Spatial range of autocrine signaling: modeling and computational analysis

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.

Development of a three-dimensional multiscale agent-based tumor model: Simulating gene-protein interaction profiles, cell phenotypes and multicellular patterns in brain cancer

Experimental evidence suggests that epidermal growth factor receptor (EGFR)-mediated activation of the signaling protein phospholipase Cgamma plays a critical role in a cancer cell's phenotypic decision to either proliferate or to migrate at a given point in time. Here, we present a novel three-dimensional multiscale agent-based model to simulate this cellular decision process in the context of a virtual brain tumor. Each tumor cell is equipped with an EGFR gene-protein interaction network module that also connects to a simplified cell cycle description. The simulation results show that over time proliferative and migratory cell populations not only oscillate but also directly impact the spatio-temporal expansion patterns of the entire cancer system. The percentage change in the concentration of the sub-cellular interaction network's molecular components fluctuates, and, for the 'proliferation-to-migration' switch we find that the phenotype triggering molecular profile to some degree varies as the tumor system grows and the microenvironment changes. We discuss potential implications of these findings for experimental and clinical cancer research.

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.

Transforming Growth Factor-Alpha: A Major Human Serum Factor that Promotes Human Keratinocyte Migration

In unwounded skin, human keratinocytes (HKs) are in contact with a plasma filtrate. In an acute wound, HKs come in contact with serum for the first time. Because human serum (HS), but not plasma, promotes HK migration, we speculated that a major HK pro-motility factor in vivo comes from serum. In this study, we compared all of the published growth factors (GFs), reported to promote HK migration, with HS. No single GF could duplicate the HK pro-motility activity in HS. Among these GFs, transforming growth factor-alpha [corrected] showed the highest HK pro-motility activity, reaching approximately 80% of the activity in HS. The order of potency was: TGFalpha > insulin > EGF > heparin binding (HB)-EGF > IGF-1 > basic fibroblast growth factor >IL-8 > HGF > IL-1 > KGF>TGFbeta. Interestingly, the combination of TGFalpha and insulin could duplicate the HK pro-motility activity in HS, although only the TGFalpha, but not insulin, levels increase in serum over plasma. Addition of neutralizing antibodies against TGFalpha to serum or depletion of TGFalpha from serum by immunoprecipitation significantly abolished its HK pro-motility activity. Plasma with added TGFalpha stimulated HK migration that reached more than 80% of the serum stimulation. Since insulin levels are identical between plasma and serum, we propose that TGFalpha is the physiologic HK pro-motility factor in HS.

Signaling between cells attached to a surface

We present a kinetic model allowing one to classify likely scenarios of protein-mediated communication between attached cells of two distinct types. In our treatment, messenger proteins, synthesized in type-1 cells, are considered to penetrate the external membrane of these cells, diffuse in the extracellular medium, associate with the receptors in the external membrane of cells of both types, and induce intracellular signal transduction cascades, influencing the development of cells. Protein degradation inside and outside cells is taken into account as well.

Mathematical model of phosphatidylinositol-4,5-bisphosphate hydrolysis mediated by epidermal growth factor receptor generating diacylglycerol

