Relationship between epidermal growth factor receptor occupancy and mitogenic response. Quantitative analysis using a steady state model system

A Phosphoproteomics Data Resource for Systems-level Modeling of Kinase Signaling Networks

Building mechanistic models of kinase-driven signaling pathways requires quantitative measurements of protein phosphorylation across physiologically relevant conditions, but this is rarely done because of the insensitivity of traditional technologies. By using a multiplexed deep phosphoproteome profiling workflow, we were able to generate a deep phosphoproteomics dataset of the EGFR-MAPK pathway in non-transformed MCF10A cells across physiological ligand concentrations with a time resolution of <12 min and in the presence and absence of multiple kinase inhibitors. An improved phosphosite mapping technique allowed us to reliably identify >46,000 phosphorylation sites on >6600 proteins, of which >4500 sites from 2110 proteins displayed a >2-fold increase in phosphorylation in response to EGF. This data was then placed into a cellular context by linking it to 15 previously published protein databases. We found that our results were consistent with much, but not all previously reported data regarding the activation and negative feedback phosphorylation of core EGFR-ERK pathway proteins. We also found that EGFR signaling is biphasic with substrates downstream of RAS/MAPK activation showing a maximum response at <3ng/ml EGF while direct substrates, such as HGS and STAT5B, showing no saturation. We found that RAS activation is mediated by at least 3 parallel pathways, two of which depend on PTPN11. There appears to be an approximately 4-minute delay in pathway activation at the step between RAS and RAF, but subsequent pathway phosphorylation was extremely rapid. Approximately 80 proteins showed a >2-fold increase in phosphorylation across all experiments and these proteins had a significantly higher median number of phosphorylation sites (~18) relative to total cellular phosphoproteins (~4). Over 60% of EGF-stimulated phosphoproteins were downstream of MAPK and included mediators of cellular processes such as gene transcription, transport, signal transduction and cytoskeletal arrangement. Their phosphorylation was either linear with respect to MAPK activation or biphasic, corresponding to the biphasic signaling seen at the level of the EGFR. This deep, integrated phosphoproteomics data resource should be useful in building mechanistic models of EGFR and MAPK signaling and for understanding how downstream responses are regulated.

Development and Evaluation of Multistructured and Hierarchical Epidermal Growth Factor-Poly ( ε -Caprolactone) Scaffolds

In this paper, we separately fabricated the poly ( ε -caprolactone) (PCL) scaffolds containing epidermal growth factor (EGF) by using our-self fabricated electrospinning machine for tissue regeneration application. Several fundamental properties, including the dimensions, wettability, and EGF release profiles, of the fabricated EGF-PCL bead, fibrous, and multistructured scaffolds were characterized by using the scanning electron microscopy (SEM), contact angle goniometer, and vertical diffusion system. The EGF release profiles of three scaffolds were measured for 200 h, and the multistructured scaffold performed stable and long EGF release properties. Furthermore, the in vitro and in vivo experiments were conducted to evaluate the performance of three types of EGF-PCL scaffolds. The NIH-3T3 fibroblast cells were cultured on the scaffolds to study the effects of the released EGF by using the Alamar Blue Cell Viability Assays, fluorescence image analysis, and SEM. The animal experiment demonstrated that the multistructured EGF-PCL scaffold achieved 95% of the wound healing rate to the cut-damaged wounds after 16 days. Moreover, the histopathological skin tissue showed that the wound regenerated well after the treatment of the multistructured EGF-PCL scaffold. The developed multistructured EGF-PCL scaffold has a high potential for the wound healing applications.

Transferring information without distortion

Despite employing diverse molecular mechanisms, many different cell signaling systems avoid losing information by transmitting it in a linear manner.

Signaling pathways as linear transmitters

One challenge in biology is to make sense of the complexity of biological networks. A good system to approach this is signaling pathways, whose well-characterized molecular details allow us to relate the internal processes of each pathway to their input-output behavior. In this study, we analyzed mathematical models of three metazoan signaling pathways: the canonical Wnt, MAPK/ERK, and Tgfβ pathways. We find an unexpected convergence: the three pathways behave in some physiological contexts as linear signal transmitters. Testing the results experimentally, we present direct measurements of linear input-output behavior in the Wnt and ERK pathways. Analytics from each model further reveal that linearity arises through different means in each pathway, which we tested experimentally in the Wnt and ERK pathways. Linearity is a desired property in engineering where it facilitates fidelity and superposition in signal transmission. Our findings illustrate how cells tune different complex networks to converge on the same behavior.

Decoding Signal Processing at the Single-Cell Level

The feedforward circuitry regulating ERK-dependent early response genes acts as a signal integrator rather than a signal persistence detector.

Diabetic Foot Ulcers and Epidermal Growth Factor: Revisiting the Local Delivery Route for a Successful Outcome

Soon after epidermal growth factor (EGF) discovery, some in vivo models appeared demonstrating its property to enhance cutaneous wound healing. EGF was the first growth factor (GF) introduced in the clinical arena as a healing enhancer, exerting its mitogenic effects on epithelial, fibroblastoid, and endothelial cells via a tyrosine kinase membrane receptor. Compelling evidences from the 90s documented that, for EGF, locally prolonged bioavailability and hourly interaction with the receptor were necessary for a successful tissue response. Eventually, the enthusiasm on the clinical use of EGF to steer the healing process was wiped out as the topical route to deliver proteins started to be questioned. The simultaneous in vivo experiments, emphasizing the impact of the parenterally administered EGF on epithelial and nonepithelial organs in terms of mitogenesis and cytoprotection, rendered the theoretical fundamentals for the injectable use of EGF and shaped the hypothesis that locally infiltrating the diabetic ulcers would lead to an effective healing. Although the diabetic chronic wounds microenvironment is hostile for local GFs bioavailability, EGF local infiltration circumvented the limitations of its topical application, thus expanding its therapeutic prospect. Our clinical pharmacovigilance and basic studies attest the significance of the GF local infiltration for chronic wounds healing.

Characterization of Laminin Binding Integrin Internalization in Prostate Cancer Cells

Laminin binding integrins α6 (CD49f) and α3 (CD49c) are persistently but differentially expressed in prostate cancer (PCa). Integrin internalization is an important determinant of their cell surface expression and function. Using flow cytometry, and first order kinetic modeling, we quantitated the intrinsic internalization rates of integrin subunits in a single cycle of internalization. In PCa cell line DU145, α6 integrin internalized with a rate constant (kactual ) of 3.25 min-1 , threefold faster than α3 integrin (1.0 min-1 ), 1.5-fold faster than the vitronectin binding αv integrin (CD51) (2.2 min-1 ), and significantly slower than the unrelated transferrin receptor (CD71) (15 min-1 ). Silencing of α3 integrin protein expression in DU145, PC3, and PC3B1 cells resulted in up to a 1.71-fold increase in kactual for α6 integrin. The internalized α6 integrin was targeted to early endosomes but not to lamp1 vesicles. Depletion of α3 integrin expression resulted in redistribution of α6β4 integrin to an observed cell-cell staining pattern that is consistent with a suprabasal distribution observed in epidermis and early PIN lesions in PCa. Depletion of α3 integrin increased cell migration by 1.8-fold, which was dependent on α6β1 integrin. Silencing of α6 integrin expression however, had no significant effect on the kactual of α3 integrin or its distribution in early endosomes. These results indicate that α3 and α6 integrins have significantly different internalization kinetics and that coordination exists between them for internalization. J. Cell. Biochem. 118: 1038-1049, 2017. © 2016 Wiley Periodicals, Inc.

