although practical limitations constrain the attainment of these objectives, the derivation of these design principles provides guidance for improved reagentless biosensor performance and metrics for quality standards in the development of biosensors. These concepts are broadly relevant to reagentless biosensor modalities.

Regenerative therapy and tissue engineering for the treatment of end-stage cardiac failure: new developments and challenges

Regeneration of myocardium through regenerative therapy and tissue engineering is appearing as a prospective treatment modality for patients with end-stage heart failure. Focusing on this area, this review highlights the new developments and challenges in the regeneration of myocardial tissue. The role of various cell sources, calcium ion and cytokine on the functional performance of regenerative therapy is discussed. The evolution of tissue engineering and the role of tissue matrix/scaffold, cell adhesion and vascularisation on tissue engineering of cardiac tissue implant are also discussed.

Three-dimensional perfused cell culture

Compelling evidence suggests the limitation and shortcomings of the current and well established cell culture method using multi-well plates, flasks and Petri dishes. These are particularly important when cell functions are sensitive to the local microenvironment, cell-cell and cell-extracellular matrix interactions. There is a clear need for advanced cell culture systems which mimic in vivo and more physiological conditions. This review summarises and analyses recent progress in three dimensional (3D) cell culture with perfusion as the next generation cell culture tools, while excluding engineered tissue culture where three dimensional scaffold has to be used for structural support and perfusion for overcoming mass transfer control. Apart from research activities in academic community, product development in industry is also included in this review.

Understanding cytokine and growth factor receptor activation mechanisms

Our understanding of the detailed mechanism of action of cytokine and growth factor receptors - and particularly our quantitative understanding of the link between structure, mechanism and function - lags significantly behind our knowledge of comparable functional protein classes such as enzymes, G protein-coupled receptors, and ion channels. In particular, it remains controversial whether such receptors are activated by a mechanism of ligand-induced oligomerization, versus a mechanism in which the ligand binds to a pre-associated receptor dimer or oligomer that becomes activated through subsequent conformational rearrangement. A major limitation to progress has been the relative paucity of methods for performing quantitative mechanistic experiments on unmodified receptors expressed at endogenous levels on live cells. In this article, we review the current state of knowledge on the activation mechanisms of cytokine and growth factor receptors, critically evaluate the evidence for and against the different proposed mechanisms, and highlight other key questions that remain unanswered. New approaches and techniques have led to rapid recent progress in this area, and the field is poised for major advances in the coming years which promise to revolutionize our understanding of this large and biologically and medically important class of receptors.

Advances in biomimetic regeneration of elastic matrix structures

Elastin is a vital component of the extracellular matrix, providing soft connective tissues with the property of elastic recoil following deformation and regulating the cellular response via biomechanical transduction to maintain tissue homeostasis. The limited ability of most adult cells to synthesize elastin precursors and assemble them into mature crosslinked structures has hindered the development of functional tissue-engineered constructs that exhibit the structure and biomechanics of normal native elastic tissues in the body. In diseased tissues, the chronic overexpression of proteolytic enzymes can cause significant matrix degradation, to further limit the accumulation and quality (e.g., fiber formation) of newly deposited elastic matrix. This review provides an overview of the role and importance of elastin and elastic matrix in soft tissues, the challenges to elastic matrix generation in vitro and to regenerative elastic matrix repair in vivo, current biomolecular strategies to enhance elastin deposition and matrix assembly, and the need to concurrently inhibit proteolytic matrix disruption for improving the quantity and quality of elastogenesis. The review further presents biomaterial-based options using scaffolds and nanocarriers for spatio-temporal control over the presentation and release of these biomolecules, to enable biomimetic assembly of clinically relevant native elastic matrix-like superstructures. Finally, this review provides an overview of recent advances and prospects for the application of these strategies to regenerating tissue-type specific elastic matrix structures and superstructures.