Phosphatidylinositol-4,5-bisphosphate (PIP2) is hydrolyzed in response to the tyrosine phosphorylation of the epidermal growth factor receptor (EGFR) and plays an important role in regulating cell proliferation and differentiation through the generation of second messengers diacylglycerol (DAG) and trisphosphate inositol (IP3) which lead to the activation of protein kinase C (PKC) and increased levels of intracellular calcium, respectively. In the paper, a mathematical model was established to simulate the accumulation of DAG due to PIP2 hydrolysis mediated by EGFR. Molecular mechanisms between DAG, PIP2, EGFR and phosphatidylinositol transfer protein (PITP) were explained successfully, and positive cooperativity which existed between phospholipase C-gamma1 (PLC-gamma1) and PIP2 was also explained. In the model the effects of parameters on simulation of PIP2 hydrolysis were analyzed and the efficacies of some molecular intervention strategies were predicted. To test the coherence between the model and the biological response to epidermal growth factor (EGF) in cells, the levels of DAG and the tyrosine phosphorylation-EGFRs in NIH3T3 mouse embryonic fibroblast (MEF) were determined by biochemical experiments which showed that the accumulation of DAG was a sigmoidal function of phosphorylation-EGFR concentration, and the consistency between the mathematical model and experimental results was confirmed. In brief, this mathematical model provided a new idea for the further study of the dynamic change of biological characteristics in inositol phospholipid hydrolysis, predicting the efficacy of molecular intervention and the relationship between the metabolisms of inositol phospholipid and other signal transduction pathways.

Model-based analysis and design of a microchannel reactor for tissue engineering

Recently developed perfusion micro-bioreactors offer the promise of more physiologic in vitro systems for tissue engineering. Successful application of such bioreactors will require a method to characterize the bioreactor environment required to elicit desired cell function. We present a mathematical model to describe nutrient/growth factor transport and cell growth inside a microchannel bioreactor. Using the model, we first show that the nature of spatial gradients in nutrient concentration can be controlled by both design and operating conditions and are a strong function of cell uptake rates. Next, we extend our model to investigate the spatial distributions of cell-secreted soluble autocrine/paracrine growth factors in the bioreactor. We show that the convective transport associated with the continuous cell culture and possible media recirculation can significantly alter the concentration distribution of the soluble signaling molecules as compared to static culture experiments and hence needs special attention when adapting static culture protocols for the bioreactor. Further, using an unsteady state model, we find that spatial gradients in nutrient/growth factor concentrations can bring about spatial variations in the cell density distribution inside the bioreactor, which can result in lowered working volume of the bioreactor. Finally, we show that the nutrient and spatial limitations can dramatically affect the composition of a co-cultured cell population. Our results are significant for the development, design, and optimization of novel micro-channel systems for tissue engineering.

A computational framework for the topological analysis and targeted disruption of signal transduction networks

In this article, optimization-based frameworks are introduced for elucidating the input-output structure of signaling networks and for pinpointing targeted disruptions leading to the silencing of undesirable outputs in therapeutic interventions. The frameworks are demonstrated on a large-scale reconstruction of a signaling network composed of nine signaling pathways implicated in prostate cancer. The Min-Input framework is used to exhaustively identify all input-output connections implied by the signaling network structure. Results reveal that there exist two distinct types of outputs in the signaling network that either can be elicited by many different input combinations or are highly specific requiring dedicated inputs. The Min-Interference framework is next used to precisely pinpoint key disruptions that negate undesirable outputs while leaving unaffected necessary ones. In addition to identifying disruptions of terminal steps, we also identify complex disruption combinations in upstream pathways that indirectly negate the targeted output by propagating their action through the signaling cascades. By comparing the obtained disruption targets with lists of drug molecules we find that many of these targets can be acted upon by existing drug compounds, whereas the remaining ones point at so-far unexplored targets. Overall the proposed computational frameworks can help elucidate input/output relationships of signaling networks and help to guide the systematic design of interference strategies.

Computational modeling of extracellular mechanotransduction

Mechanotransduction may occur through numerous mechanisms, including potentially through autocrine signaling in a dynamically changing extracellular space. We developed a computational model to analyze how alterations in the geometry of an epithelial lateral intercellular space (LIS) affect the concentrations of constitutively shed ligands inside and below the LIS. The model employs the finite element method to solve for the concentration of ligands based on the governing ligand diffusion-convection equations inside and outside of the LIS, and assumes idealized parallel plate geometry and an impermeable tight junction at the apical surface. Using the model, we examined the temporal relationship between geometric changes and ligand concentration, and the dependence of this relationship on system characteristics such as ligand diffusivity, shedding rate, and rate of deformation. Our results reveal how the kinetics of mechanical deformation can be translated into varying rates of ligand accumulation, a potentially important mechanism for cellular discrimination of varying rate-mechanical processes. Furthermore, our results demonstrate that rapid changes in LIS geometry can transiently increase ligand concentrations in underlying media or tissues, suggesting a mechanism for communication of mechanical state between epithelial and subepithelial cells. These results underscore both the plausibility and complexity of the proposed extracellular mechanotransduction mechanism.