Recent advances in biomaterials for the treatment of diabetic foot ulcers

Diabetes mellitus is one of the most challenging epidemics facing the world today, with over 300 million patients affected worldwide.

Push-Pull and Feedback Mechanisms Can Align Signaling System Outputs with Inputs

Many cell signaling systems, including the yeast pheromone response system, exhibit "dose-response alignment" (DoRA), in which output of one or more downstream steps closely matches the fraction of occupied receptors. DoRA can improve the fidelity of transmitted dose information. Here, we searched systematically for biochemical network topologies that produced DoRA. Most networks, including many containing feedback and feedforward loops, could not produce DoRA. However, networks including "push-pull" mechanisms, in which the active form of a signaling species stimulates downstream activity and the nominally inactive form reduces downstream activity, enabled perfect DoRA. Networks containing feedbacks enabled DoRA, but only if they also compared feedback to input and adjusted output to match. Our results establish push-pull as a non-feedback mechanism to align output with variable input and maximize information transfer in signaling systems. They also suggest genetic approaches to determine whether particular signaling systems use feedback or push-pull control.

Conservation of protein abundance patterns reveals the regulatory architecture of the EGFR-MAPK pathway

Various genetic mutations associated with cancer are known to alter cell signaling, but it is not clear whether they dysregulate signaling pathways by altering the abundance of pathway proteins. Using a combination of RNA sequencing and ultrasensitive targeted proteomics, we defined the primary components-16 core proteins and 10 feedback regulators-of the epidermal growth factor receptor (EGFR)-mitogen-activated protein kinase (MAPK) pathway in normal human mammary epithelial cells and then quantified their absolute abundance across a panel of normal and breast cancer cell lines as well as fibroblasts. We found that core pathway proteins were present at very similar concentrations across all cell types, with a variance similar to that of proteins previously shown to display conserved abundances across species. In contrast, EGFR and transcriptionally controlled feedback regulators were present at highly variable concentrations. The absolute abundance of most core proteins was between 50,000 and 70,000 copies per cell, but the adaptors SOS1, SOS2, and GAB1 were found at far lower amounts (2000 to 5000 copies per cell). MAPK signaling showed saturation in all cells between 3000 and 10,000 occupied EGFRs, consistent with the idea that adaptors limit signaling. Our results suggest that the relative stoichiometry of core MAPK pathway proteins is very similar across different cell types, with cell-specific differences mostly restricted to variable amounts of feedback regulators and receptors. The low abundance of adaptors relative to EGFR could be responsible for previous observations that only a fraction of total cell surface EGFR is capable of rapid endocytosis, high-affinity binding, and mitogenic signaling.

Role of EGF receptor ligands in TCDD-induced EGFR down-regulation and cellular proliferation

In cultures of normal human epidermal keratinocytes (NHEKs), 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) induces the expression of the epidermal growth factor receptor ligands transforming growth factor-α (TGF-α) and epiregulin (EREG). TCDD also down-regulates EGF receptors (EGFR), suggesting that decreases in signaling contribute to the effects of TCDD. In this study, we treated post-confluent NHEKs with 10 nM TCDD and assessed its effects on EGFR binding, EGFR ligand secretion, basal ERK activity, and proliferation. TCDD caused time-dependent deceases in [(125)I]-EGF binding to levels 78% of basal cell values at 72 h. Amphiregulin (AREG) levels increased with time in culture in basal and TCDD-treated cells, while TGF-α and epiregulin (EREG) secretion were stimulated by TCDD. Inhibiting EGFR ligand release with the metalloproteinase inhibitor batimastat prevented EGFR down-regulation and neutralizing antibodies for AREG and EREG relieved receptor down-regulation. In contrast, neutralizing TGF-α intensified EGFR down-regulation. Treating NHEKs with AREG or TGF-α caused rapid internalization of receptors with TGF-α promoting recycling within 90 min. EREG had limited effects on rapid internalization or recycling. TCDD treatment increased ERK activity, a response reduced by batimastat and the neutralization of all three ligands indicating that the EGFR and its ligands maintain ERK activity. All three EGFR ligands were required for the maintenance of total cell number in basal and TCDD-treated cultures. The EGFR inhibitor PD1530305 blocked basal and TCDD-induced increases in the number of cells labeled by 5-ethynyl-2'-deoxyuridine, identifying an EGFR-dependent pool of proliferating cells that is larger in TCDD-treated cultures. Overall, these data indicate that TCDD-induced EGFR down-regulation in NHEKs is caused by AREG, TGF-α, and EREG, while TGF-α enhances receptor recycling to maintain a pool of EGFR at the cell surface. These receptors are required for ERK activity, maintenance of total cell number, and stimulating the proliferation of a small subset cells.

Receptor Level Mechanisms Are Required for Epidermal Growth Factor (EGF)-stimulated Extracellular Signal-regulated Kinase (ERK) Activity Pulses

In both physiological and cell culture systems, EGF-stimulated ERK activity occurs in discrete pulses within individual cells. Many feedback loops are present in the EGF receptor (EGFR)-ERK network, but the mechanisms driving pulsatile ERK kinetics are unknown. Here, we find that in cells that respond to EGF with frequency-modulated pulsatile ERK activity, stimulation through a heterologous TrkA receptor system results in non-pulsatile, amplitude-modulated activation of ERK. We further dissect the kinetics of pulse activity using a combination of FRET- and translocation-based reporters and find that EGFR activity is required to maintain ERK activity throughout the 10-20-minute lifetime of pulses. Together, these data indicate that feedbacks operating within the core Ras-Raf-MEK-ERK cascade are insufficient to drive discrete pulses of ERK activity and instead implicate mechanisms acting at the level of EGFR.

Sensitive targeted quantification of ERK phosphorylation dynamics and stoichiometry in human cells without affinity enrichment

Targeted mass spectrometry is a promising technology for site-specific quantification of posttranslational modifications. However, a major constraint is the limited sensitivity for quantifying low-abundance PTMs, requiring the use of affinity reagents for enrichment. Herein, we demonstrate the direct site-specific quantification of ERK phosphorylation isoforms (pT, pY, pTpY) and their relative stoichiometry using a sensitive targeted MS approach termed high-pressure, high-resolution separations with intelligent selection, and multiplexing (PRISM). PRISM provides effective enrichment of target peptides into a given fraction from complex mixture, followed by selected reaction monitoring quantification. Direct quantification of ERK phosphorylation in human mammary epithelial cells (HMEC) was demonstrated from as little as 25 μg tryptic peptides from whole cell lysates. Compared to immobilized metal-ion affinity chromatography, PRISM provided ∼10-fold higher signal intensities, presumably due to the better peptide recovery of PRISM. This approach was applied to quantify ERK phosphorylation dynamics in HMEC treated by different doses of epidermal growth factor at both the peak activation (10 min) and steady state (2 h). The maximal ERK activation was observed with 0.3 and 3 ng/mL doses for 10 min and 2 h time points, respectively. The dose-response profiles of individual phosphorylated isoforms showed that singly phosphorylated pT-ERK never increases significantly, while the increase of pY-ERK paralleled that of pTpY-ERK. This data supports for a processive, rather than distributed model of ERK phosphorylation. The PRISM-SRM quantification of protein phosphorylation illustrates the potential for simultaneous quantification of multiple PTMs.