Migration of connective tissue-derived cells is mediated by ultra-low concentration gradient fields of EGF

The directed migration of cells towards chemical stimuli incorporates simultaneous changes in both the concentration of a chemotactic agent and its concentration gradient, each of which may influence cell migratory response. In this study, we utilized a microfluidic system to examine the interactions between epidermal growth factor (EGF) concentration and EGF gradient in stimulating the chemotaxis of connective tissue-derived fibroblast cells. Cells seeded within microfluidic devices were exposed to concentration gradients established by EGF concentrations that matched or exceeded those required for maximum chemotactic responses seen in transfilter migration assays. The migration of individual cells within the device was measured optically after steady-state gradients had been experimentally established. Results illustrate that motility was maximal at EGF concentration gradients between .01- and 0.1-ng/(mL.mm) for all concentrations used. In contrast, the number of motile cells continually increased with increasing gradient steepness for all concentrations examined. Microfluidics-based experiments exposed cells to minute changes in EGF concentration and gradient that were in line with the acute EGFR phosphorylation measured. Correlation of experimental data with established mathematical models illustrated that the fibroblasts studied exhibit an unreported chemosensitivity to minute changes in EGF concentration, similar to that reported for highly motile cells, such as macrophages. Our results demonstrate that shallow chemotactic gradients, while previously unexplored, are necessary to induce the rate of directed cellular migration and the number of motile cells in the connective tissue-derived cells examined.

Autocrine-controlled formation and function of tissue-like aggregates by primary hepatocytes in micropatterned hydrogel arrays

The liver carries out a variety of essential functions regulated in part by autocrine signaling, including hepatocyte-produced growth factors and extracellular matrix (ECM). The local concentrations of autocrine factors are governed by a balance between receptor-mediated binding at the cell surface and diffusion into the local matrix and are thus expected to be influenced by the dimensionality of the cell culture environment. To investigate the role of growth factor and ECM-modulated autocrine signaling in maintaining appropriate primary hepatocyte survival, metabolic functions, and polarity, we created three-dimensional cultures of defined geometry using micropatterned semisynthetic polyethylene glycol-fibrinogen hydrogels to provide a mechanically compliant, nonadhesive material platform that could be modified by cell-secreted factors. We found that in the absence of exogenous peptide growth factors or ECM, hepatocytes retain the epidermal growth factor (EGF) receptor ligands (EGF and transforming growth factor-α) and the proto-oncogenic mesenchymal epithelial transition factor (c-MET) ligand hepatocyte growth factor (HGF), along with fibronectin. Further, hepatocytes cultured in this three-dimensional microenvironment maintained high levels of liver-specific functions over the 10-day culture period. Function-blocking inhibitors of α5β1 or EGF receptor dramatically reduced cell viability and function, suggesting that signaling by both these receptors is needed for in vitro survival and function of hepatocytes in the absence of other exogenous signals.

Multiple mechanisms are responsible for transactivation of the epidermal growth factor receptor in mammary epithelial cells

The number of distinct signaling pathways that can transactivate the epidermal growth factor receptor (EGFR) in a single cell type is unclear. Using a single strain of human mammary epithelial cells, we found that a wide variety of agonists, such as lysophosphatidic acid (LPA), uridine triphosphate, growth hormone, vascular endothelial growth factor, insulin-like growth factor-1 (IGF-1), and tumor necrosis factor-alpha, require EGFR activity to induce ERK phosphorylation. In contrast, hepatocyte growth factor can stimulate ERK phosphorylation independent of the EGFR. EGFR transactivation also correlated with an increase in cell proliferation and could be inhibited with metalloprotease inhibitors. However, there were significant differences with respect to transactivation kinetics and sensitivity to different inhibitors. In particular, IGF-1 displayed relatively slow transactivation kinetics and was resistant to inhibition by the selective ADAM-17 inhibitor WAY-022 compared with LPA-induced transactivation. Studies using anti-ligand antibodies showed that IGF-1 transactivation required amphiregulin production, whereas LPA was dependent on multiple ligands. Direct measurement of ligand shedding confirmed that LPA treatment stimulated shedding of multiple EGFR ligands, but paradoxically, IGF-1 had little effect on the shedding rate of any ligand, including amphiregulin. Instead, IGF-1 appeared to work by enhancing EGFR activation of Ras in response to constitutively produced amphiregulin. This enhancement of EGFR signaling was independent of both receptor phosphorylation and PI-3-kinase activity, suggestive of a novel mechanism. Our studies demonstrate that within a single cell type, the EGFR autocrine system can couple multiple signaling pathways to ERK activation and that this modulation of EGFR autocrine signaling can be accomplished at multiple regulatory steps.