Spatial modeling of dimerization reaction dynamics in the plasma membrane: Monte Carlo vs. continuum differential equations

Bimolecular reactions in the plasma membrane, such as receptor dimerization, are a key signaling step for many signaling systems. For receptors to dimerize, they must first diffuse until a collision happens, upon which a dimerization reaction may occur. Therefore, study of the dynamics of cell signaling on the membrane may require the use of a spatial modeling framework. Despite the availability of spatial simulation methods, e.g., stochastic spatial Monte Carlo (MC) simulation and partial differential equation (PDE) based approaches, many biological models invoke well-mixed assumptions without completely evaluating the importance of spatial organization. Whether one is to utilize a spatial or non-spatial simulation framework is therefore an important decision. In order to evaluate the importance of spatial effects a priori, i.e., without performing simulations, we have assessed the applicability of a dimensionless number, known as second Damköhler number (Da), defined here as the ratio of time scales of collision and reaction, for 2-dimensional bimolecular reactions. Our study shows that dimerization reactions in the plasma membrane with Da approximately >0.1 (tested in the receptor density range of 10(2)-10(5)/microm(2)) require spatial modeling. We also evaluated the effective reaction rate constants of MC and simple deterministic PDEs. Our simulations show that the effective reaction rate constant decreases with time due to time dependent changes in the spatial distribution of receptors. As a result, the effective reaction rate constant of simple PDEs can differ from that of MC by up to two orders of magnitude. Furthermore, we show that the fluctuations in the number of copies of signaling proteins (noise) may also depend on the diffusion properties of the system. Finally, we used the spatial MC model to explore the effect of plasma membrane heterogeneities, such as receptor localization and reduced diffusivity, on the dimerization rate. Interestingly, our simulations show that localization of epidermal growth factor receptor (EGFR) can cause the diffusion limited dimerization rate to be up to two orders of magnitude higher at higher average receptor densities reported for cancer cells, as compared to a normal cell.

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.

Cardiomyocyte hypertrophy and degradation of connexin43 through spatially restricted autocrine/paracrine heparin-binding EGF

Growth factor signaling can affect tissue remodeling through autocrine/paracrine mechanisms. Recent evidence indicates that EGF receptor transactivation by heparin-binding EGF (HB-EGF) contributes to hypertrophic signaling in cardiomyocytes. Here, we show that HB-EGF operates in a spatially restricted circuit in the extracellular space within the myocardium, revealing the critical nature of the local microenvironment in intercellular signaling. This highly localized microenvironment of HB-EGF signaling was demonstrated with 3D morphology, consistent with predictions from a computational model of EGF signaling. HB-EGF secretion by a given cardiomyocyte in mouse left ventricles led to cellular hypertrophy and reduced expression of connexin43 in the overexpressing cell and in immediately adjacent cells but not in cells farther away. Thus, HB-EGF acts as an autocrine and local paracrine cardiac growth factor that leads to loss of gap junction proteins within a spatially confined microenvironment. These findings demonstrate how cells can coordinate remodeling with their immediate neighboring cells with highly localized extracellular EGF signaling.

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.