Fibrin as a delivery system in wound healing tissue engineering applications

Fibrin is formed in the body upon initiation of the clotting cascade and is produced commercially for use as a tissue sealant and hemostasis device during surgical procedures. Experimentally fibrin is being increasingly used as a vector to deliver growth factors, cells, drugs and genes in tissue engineering applications mimicking aspects of the extra cellular matrix. Growth factors (GFs) are central to wound healing, inducing cell proliferation, migration and differentiation. Attempts have been made to augment wound healing with GFs, however widespread clinical use has been hindered in vivo due to their rapid metabolism within the body. Fibrin hydrogels protect GFs from rapid degradation and the composition of which can be altered to achieve their optimal release. This article reviews the use of fibrin for the delivery of GFs and details the various strategies that have evolved to alter the release rate so as to enhance the regenerative process, including bi-domain peptides, plasmin degradation sequences and heparin incorporation. This paper also reviews other recent advances in this field, such as dual delivery of cells and GF or sequential release of multiple GF.

Analysis of the quantitative balance between insulin-like growth factor (IGF)-1 ligand, receptor, and binding protein levels to predict cell sensitivity and therapeutic efficacy

Background

The insulin-like growth factor (IGF) system impacts cell proliferation and is highly activated in ovarian cancer. While an attractive therapeutic target, the IGF system is complex with two receptors (IGF1R, IGF2R), two ligands (IGF1, IGF2), and at least six high affinity IGF-binding proteins (IGFBPs) that regulate the bioavailability of IGF ligands. We hypothesized that a quantitative balance between these different network components regulated cell response.

Results

OVCAR5, an immortalized ovarian cancer cell line, were found to be sensitive to IGF1, with the dose of IGF1 (i.e., the total mass of IGF1 available) a more reliable predictor of cell response than ligand concentration. The applied dose of IGF1 was depleted by both cell-secreted IGFBPs and endocytic trafficking, with IGFBPs sequestering up to 90% of the available ligand. To explore how different variables (i.e., IGF1, IGFBPs, and IGF1R levels) impacted cell response, a mass-action steady-state model was developed. Examination of the model revealed that the level of IGF1-IGF1R complexes per cell was directly proportional to the extent of proliferation induced by IGF1. Model analysis suggested, and experimental results confirmed, that IGFBPs present during IGF1 treatment significantly decreased IGF1-mediated proliferation. We utilized this model to assess the efficacy of IGF1 and IGF1R antibodies against different network compositions and determined that IGF1R antibodies were more globally effective due to the receptor-limited state of the network.

Conclusions

Changes that affect IGF1R occupancy have predictable effects on IGF1-induced proliferation and our model captured these effects. Analysis of this model suggests that IGF1R antibodies will be more effective than IGF1 antibodies, although the difference was minimal in conditions with low levels of IGF1 and IGFBPs. Examining how different components of the IGF system influence cell response will be critical to improve our understanding of the IGF signaling network in ovarian cancer.

Kinetics of epidermal growth factor/receptor binding on cells measured by total internal reflection/fluorescence recovery after photobleaching

Total internal reflection fluorescence (TIRF) microscopy is used to measure the dissociation kinetic rate of fluorescein-labeled epidermal growth factor from its specific receptors on the surface of intact but mildly fixed A431 human epidermoid cells in culture. Prior applications of TIRF microscopy have been limited to nonreceptor binding or to model membrane systems. The evanescent field excites fluorescence selectively at the surface of the cell proximal to the coverslip. "Prismless" epiillumination TIR is employed to avoid space limitations and is achieved by passing the excitation laser beam through a high (1.4)-aperture objective so that the light is incident at the glass/water interface beyond the critical angle. Long-term focus is maintained by a special feedback system. Of the possible effects that can influence the time course of the postbleach fluorescence recoveries-the EGF/receptor dissociation ratek 2, the bulk solution diffusion rate of EGF, and the cell surface motion of the receptors-we infer that the dissociation ratek 2 dominates. Several fitting schemes are compared and indicate the presence of a multiplicity of values fork 2, ranging from about 0.05 to 0.004 s(-1), with an average value of about 0.012 s(-1). These results compare well with values previously obtained by radiolabel/washing techniques. The significance of the results in terms of kinetic models and the advantages of the TIRF technique for these sorts of measurements are discussed.

Mechanistic model of natural killer cell proliferative response to IL-15 receptor stimulation

Natural killer (NK) cells are innate lymphocytes that provide early host defense against intracellular pathogens, such as viruses. Although NK cell development, homeostasis, and proliferation are regulated by IL-15, the influence of IL-15 receptor (IL-15R)-mediated signaling at the cellular level has not been quantitatively characterized. We developed a mathematical model to analyze the kinetic interactions that control the formation and localization of IL-15/IL-15R complexes. Our computational results demonstrated that IL-15/IL-15R complexes on the cell surface were a key determinant of the magnitude of the IL-15 proliferative signal and that IL-15R occupancy functioned as an effective surrogate measure of receptor signaling. Ligand binding and receptor internalization modulated IL-15R occupancy. Our work supports the hypothesis that the total number and duration of IL-15/IL-15R complexes on the cell surface crosses a quantitative threshold prior to the initiation of NK cell division. Furthermore, our model predicted that the upregulation of IL-15Rα on NK cells substantially increased IL-15R complex formation and accelerated the expansion of dividing NK cells with the greatest impact at low IL-15 concentrations. Model predictions of the threshold requirement for NK cell recruitment to the cell cycle and the subsequent exponential proliferation correlated well with experimental data. In summary, our modeling analysis provides quantitative insight into the regulation of NK cell proliferation at the receptor level and provides a framework for the development of IL-15 based immunotherapies to modulate NK cell proliferation.

Natural killer (NK) cells are innate immune cells that are important in our bodies' initial defenses against pathogens, like viruses. NK cells rapidly proliferate early during viral infections to provide an expanded pool of effector cells to suppress the infection. This proliferative response is driven by a cytokine called interleukin-15 (IL-15); however, the influence of IL-15 and its receptor (IL-15R) in stimulating NK cell proliferation has not been quantitatively characterized at the cellular level. To better understand the factors controlling the vigorous expansion of NK cells during infections, we developed a mathematical model incorporating IL-15R binding and trafficking parameters that regulate the number of cell-surface IL-15/IL-15R signaling complexes. The analysis of this model provided us with insight on how IL-15-driven NK cell expansion can be modulated through changes in receptor kinetics and expression. Based on model predictions, we were able to draw inferences about NK cell population dynamics and to compare these conclusions with quantitative experimental results. Our results and model have applicability to studies designed to manipulate cell responses in the context of immunotherapies.