The kinetics of the hydrogen/deuterium exchange of epidermal growth factor receptor ligands

Five highly homologous epidermal growth factor receptor ligands were studied by mass spectral analysis, hydrogen/deuterium (H/D) exchange via attenuated total reflectance Fourier transform-infrared spectroscopy, and two-dimensional correlation analysis. These studies were performed to determine the order of events during the exchange process, the extent of H/D exchange, and associated kinetics of exchange for a comparative analysis of these ligands. Furthermore, the secondary structure composition of amphiregulin (AR) and heparin-binding-epidermal growth factor (HB-EGF) was determined. All ligands were found to have similar contributions of 3(10)-helix and random coil with varying contributions of beta-sheets and beta-turns. The extent of exchange was 40%, 65%, 55%, 65%, and 98% for EGF, transforming growth factor-alpha (TGF-alpha), AR, HB-EGF, and epiregulin (ER), respectively. The rate constants were determined and classified as fast, intermediate, and slow: for EGF the 0.20 min(-1) (Tyr), 0.09 min(-1) (Arg, beta-turns), and 1.88 x 10(-3) min(-1) (beta-sheets and 3(10)-helix); and for TGF-alpha 0.91 min(-1) (Tyr), 0.27 min(-1) (Arg, beta-turns), and 1.41 x 10(-4) min(-1) (beta-sheets). The time constants for AR 0.47 min(-1) (Tyr), 0.04 min(-1) (Arg), and 1.00 x 10(-4) min(-1) (buried 3(10)-helix, beta-turns, and beta-sheets); for HB-EGF 0.89 min(-1) (Tyr), 0.14 min(-1) (Arg and 3(10)-helix), and 1.00 x 10(-3) min(-1) (buried 3(10)-helix, beta-sheets, and beta-turns); and for epiregulin 0.16 min(-1) (Tyr), 0.03 min(-1) (Arg), and 1.00 x 10(-4) min(-1) (3(10)-helix and beta-sheets). These results provide essential information toward understanding secondary structure, H/D exchange kinetics, and solvation of these epidermal growth factor receptor ligands in their unbound state.

EGF-receptor-mediated mammary epithelial cell migration is driven by sustained ERK signaling from autocrine stimulation

EGF family ligands are synthesized as membrane-anchored precursors whose proteolytic release yields mature diffusible factors that can activate cell surface receptors in autocrine or paracrine mode. Expression of these ligands is altered in pathological states and in physiological processes, such as development and tissue regeneration. Despite the widely documented biological importance of autocrine EGF signaling, quantitative relationships between protease-mediated ligand release and consequent cell behavior have not been rigorously investigated. We thus explored the relationship between autocrine EGF release rates and cell behavioral responses along with activation of ERK, a key downstream signal, by expressing chimeric ligand precursors and modulating their proteolytic shedding using a metalloprotease inhibitor in human mammary epithelial cells. We found that ERK activation increased monotonically with increasing ligand release rate despite concomitant downregulation of EGF receptor levels. Cell migration speed was directly related to ligand release rate and proportional to steady-state phospho-ERK levels. Moreover, migration speed was significantly greater for autocrine stimulation compared with exogenous stimulation, even at comparable phospho-ERK levels. By contrast, cell proliferation rates were approximately equivalent at all ligand release rates and were similar regardless of whether the ligand was presented endogenously or exogenously. Thus, in our mammary epithelial cell system, migration and proliferation are differentially sensitive to the mode of EGF ligand presentation.

Interstitial flow and its effects in soft tissues

Interstitial flow plays important roles in the morphogenesis, function, and pathogenesis of tissues. To investigate these roles and exploit them for tissue engineering or to overcome barriers to drug delivery, a comprehensive consideration of the interstitial space and how it controls and affects such processes is critical. Here we attempt to review the many physical and mathematical correlations that describe fluid and mass transport in the tissue interstitium; the factors that control and affect them; and the importance of interstitial transport on cell biology, tissue morphogenesis, and tissue engineering. Finally, we end with some discussion of interstitial transport issues in drug delivery, cell mechanobiology, and cell homing toward draining lymphatics.