Simulating the impact of a molecular 'decision-process' on cellular phenotype and multicellular patterns in brain tumors

Experimental evidence indicates that human brain cancer cells proliferate or migrate, yet do not display both phenotypes at the same time. Here, we present a novel computational model simulating this cellular decision-process leading up to either phenotype based on a molecular interaction network of genes and proteins. The model's regulatory network consists of the epidermal growth factor receptor (EGFR), its ligand transforming growth factor-alpha (TGF alpha), the downstream enzyme phospholipaseC-gamma (PLC gamma) and a mitosis-associated response pathway. This network is activated by autocrine TGF alpha secretion, and the EGFR-dependent downstream signaling this step triggers, as well as modulated by an extrinsic nutritive glucose gradient. Employing a framework of mass action kinetics within a multiscale agent-based environment, we analyse both the emergent multicellular behavior of tumor growth and the single-cell molecular profiles that change over time and space. Our results show that one can indeed simulate the dichotomy between cell migration and proliferation based solely on an EGFR decision network. It turns out that these behavioral decisions on the single cell level impact the spatial dynamics of the entire cancerous system. Furthermore, the simulation results yield intriguing experimentally testable hypotheses also on the sub-cellular level such as spatial cytosolic polarization of PLC gamma towards an extrinsic chemotactic gradient. Implications of these results for future works, both on the modeling and experimental side are discussed.

ApoE-mediated cholesterol efflux from macrophages: separation of autocrine and paracrine effects

Macrophages in the vessel wall secrete high levels of apolipoprotein E (apoE). Cholesterol efflux from macrophages to apoE has been shown to decrease foam cell formation and prevent atherosclerosis. An apoE molecule can mediate cholesterol efflux from the macrophage that originally secreted it (autocrine effect) or from surrounding macrophages (paracrine effect). Traditional methodologies have not been able to separate these serial effects. The novel methodology presented here was developed to separate autocrine and paracrine effects by using a simple mathematical model to interpret the effects of dilution on apoE-mediated cholesterol efflux. Our results show that, at very dilute concentrations, the paracrine effect of apoE is not evident and the autocrine effect becomes the dominant mediator of efflux. However, at saturating concentrations, paracrine apoE causes 80-90% of the apoE-mediated cholesterol efflux, whereas autocrine apoE is responsible for the remaining 10-20%. These results suggest that the relative importance of autocrine and paracrine apoE depends on the size of the local distribution volume, a factor not considered in previous in vitro studies of apoE function. Furthermore, autocrine effects of apoE could be critical in the prevention of foam cell formation in vivo. This novel methodology may be applicable to other types of mixed autocrine/paracrine systems, such as signal transduction systems.

A diffusion–reaction model for DNA microarray assays

DNA microarrays are extensively used for the quantification of the degree of differential mRNA expression. The assay involves hybridization of mobile DNA strands with immobilized complementary DNA strands to form duplexes. The overall duplex formation rate depends on the rate of transport of strands in solution to the corresponding spot on the surface, and the rate of the hybridization reaction. We present a theoretical model that incorporates both kinetics of the reversible hybridization reaction and diffusional transport of the labeled strands, and analyze DNA microarray hybridization using this model. Simulations are carried out in a geometrically realistic domain for labeled DNA concentrations corresponding to rare and abundant transcripts for typical assay conditions. The rate of strand diffusion in solution is shown to strongly affect the overall hybridization rate. We compute the minimum inter-spot spacing for replicate spots to enhance sensitivity. We also determine the hybridization time for which reliable estimates of the relative mRNA abundance of two species can be obtained using total fluorescence intensities. An analytical solution for the concentration distribution of mobile strands at intermediate hybridization times provides a convenient tool to calculate the mobile strand concentration profiles. This model provides a framework for the process analysis of all microarray assays currently used for genomic transcriptional analysis.

Signal propagation and failure in discrete autocrine relays

A mechanistic model of discrete one-dimensional arrays of autocrine cells interacting via diffusible signals is investigated. Under physiologically relevant assumptions, the model is reduced to a system of ordinary differential equations for the intracellular variables, with a particular, biophysically derived type of long-range coupling between cells. Exact discrete traveling wave and static kink solutions are obtained in the model with sharp threshold nonlinearity. It is argued that the considered mechanism may be used extensively for transmission of information in tissues during homeostasis and development.