Computational modeling of ERBB2-amplified breast cancer identifies combined ErbB2/3 blockade as superior to the combination of MEK and AKT inhibitors

Crosstalk and compensatory circuits within cancer signaling networks limit the activity of most targeted therapies. For example, altered signaling in the networks activated by the ErbB family of receptors, particularly in ERBB2-amplified cancers, contributes to drug resistance. We developed a multiscale systems model of signaling networks in ERBB2-amplified breast cancer to quantitatively investigate relationships between biomarkers (markers of network activity) and combination drug efficacy. This model linked ErbB receptor family signaling to breast tumor growth through two kinase cascades: the PI3K/AKT survival pathway and the Ras/MEK/ERK growth and proliferation pathway. The model predicted molecular mechanisms of resistance to individual therapeutics. In particular, ERBB2-amplified breast cancer cells stimulated with the ErbB3 ligand heregulin were resistant to growth arrest induced by inhibitors of AKT and MEK or coapplication of two inhibitors of the receptor ErbB2 [Herceptin (trastuzumab) and Tykerb (lapatinib)]. We used model simulations to predict the response of ErbB2-positive breast cancer xenografts to combination therapies and verified these predictions in mice. Treatment with trastuzumab, lapatinib, and the ErbB3 inhibitor MM-111 was more effective in inhibiting tumor growth than the combination of AKT and MEK inhibitors and even induced tumor regression, indicating that targeting both ErbB3 and ErbB2 may be an improved therapeutic approach for ErbB2-positive breast cancer patients.

Mathematical modelling and computational study of two-dimensional and three-dimensional dynamics of receptor-ligand interactions in signalling response mechanisms

Cell signalling processes involve receptor trafficking through highly connected networks of interacting components. The binding of surface receptors to their specific ligands is a key factor for the control and triggering of signalling pathways. But the binding process still presents many enigmas and, by analogy with surface catalytic reactions, two different mechanisms can be conceived: the first mechanism is related to the Eley-Rideal (ER) mechanism, i.e. the bulk-dissolved ligand interacts directly by pure three-dimensional (3D) diffusion with the specific surface receptor; the second mechanism is similar to the Langmuir-Hinshelwood (LH) process, i.e. 3D diffusion of the ligand to the cell surface followed by reversible ligand adsorption and subsequent two-dimensional (2D) surface diffusion to the receptor. A situation where both mechanisms simultaneously contribute to the signalling process could also occur. The aim of this paper is to perform a computational study of the behavior of the signalling response when these different mechanisms for ligand-receptor interactions are integrated into a model for signal transduction and ligand transport. To this end, partial differential equations have been used to develop spatio-temporal models that show trafficking dynamics of ligands, cell surface components, and intracellular signalling molecules through the different domains of the system. The mathematical modeling developed for these mechanisms has been applied to the study of two situations frequently found in cell systems: (a) dependence of the signal response on cell density; and (b) enhancement of the signalling response in a synaptic environment.

A comprehensive, multi-scale dynamical model of ErbB receptor signal transduction in human mammary epithelial cells

The non-receptor tyrosine kinase Src and receptor tyrosine kinase epidermal growth factor receptor (EGFR/ErbB1) have been established as collaborators in cellular signaling and their combined dysregulation plays key roles in human cancers, including breast cancer. In part due to the complexity of the biochemical network associated with the regulation of these proteins as well as their cellular functions, the role of Src in EGFR regulation remains unclear. Herein we present a new comprehensive, multi-scale dynamical model of ErbB receptor signal transduction in human mammary epithelial cells. This model, constructed manually from published biochemical literature, consists of 245 nodes representing proteins and their post-translational modifications sites, and over 1,000 biochemical interactions. Using computer simulations of the model, we find it is able to reproduce a number of cellular phenomena. Furthermore, the model predicts that overexpression of Src results in increased endocytosis of EGFR in the absence/low amount of the epidermal growth factor (EGF). Our subsequent laboratory experiments also suggest increased internalization of EGFR upon Src overexpression under EGF-deprived conditions, further supporting this model-generated hypothesis.

Cell surface concentrations and concentration ranges for testing in vitro autocrine loops and small molecules

A common assumption made when performing in vitro cellular assays is that the concentration of substances in the culture system is uniform. However, since the cells that internalize and secrete substances reside at the bottom of the well, it is conceivable that a concentration gradient could arise across the fluid layer. Importantly, the concentration of a substance in the vicinity of a cell, which is the concentration of interest, cannot be measured via existing methods. In this work a simple strategy for estimating the concentration of a chemical species at the surface of a cell is presented. Finally, this result is used to outline a method for determining the appropriate concentration ranges for testing in vitro autocrine loops and small molecules.

Functionalized silk biomaterials for wound healing

Silk protein-biomaterial wound dressings with epidermal growth factor (EGF) and silver sulfadiazine were studied with a cutaneous excisional mouse wound model. Three different material designs and two different drug incorporation techniques were studied to compare wound healing responses. Material formats included silk films, lamellar porous silk films and electrospun silk nanofibers, each studied with the silk matrix alone and with drug loading or drug coatings on the silk matrices. Changes in wound size and histological assessments of wound tissues showed that the functionalized silk biomaterial wound dressings increased wound healing rate, including reepithelialization, dermis proliferation, collagen synthesis and reduced scar formation, when compared to air-permeable Tegaderm tape (3M) (- control) and a commercial wound dressing, Tegaderm Hydrocolloid dressing (3M) (+ control). All silk biomaterials were effective for wound healing, while the lamellar porous films and electrospun nanofibers and the incorporation of EGF/silver sulfadiazine, via drug loading or coating, provided the most rapid wound healing responses. This systematic approach to evaluating functionalized silk biomaterial wound dressings demonstrates a useful strategy to select formulations for further study towards new treatment options for chronic wounds.

Frequency-modulated pulses of ERK activity transmit quantitative proliferation signals

The EGF-stimulated ERK/MAPK pathway is a key conduit for cellular proliferation signals and a therapeutic target in many cancers. Here, we characterize two central quantitative aspects of this pathway: the mechanism by which signal strength is encoded and the response curve relating signal output to proliferation. Under steady-state conditions, we find that ERK is activated in discrete, asynchronous pulses with frequency and duration determined by extracellular concentrations of EGF spanning the physiological range. In genetically identical sister cells, cell-to-cell variability in pulse dynamics influences the decision to enter S phase. While targeted inhibition of EGFR reduces the frequency of ERK activity pulses, inhibition of MEK reduces their amplitude. Continuous response curves measured in multiple cell lines reveal that proliferation is effectively silenced only when ERK pathway output falls below a threshold of ~10%, indicating that high-dose targeting of the pathway is necessary to achieve therapeutic efficacy.

Engineering dynamics of growth factors and other therapeutic ligands

Peptide growth factors and other receptor-binding cytokine ligands are of interest in contemporary molecular health care approaches in applications such as wound healing, tissue regeneration, and gene therapy. Development of effective technologies based on operation of these regulatory molecules requires an ability to deliver the ligands to target cells in a reliable and well-characterizable manner. Quantitative information concerning the fate of peptide ligands within tissues is necessary for adequate interpretation of experimental observations at the tissue level and for truly rational engineering design of ligand-based therapies. To address this need, we are undertaking efforts to elucidate effects of key molecular and cellular parameters on temporal and spatial distribution of cytokines in cell population and cell/matrix systems. In this article we summarize some of our recent findings on dynamics of growth factor depletion by cellular endocytic trafficking, growth factor transport through cellular matrices, and growth factor production and release by autocrine cell systems. (c) 1996 John Wiley & Sons, Inc.