3D computation modelling of the influence of cytokine secretion on Th‐cell development suggests that negative selection (inhibition of Th1 cells) is more effective than positive selection by IL‐4 for Th2 cell dominance

Th-cell development has been suggested to include selective mechanisms in which certain cytokines select either Th1 or Th2 cells to proliferate and grow. The selective theory is based on the observation that Th2 cells secrete IL-4, a cytokine that promotes Th2 development, whereas Th1 cells secrete interferon-gamma (IFN-gamma) that favours Th1 development, and both positive and negative selective influences have been suggested to operate. In this study, we investigate the role of autocrine secretion and utilization of IL-4 by Th2 cells and address the question of whether an activated Th2 cell can be positively selected by IL-4 secreted from other Th2 cells. We present a spatial three dimensional (3D) modelling approach to simulate the interaction between the IL-4 ligand and its IL-4 receptors expressed on discrete IL-4 secreting cells. The simulations, based on existing experimental data on the IL-4 receptor-ligand system, illustrate how Th-cell development is highly dependent on the distance between cells that are communicating. The model suggests that a single Th2 cell is likely to communicate with possible target cells within a range of approximately 100 microm and that an activated Th2 cell manages to fill most of its own IL-4 receptors, even at a low secretion rate. The predictions made by the model suggest that negative selection against Th1 cells is more effective than positive selection by IL-4 for promoting Th2 dominance.

Capturing complex 3D tissue physiology in vitro

The emergence of tissue engineering raises new possibilities for the study of complex physiological and pathophysiological processes in vitro. Many tools are now available to create 3D tissue models in vitro, but the blueprints for what to make have been slower to arrive. We discuss here some of the 'design principles' for recreating the interwoven set of biochemical and mechanical cues in the cellular microenvironment, and the methods for implementing them. We emphasize applications that involve epithelial tissues for which 3D models could explain mechanisms of disease or aid in drug development.

Custom design of the cardiac microenvironment with biomaterials

Many strategies for repairing injured myocardium are under active investigation, with some early encouraging results. These strategies include cell therapies, despite little evidence of long-term survival of exogenous cells, and gene or protein therapies, often with incomplete control of locally-delivered dose of the factor. We propose that, ultimately, successful repair and regeneration strategies will require quantitative control of the myocardial microenvironment. This precision control can be engineered through designed biomaterials that provide quantitative adhesion, growth, or migration signals. Quantitative timed release of factors can be regulated by chemical design to direct cellular differentiation pathways such as angiogenesis and vascular maturation. Smart biomaterials respond to the local environment, such as protease activity or mechanical forces, with controlled release or activation. Most of these new biomaterials provide much greater flexibility for regenerating tissues ex vivo, but emerging technologies like self-assembling nanofibers can now establish intramyocardial cellular microenvironments by injection. This may allow percutaneous cardiac regeneration and repair approaches, or injectable-tissue engineering. Finally, materials can be made to multifunction by providing sequential signals with custom design of differential release kinetics for individual factors. Thus, new rationally-designed biomaterials no longer simply coexist with tissues, but can provide precision bioactive control of the microenvironment that may be required for cardiac regeneration and repair.

Models of cell signaling pathways

Cellular signaling circuits handle an enormous range of computations. Beyond the housekeeping, replicating and other functions of individual cells, signaling circuits must implement the immensely complex logic of development and function of multicellular organisms. Computer models are useful tools to understand this complexity. Recent studies have extended such models to include electrical, mechanical and spatial details of signaling, and to address the stochastic effects that arise when small numbers of molecules interact. Increasing numbers of models have been developed in close conjunction with experiments, and this interplay gives a deeper and more reliable insight into signaling function.