Short-term information processing, long-term responses: Insights by mathematical modeling of signal transduction. Early activation dynamics of key signaling mediators can be predictive for cell fate decisions

How do cells interpret information from their environment and translate it into specific cell fate decisions? We propose that cell fate is already encoded in early signaling events and thus can be predicted from defined signal properties. Specifically, we hypothesize that the time integral of activated key signaling molecules can be correlated to cellular behavior such as proliferation or differentiation. The identification of these decisive key signal mediators and their connection to cell fate is facilitated by mathematical modeling. A possible mechanistic linkage between signaling dynamics and cellular function is the directed control of gene regulatory networks by defined signals. Targeted experiments in combination with mathematical modeling can increase our understanding of how cells process information and realize distinct cell fates.

Dose-response aligned circuits in signaling systems

Cells use biological signal transduction pathways to respond to environmental stimuli and the behavior of many cell types depends on precise sensing and transmission of external information. A notable property of signal transduction that was characterized in the Saccharomyces cerevisiae yeast cell and many mammalian cells is the alignment of dose-response curves. It was found that the dose response of the receptor matches closely the dose responses of the downstream. This dose-response alignment (DoRA) renders equal sensitivities and concordant responses in different parts of signaling system and guarantees a faithful information transmission. The experimental observations raise interesting questions about the nature of the information transmission through DoRA signaling networks and design principles of signaling systems with this function. Here, we performed an exhaustive computational analysis on network architectures that underlie the DoRA function in simple regulatory networks composed of two and three enzymes. The minimal circuits capable of DoRA were examined with Michaelis-Menten kinetics. Several motifs that are essential for the dynamical function of DoRA were identified. Systematic analysis of the topology space of robust DoRA circuits revealed that, rather than fine-tuning the network's parameters, the function is primarily realized by enzymatic regulations on the controlled node that are constrained in limiting regions of saturation or linearity.

Predicting the F(ab)-mediated effect of monoclonal antibodies in vivo by combining cell-level kinetic and pharmacokinetic modelling

Cell-level kinetic models for therapeutically relevant processes increasingly benefit the early stages of drug development. Later stages of the drug development processes, however, rely on pharmacokinetic compartment models while cell-level dynamics are typically neglected. We here present a systematic approach to integrate cell-level kinetic models and pharmacokinetic compartment models. Incorporating target dynamics into pharmacokinetic models is especially useful for the development of therapeutic antibodies because their effect and pharmacokinetics are inherently interdependent. The approach is illustrated by analysing the F(ab)-mediated inhibitory effect of therapeutic antibodies targeting the epidermal growth factor receptor. We build a multi-level model for anti-EGFR antibodies by combining a systems biology model with in vitro determined parameters and a pharmacokinetic model based on in vivo pharmacokinetic data. Using this model, we investigated in silico the impact of biochemical properties of anti-EGFR antibodies on their F(ab)-mediated inhibitory effect. The multi-level model suggests that the F(ab)-mediated inhibitory effect saturates with increasing drug-receptor affinity, thereby limiting the impact of increasing antibody affinity on improving the effect. This indicates that observed differences in the therapeutic effects of high affinity antibodies in the market and in clinical development may result mainly from Fc-mediated indirect mechanisms such as antibody-dependent cell cytotoxicity.

Quantitative study of cytotoxic T-lymphocyte immunotherapy for nasopharyngeal carcinoma

BACKGROUND

In clinical practice, the common strategy for immunotherapy of nasopharyngeal carcinoma (NPC) is to infuse cytotoxic T-lymphocyte (CTL) lines several times by intravenous injection, but it is difficult by laboratory research to investigate the relationship between treatment time-point, the amount of CTL added and the therapeutic effect. The objective of this study is to establish a mathematical model to study the therapeutic effect of different treatment time-points and amounts of CTL, and to predict the change in therapeutic effect when the percentage of EBV LMP2-specific CTL is increased from 10% to 20%.

RESULTS

The concentration of epidermal growth factor receptor (EGFR) in the tumor cell cytomembranes increases after CTL is added. Concurrently, there is a marked downward trend of the phosphorylated transforming growth factor-α (TGFα)-EGFR complex in the tumor cell cytomembranes, which indicates restriction of tumor growth after CTL immunotherapy. The relationships among the time of addition of CTL, the amount of CTL added, different CTL specificities for LMP2 and the increment rate k of the total number of tumor cells were evaluated.

CONCLUSIONS

The simulation results quantify the relationships among treatment time-points, amount of CTL added, and the corresponding therapeutic effect of immunotherapy for NPC.

Mechanical control of spheroid growth: distinct morphogenetic regimes

We develop a model of transport and growth in epithelio-mesenchymal interactions. Analysis of the growth of an avascular solid spheroid inside a passive mesenchyme or gel shows that sustained volumetric growth requires four generic mechanisms: (1) growth factor, (2) protease, (3) control of cellularity, and (4) swelling. The model reveals a bifurcation delineating two distinct morphogenetic regimes: (A) steady growth, (B) growth arrested by capsule formation in the mesenchyme. In both morphogenetic regimes, growth velocity is constant unless and until a complete capsule forms. Comprehensive exploration of the large parameter space reveals that the bifurcation is determined by just two ratios representing the relative strengths of growth and proteolytic activity. Growth velocity is determined only by the ratio governing growth, independent of proteolytic activity. There is a continuum of interior versus surface growth, with fastest growth at the surface. The model provides a theoretical basis for explaining observations of growth arrest despite proteolysis of surrounding tissue, and gives a quantitative framework for the design and interpretation of experiments involving spheroids, and tissues which are locally equivalent to spheroids.

Receptor differential activation and cooperativity better explain cellular preference for different chemoattractant gradient shapes in an EGFR system

This manuscript describes mathematical models that apply an aggregating receptor scheme to the epidermal growth factor receptor (EGFR) system to interpret and predict directed cell migration behaviors in differently-shaped chemoattractant gradients. This method incorporates the latest biochemical insights on ligand-receptor activation kinetics and receptor cooperativity into the commonly used difference in the fractional receptor occupancy (DFRO) model for explaining chemotaxis. The enhanced model derives the functionally more relevant value of difference in fractional receptor activation (DFRA). This DFRA analysis encompasses all features and predictions of the DFRO analyses. Importantly, DFRA analysis can additionally explain in vitro microfluidic chemotaxis experiments that are difficult to explain using only DFRO concepts such as why some cells may migrate well only in a higher concentration regime of exponential chemoattractant gradients. The DFRA analysis also suggests receptor activation strategies that cells may use to tune their responsiveness to differently-shaped in vivo gradients. DFRA analysis is conceptually and computationally straightforward. The results it provides are envisioned to serve as quick semi-quantitative guides to design chemotaxis experiments and to develop hypotheses for interpretation of results from directed cell migration experiments.

Systematic quantification of negative feedback mechanisms in the extracellular signal-regulated kinase (ERK) signaling network

Cell responses are actuated by tightly controlled signal transduction pathways. Although the concept of an integrated signaling network replete with interpathway cross-talk and feedback regulation is broadly appreciated, kinetic data of the type needed to characterize such interactions in conjunction with mathematical models are lacking. In mammalian cells, the Ras/ERK pathway controls cell proliferation and other responses stimulated by growth factors, and several cross-talk and feedback mechanisms affecting its activation have been identified. In this work, we take a systematic approach to parse the magnitudes of multiple regulatory mechanisms that attenuate ERK activation through canonical (Ras-dependent) and non-canonical (PI3K-dependent) pathways. In addition to regulation of receptor and ligand levels, we consider three layers of ERK-dependent feedback: desensitization of Ras activation, negative regulation of MEK kinase (e.g. Raf) activities, and up-regulation of dual-specificity ERK phosphatases. Our results establish the second of these as the dominant mode of ERK self-regulation in mouse fibroblasts. We further demonstrate that kinetic models of signaling networks, trained on a sufficient diversity of quantitative data, can be reasonably comprehensive, accurate, and predictive in the dynamical sense.

Transport of epidermal growth factor in the stroke-injured brain

Stroke is a neurological disorder that currently has no cure. Intrathecal delivery of growth factors, specifically recombinant human epidermal growth factor (rhEGF), stimulates endogenous neural precursor cells in the subventricular zone (SVZ) and promotes tissue regeneration in animal models of stroke. In this model, rhEGF is delivered with an invasive minipump/catheter system, which causes trauma to the brain. A less invasive strategy is to deliver rhEGF from the brain cortex; however, this requires the protein to diffuse through the brain, from the site of injection to the SVZ. Although this method of delivery has great potential, diffusion is limited by rapid removal from the extracellular space and hence for successful translation into the clinic strategies are needed to increase the diffusion distance. Using integrative optical imaging we investigate diffusion of rhEGF vs. poly(ethylene glycol)-modified rhEGF (PEG-rhEGF) in brain slices of both uninjured and stroke-injured animals. For the first time, we quantitatively show that PEG modification reduces the rate of growth factor elimination by over an order of magnitude. For rhEGF this corresponds to a two to threefold increase in predicted brain penetration distance, which we confirm with in vivo data.

Regulation of mammalian cell growth by autocrine growth factors: analysis of consequences for inoculum cell density effects

Effects of inoculum cell density on mammalian cell growth in culture have been observed in a variety of experimental systems. Although these effects have been attributed generally to medium conditioning by the cells, there has previously been no quantitative theory proposed for this phenomenon based on developments in molecular and cell biology. In this article, we offer such a theory founded on the regulatory action of autocrine growth factors. A particularly relevant example of these is platelet- derived growth factor (PDGF), which is produced by fibroblastic cells in response to stimulation by transforming growth factor beta (TGFbeta), a common serum constituent, and provides a mitogenic signal for the same cells. A simple mathematical model for the production, diffusive transport, and binding of autocrine growth factors to cell surface receptors, coupled to a model for the dependence of cell proliferation on growth factor receptor binding allows prediction of initial cell population growth rate as a function of inoculum cell density. We focus on situations involving anchorage-dependent cell growth, in which the cells are attached to a surface. A number of clear results are obtained, most notably the following: 1) for cells cultured on spherical microcarrier bead surfaces, the inoculum cell density needed to produce a given growth rate is linearly proportional to the bead radius; and 2) all other factors being equal, the inoculum cell density on a unit surface area basis needed to produce a given growth rate is greater for spherical microcarrier surfaces than for flat culture dish surfaces. These two results are consistent with the experimental observations of Hu and coworkers(1,2) for fibroblast growth in minimal medium plus serum. The model also allows elucidation of the influence of other system parameters, both biological and physical, on initial cell proliferation rate and the inoculum cell density dependence.

Cell signaling: what is the signal and what information does it carry?

This paper reviews key findings from quantitative study of the yeast pheromone response system. Most come from single cell experiments that quantify molecular events the system uses to operate. After induction, signal propagation is relatively slow; peak activity takes minutes to reach the nucleus. At each measurement point along the transmission chain, signal rises, overshoots, peaks, and declines toward steady state. At at least one measurement point, this decline depends on negative feedback. The system senses and relays percent receptor occupancy, and one effect of the feedback is to maximize precision of this transmitted information. Over time, the system constantly adjusts quantitative behaviors to convey extracellular ligand concentration faithfully. These behaviors and mechanisms that control them are likely to be general for metazoan signaling systems.

Biofunctionalized electrospun silk mats as a topical bioactive dressing for accelerated wound healing

Materials able to deliver topically bioactive molecules represent a new generation of biomaterials. In this article, we describe the use of silk mats, made of electrospun nanoscale silk fibers containing epidermal growth factor (EGF), for the promotion of wound healing processes. In our experiments, we demonstrated that EGF is incorporated into the silk mats and slowly released in a time-dependent manner (25% EGF release in 170h). We tested these materials using a new model of wounded human skin-equivalents displaying the same structure as human skin and able to heal using the same molecular and cellular mechanisms found in vivo. This human three-dimensional model allows us to demonstrate that the biofunctionalized silk mats, when placed on the wounds as a dressing, aid the healing by increasing the time of wound closure by the epidermal tongue by 90%. The preservation of the structure of the mats during the healing period as demonstrated by electronic microscopy, the biological action of the dressing, as well as the biocompatibility of the silk demonstrate that this biomaterial is a new and very promising material for medical applications, especially for patients suffering from chronic wounds.

Negative feedback that improves information transmission in yeast signalling

Haploid Saccharomyces cerevisiae yeast cells use a prototypic cell signalling system to transmit information about the extracellular concentration of mating pheromone secreted by potential mating partners. The ability of cells to respond distinguishably to different pheromone concentrations depends on how much information about pheromone concentration the system can transmit. Here we show that the mitogen-activated protein kinase Fus3 mediates fast-acting negative feedback that adjusts the dose response of the downstream system response to match the dose response of receptor-ligand binding. This 'dose-response alignment', defined by a linear relationship between receptor occupancy and downstream response, can improve the fidelity of information transmission by making downstream responses corresponding to different receptor occupancies more distinguishable and reducing amplification of stochastic noise during signal transmission. We also show that one target of the feedback is a previously uncharacterized signal-promoting function of the regulator of G-protein signalling protein Sst2. Our work suggests that negative feedback is a general mechanism used in signalling systems to align dose responses and thereby increase the fidelity of information transmission.

Screening the cellular microenvironment: a role for microfluidics

The cellular microenvironment is an increasingly discussed topic in cell biology as it has been implicated in the progression of cancer and the maintenance of stem cells. The microenvironment of a cell is an organized combination of extracellular matrix (ECM), cells, and interstitial fluid that influence cellular phenotype through physical, mechanical, and biochemical mechanisms. Screening can be used to map combinations of cells and microenvironments to phenotypic outcomes in a way that can help develop more predictive in vitro models and to better understand phenotypic mechanisms from a systems biology perspective. This paper examines microenvironmental screening in terms of outcomes and benefits, key elements of the screening process, challenges for implementation, and a possible role for microfluidics as the screening platform. To assess microfluidics for use in microenvironmental screening, examples and categories of micro-scale and microfluidic technology are highlighted. Microfluidic technology shows promise for simultaneous control of multiple parameters of the microenvironment and can provide a base for scaling advanced cell-based experiments into automated high-throughput formats.