Ligand depletion negatively controls the mitogenic activity of epidermal growth factor

EGF activates the ErbB1 receptor, but there appears only a limited correlation between its receptor binding affinity and mitogenic activity. This is indicated by our present observation that in cells with high ErbB1 expression, including SUM102 breast tumor cells, low affinity EGF/Notch chimeras have similarly high mitogenic activity as EGF, in spite of the fact that EGF is superior in inducing receptor tyrosine phosphorylation and p42/p44 MAP-kinase activity. However, as a result of receptor-mediated internalisation high-affinity ligands such as EGF are depleted much more rapidly from the extracellular medium than low-affinity EGF/Notch chimeras. As a consequence, the mitogenic activity of EGF on ErbB1 overexpressing cells is limited by substantial degradation of internalised ligand in the period before cells enter S-phase, a phenomenon that is not observed for low affinity mutant ligands. The mitogenic activity of EGF on ErbB1 overexpressing cells does therefore not only depend on the applied concentration but also on the total amount of ligand added, and is strongly underestimated when tested in a limited assay volume. No such dependence on the incubation volume was observed for EGF activity on cells with low ErbB1 expression levels and on cells for which EGF is growth inhibitory.

Ligand accumulation in autocrine cell cultures

Cell-culture assays are routinely used to analyze autocrine signaling systems, but quantitative experiments are rarely possible. To enable the quantitative design and analysis of experiments with autocrine cells, we develop a biophysical theory of ligand accumulation in cell-culture assays. Our theory predicts the ligand concentration as a function of time and measurable parameters of autocrine cells and cell-culture experiments. The key step of our analysis is the derivation of the survival probability of a single ligand released from the surface of an autocrine cell. An expression for this probability is derived using the boundary homogenization approach and tested by stochastic simulations. We use this expression in the integral balance equations, from which we find the Laplace transform of the ligand concentration. We demonstrate how the theory works by analyzing the autocrine epidermal growth factor receptor system and discuss the extension of our methods to other experiments with cultured autocrine cells.

Ligand trapping in epithelial layers and cell cultures

We analyze a stochastic model that describes receptor-mediated ligand trapping in epithelial layers and cell culture assays. In both cases, the problem is reduced to diffusion of a Brownian particle between the partially absorbing and reflective surfaces. We derive an analytical expression for the spatial distribution of the trapping points and identify the domains of applicability of the two limiting regimes. We conclude that a thin layer approximation is applicable for ligand trapping in epithelial layers while a typical cell culture experiment is appropriately described within an infinite layer approximation.

Stochastic model of autocrine and paracrine signals in cell culture assays

Autocrine signaling systems are commonly studied under cell culture conditions. In a typical cell culture assay, a layer of liquid medium covers a random two-dimensional dispersion of cells, which secrete ligands. In a growing number of experiments, it is important to characterize the spatial range of autocrine and paracrine cell communication. Currently, the spatial distribution of diffusing signals can be analyzed only indirectly, from their effects on the intracellular signaling or physiological responses of autocrine cells. To directly characterize the spatial range of secreted ligands, we propose a stochastic model for autocrine cell cultures and analyze it using a combination of analytical and computational tools. The two main results derived within the framework of this model are 1), an expression for the fraction of autocrine trajectories, i.e., the probability for a ligand to be trapped by the same cell from which it has been secreted; and 2), an expression for the spatial distribution of trapping points of paracrine trajectories. We test these analytical results by stochastic simulations with efficient Brownian dynamics code and apply our model to analyze the spatial operation of autocrine epidermal growth factor receptor systems.

Signaling in morphogenesis: transport cues in morphogenesis

Extracellular transport processes play critical roles in morphogenesis. While diffusive transport effects on morphogenesis are well illustrated in examples like blood capillary architecture and in cell morphogenetic responses to the local extracellular protein environment, the effects of fluid convection, although important in many developing and regenerating tissues, are not well understood. Convective forces are present whenever a hydrated tissue undergoes dynamic mechanical strain, and so convection could not only dominate the transport of large molecules like proteins, but might also serve as a mechanism for mechanosensing. The complex interdependence of mechanical forces, protein transport and extracellular morphogen gradients needs to be elucidated in a comprehensive way in order for the importance of transport on morphogenesis to be fully appreciated.