A mathematical model for the effects of HER2 overexpression on cell proliferation in breast cancer

We present a mathematical model to study the effects of HER2 over-expression on cell proliferation in breast cancer. The model illustrates the proliferative behavior of cells as a function of HER2 and EGFR receptors numbers, and the growth factor EGF. This mathematical model comprises kinetic equations describing the cell surface binding of EGF growth factor to EGFR and HER2 receptors, coupled to a model for the dependence of cell proliferation rate on growth factor receptors binding. The simulation results from this model predict: (1) a growth advantage associated with excess HER2 receptors; (2) that HER2-over-expression is an insufficient parameter to predict the proliferation response of cancer cells to epidermal growth factors; and (3) the EGFR receptor expression level in HER2-over-expressing cells plays a key role in mediating the proliferation response to receptor-ligand signaling. This mathematical model also elucidates the interaction and roles of other model parameters in determining cell proliferation rate of HER2-over-expressing cells.

Concurrent EGFr and Cox-2 expression in colorectal cancer: proliferation impact and tumour spreading

BACKGROUND

Many reports were produced on single epidermal growth factor receptor (EGFr) and cyclo-oxygenase-2 (Cox-2) evaluation using immunohistochemical techniques (IHC), but very few works considered concurrent expression of these two proteins in the light of their impact on proliferation and tumour spreading. At least three molecular pathways (EGFr, Cox-2, and APC/beta-catenin molecular cascade) may interact in this malignancy giving rise to cross talking effects on proliferation and cancer spreading.

PATIENTS AND METHODS

To better detail these two latter aggressive features, we studied 205 sporadic colorectal cancer patients, comparing concurrent expression of EGFr, Cox-2, Ki-67, Cyclins D1-A, and E, with tumour spreading (budding) (BUD) and pN status.

RESULTS

Our results point to a different aggressive molecular profile due to Cox-2 expression. Cox-2 High expressing cases showed a clear EGFr proliferation-promoting role. On the contrary, EGFr seems directly involved in cancer cells spreading rather than in promoting cancer proliferation in Cox-2 Low/Negative cases.

CONCLUSIONS

Immunohistochemical profiling of colorectal cancer seems to be a promising approach, not only to define prognostic impact, but also to detail proliferation-related molecular interplays between EGFr and Cox-2 pathways, with these two latter proteins, at present, being the hottest pharmacological targets for colorectal cancer (CRC) chemoprevention and therapy.

Self-assembling peptide nanofiber scaffolds accelerate wound healing

Cutaneous wound repair regenerates skin integrity, but a chronic failure to heal results in compromised tissue function and increased morbidity. To address this, we have used an integrated approach, using nanobiotechnology to augment the rate of wound reepithelialization by combining self-assembling peptide (SAP) nanofiber scaffold and Epidermal Growth Factor (EGF). This SAP bioscaffold was tested in a bioengineered Human Skin Equivalent (HSE) tissue model that enabled wound reepithelialization to be monitored in a tissue that recapitulates molecular and cellular mechanisms of repair known to occur in human skin. We found that SAP underwent molecular self-assembly to form unique 3D structures that stably covered the surface of the wound, suggesting that this scaffold may serve as a viable wound dressing. We measured the rates of release of EGF from the SAP scaffold and determined that EGF was only released when the scaffold was in direct contact with the HSE. By measuring the length of the epithelial tongue during wound reepithelialization, we found that SAP scaffolds containing EGF accelerated the rate of wound coverage by 5 fold when compared to controls without scaffolds and by 3.5 fold when compared to the scaffold without EGF. In conclusion, our experiments demonstrated that biomaterials composed of a biofunctionalized peptidic scaffold have many properties that are well-suited for the treatment of cutaneous wounds including wound coverage, functionalization with bioactive molecules, localized growth factor release and activation of wound repair.

Receptor downregulation and desensitization enhance the information processing ability of signalling receptors

Background

In addition to initiating signaling events, the activation of cell surface receptors also triggers regulatory processes that restrict the duration of signaling. Acute attenuation of signaling can be accomplished either via ligand-induced internalization of receptors (endocytic downregulation) or via ligand-induced receptor desensitization. These phenomena have traditionally been viewed in the context of adaptation wherein the receptor system enters a refractory state in the presence of sustained ligand stimuli and thereby prevents the cell from over-responding to the ligand. Here we use the epidermal growth factor receptor (EGFR) and G-protein coupled receptors (GPCR) as model systems to respectively examine the effects of downregulation and desensitization on the ability of signaling receptors to decode time-varying ligand stimuli.

Results

Using a mathematical model, we show that downregulation and desensitization mechanisms can lead to tight and efficient input-output coupling thereby ensuring synchronous processing of ligand inputs. Frequency response analysis indicates that upstream elements of the EGFR and GPCR networks behave like low-pass filters with the system being able to faithfully transduce inputs below a critical frequency. Receptor downregulation and desensitization increase the filter bandwidth thereby enabling the receptor systems to decode inputs in a wider frequency range. Further, system-theoretic analysis reveals that the receptor systems are analogous to classical mechanical over-damped systems. This analogy enables us to metaphorically describe downregulation and desensitization as phenomena that make the systems more resilient in responding to ligand perturbations thereby improving the stability of the system resting state.

Conclusion

Our findings suggest that in addition to serving as mechanisms for adaptation, receptor downregulation and desensitization can play a critical role in temporal information processing. Furthermore, engineering metaphors such as the ones described here could prove to be invaluable in understanding the design principles of biological systems.

Characteristics of soluble and membrane-bound forms of haemopoietic growth factor receptors: relationships to biological function

In order to understand how extracellular growth factors (colony-stimulating factors, CSFs) induce biological responses in haemopoietic cells it is necessary first to describe the primary binding characteristics of isolated receptors and then to determine how living cells modify these binding characteristics and process the ligand-receptor complexes. We have solubilized multi-CSF (interleukin 3) and granulocyte macrophage CSF (GM-CSF) receptors in 1% Triton X-100 and developed methods to study their binding characteristics in solution. Whilst the multi-CSF receptor exhibits the same binding characteristics in solution and in the cellular state, the GM-CSF receptor appears to be converted to a lower affinity form in solution. In intact cells at biological temperatures both types of receptor and ligand are internalized and degraded under steady-state conditions; the kinetic processes underlying the maintenance of the steady state are characteristic for each type of receptor and each type of cell. We have determined the kinetic constants for a variety of CSFs and cell types and correlated steady-state receptor occupancy with biological responses. The importance of CSF utilization rate by responsive cells has also been evaluated as a mechanism for limiting biological responses.

Cellular signaling is potentially regulated by cell density in receptor trafficking networks

Previous work has shown that receptor trafficking is a potential site for the control of signaling pathways. In most biological experiments, the ligand concentration and cell density vary within a wide range among different systems. However, there is less attention to systematically analyze how much cellular signal response is affected by cell densities. Here, we use a quantitative mathematical model to investigate signal responses in different receptor trafficking networks by simultaneous variations of ligand concentration and cell density. Computational analysis of the model revealed that receptor trafficking networks have potential sigmoid responses to ratio between ligand and surface receptor number per cell, which is a key factor to control the signaling responses in receptor trafficking networks. Furthermore, cell density also affects the robustness of dose-response curve upon the variation of binding affinity.

Cell surface receptors for signal transduction and ligand transport: a design principles study

Receptors constitute the interface of cells to their external environment. These molecules bind specific ligands involved in multiple processes, such as signal transduction and nutrient transport. Although a variety of cell surface receptors undergo endocytosis, the systems-level design principles that govern the evolution of receptor trafficking dynamics are far from fully understood. We have constructed a generalized mathematical model of receptor–ligand binding and internalization to understand how receptor internalization dynamics encodes receptor function and regulation. A given signaling or transport receptor system represents a particular implementation of this module with a specific set of kinetic parameters. Parametric analysis of the response of receptor systems to ligand inputs reveals that receptor systems can be characterized as being: i) avidity-controlled where the response control depends primarily on the extracellular ligand capture efficiency, ii) consumption-controlled where the ability to internalize surface-bound ligand is the primary control parameter, and iii) dual-sensitivity where both the avidity and consumption parameters are important. We show that the transferrin and low-density lipoprotein receptors are avidity-controlled, the vitellogenin receptor is consumption-controlled, and the epidermal growth factor receptor is a dual-sensitivity receptor. Significantly, we show that ligand-induced endocytosis is a mechanism to enhance the accuracy of signaling receptors rather than merely serving to attenuate signaling. Our analysis reveals that the location of a receptor system in the avidity-consumption parameter space can be used to understand both its function and its regulation.

Cells interact with their environment using molecules on their surface known as receptors. Receptors bind specific companion molecules known as ligands, which either carry information about the outside environment or are critical cell nutrients. Signaling receptors bind the former ligand type and convert information about the outside environment to a cell response such as migration or growth. Transport receptors bind the latter class of ligand and deliver them to the cell interior. A variety of receptors are internalized into the cell through a process known as endocytosis. Receptors display a wide range of endocytosis patterns, but the functional motivation behind the observed differences is not well understood. We have constructed a generalized model to understand how receptor endocytosis and other receptor–ligand properties affect the function of receptor systems. We find that the efficiency and robustness of receptor systems are encoded by two fundamental parameters: i) the avidity which quantifies the ability of a receptor system to capture ligand, and ii) the consumption which quantifies the ability to internalize bound ligand. By examining a number of receptor systems, we demonstrate that the internalization dynamics of receptor systems can be explained by examining its effect on the avidity and consumption parameters.

Endosomal receptor kinetics determine the stability of intracellular growth factor signalling complexes

There is an emerging paradigm that growth factor signalling continues in the endosome and that cell response to a growth factor is defined by the integration of cell surface and endosomal events. As activated receptors in the endosome are exposed to a different set of binding partners, they probably elicit differential signals compared with when they are at the cell surface. As such, complete appreciation of growth factor signalling requires understanding of growth factor-receptor binding and trafficking kinetics both at the cell surface and in endosomes. Growth factor binding to surface receptors is well characterized, and endosomal binding is assumed to follow surface kinetics if one accounts for changes in pH. Yet, specific binding kinetics within the endosome has not been examined in detail. To parse the factors governing the binding state of endosomal receptors we analysed a whole-cell mathematical model of epidermal growth factor receptor trafficking and binding. We discovered that the stability of growth factor-receptor complexes within endosomes is governed by three primary independent factors: the endosomal dissociation constant, total endosomal volume and the number of endosomal receptors. These factors were combined into a single dimensionless parameter that determines the endosomal binding state of the growth factor-receptor complex and can distinguish different growth factors from each other and different cell states. Our findings indicate that growth factor binding within endosomal compartments cannot be appreciated solely on the basis of the pH-dependence of the dissociation constant and that the concentration of receptors in the endosomal compartment must also be considered.

An integrated agent-mathematical model of the effect of intercellular signalling via the epidermal growth factor receptor on cell proliferation

We have previously developed Epitheliome, a software agent representation of the growth and repair characteristics of epithelial cell populations, where cell behaviour is governed by a number of simple rules. In this paper, we describe how this model has been extended to incorporate an example of a molecular 'mechanism' behind a rule-in this case, how signalling by both endogenous and exogenous ligands of the epidermal growth factor receptor (EGFR) can impact on the proliferation of cell agents. We have developed a mathematical model representing release of endogenous ligand by cells, three-dimensional diffusion of the secreted molecules through a volume of cell culture medium, ligand-receptor binding, and bound receptor internalization and trafficking. Information relating to quantities of molecular species associated with each cell agent is frequently exchanged between the agent and signalling models, and the ratio of bound to free receptors determines cell cycle progression and hence the proliferative behaviour of the cell agents. We have applied this integrated model to examine the effect of plating density on tissue growth via autocrine/paracrine signalling. This predicts that cell growth is dependent on the concentration of exogenous ligand, but where this is limited, then growth becomes dependent on cell density and the availability of endogenous ligand. We have further modified the calcium concentration of the medium to modulate the formation of intercellular bonds between cells and shown that the increased propensity for cells to form colonies in physiological calcium does not result in significantly different patterns of receptor occupancy. In conclusion, our approach demonstrates that by combining agent-based and mathematical modelling paradigms, it is possible to probe the complex feedback relationship between the behaviour of individual cells and their interaction with one another and their environment.

The effects of EGF-receptor density on multiscale tumor growth patterns

We studied the effects of epidermal growth factor receptor (EGFR) density on tumor growth dynamics, both on the sub- and the multi-cellular level using our previously developed model. This algorithm simulates the growth of a brain tumor using a multi-scale two-dimensional agent-based approach with an integrated transforming growth factor alpha (TGFalpha) induced EGFR-gene-protein interaction network. The results confirm that increasing cell receptor density correlates with an acceleration of the tumor system's spatio-temporal expansion dynamics. This multicellular behavior cannot be explained solely on the basis of spatial sub-cellular dynamics, which remain qualitatively similar amongst the three glioma cell lines investigated here in silico. Rather, we find that cells with higher EGFR density show an early increase in the phenotypic switching activity between proliferative and migratory traits, linked to a higher level of initial auto-stimulation by the PLCgamma-mediated TGFalpha-EGFR autocrine network. This indicates a more active protein level interaction in these chemotactically acting tumor systems and supports the role of post-translational regulation for the implemented EGFR pathway. Implications of these results for experimental cancer research are discussed.

Deterministic model of dermal wound invasion incorporating receptor-mediated signal transduction and spatial gradient sensing

During dermal wound healing, platelet-derived growth factor (PDGF) serves as both a chemoattractant and mitogen for fibroblasts, potently stimulating their invasion of the fibrin clot over a period of several days. A mathematical model of this process is presented, which accurately accounts for the sensitivity of PDGF gradient sensing through PDGF receptor/phosphoinositide 3-kinase-mediated signal transduction. Analysis of the model suggests that PDGF receptor-mediated endocytosis and degradation of PDGF allows a constant PDGF concentration profile to be maintained at the leading front of the fibroblast density profile as it propagates, at a constant rate, into the clot. Thus, the constant PDGF gradient can span the optimal concentration range for asymmetric phosphoinositide 3-kinase signaling and fibroblast chemotaxis, with near-maximal invasion rates elicited over a relatively broad range of PDGF secretion rates. A somewhat surprising finding was that extremely sharp PDGF gradients do not necessarily stimulate faster progression through the clot, because maintaining such a gradient through PDGF consumption is a potentially rate-limiting process.