Self-organization of polarized cell signaling via autocrine circuits: computational model analysis

Recent studies have suggested that autocrine signaling through epidermal growth factor receptor (EGFR) might be involved in generating or maintaining an intrinsic polarity in tissue cells, possibly via spatial localization of EGFR-mediated signaling. The difficulty of experimental investigation of autocrine signaling makes especially valuable an application of computational modeling for critical hypotheses about the dynamic operation of the underlying signaling circuits, both intracellular and extracellular. Toward this end, we develop and analyze here a spatially distributed dynamic computational model of autocrine EGFR signaling. Under certain conditions, the model spontaneously evolves into a state wherein sustained signaling is spatially localized on smaller than cell dimension, conferring a polarity to the otherwise nonpolar model cell. Conditions of a sufficiently large rate of autocrine EGFR ligand release and of a sufficiently small exogenous ligand concentration are qualitatively consistent with experimental observations of EGFR-mediated migration. Thus, computational analysis supports the concept that autocrine EGFR signaling circuits could play a role in helping generate and/or maintain an intrinsic cell spatial polarity, possibly related to migration as well as tissue organization. We additionally offer particular suggestions for critical nodes in the EGFR signaling circuits governing this self-organization capability.

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.

Topological analysis of mass-balanced signaling networks: a framework to obtain network properties including crosstalk

Signal transduction networks have only been studied at a small scale because large-scale reconstructions and suitable in silico analysis methods have not been available. Since reconstructions of large signaling networks are progressing well there is now a need to develop a framework for analysing structural properties of signaling networks. One such framework is presented here, one that is based on systemically independent pathways and a mass-balanced representation of signaling events. This approach was applied to a prototypic signaling network and it allowed for: (1) a systemic analysis of all possible input/output relationships, (2) a quantitative evaluation of network crosstalk, or the interconnectivity of systemically independent pathways, (3) a measure of the redundancy in the signaling network, (4) the participation of reactions in signaling pathways, and (5) the calculation of correlated reaction sets. These properties emerge from network structure and can only be derived and studied within a defined mathematical framework. The calculations presented are the first of their kind for a signaling network, while similar analysis has been extensively performed for prototypic and genome-scale metabolic networks. This approach does not yet account for dynamic concentration profiles. Due to the scalability of the stoichiometric formalism used, the results presented for the prototypic signaling network can be obtained for large signaling networks once their reconstruction is completed.

Mechanotransduction through growth-factor shedding into the extracellular space

Physical forces elicit biochemical signalling in a diverse array of cells, tissues and organisms, helping to govern fundamental biological processes. Several hypotheses have been advanced that link physical forces to intracellular signalling pathways, but in many cases the molecular mechanisms of mechanotransduction remain elusive. Here we find that compressive stress shrinks the lateral intercellular space surrounding epithelial cells, and triggers cellular signalling via autocrine binding of epidermal growth factor family ligands to the epidermal growth factor receptor. Mathematical analysis predicts that constant rate shedding of autocrine ligands into a collapsing lateral intercellular space leads to increased local ligand concentrations that are sufficient to account for the observed receptor signalling; direct experimental comparison of signalling stimulated by compressive stress versus exogenous soluble ligand supports this prediction. These findings establish a mechanism by which mechanotransduction arises from an autocrine ligand-receptor circuit operating in a dynamically regulated extracellular volume, not requiring induction of force-dependent biochemical processes within the cell or cell membrane.

Model of competitive binding of vascular endothelial growth factor and placental growth factor to VEGF receptors on endothelial cells

Placental growth factor (PlGF) competes with vascular endothelial growth factor (VEGF) for binding to VEGF receptor (VEGFR)-1 but does not bind VEGFR2. Experiments show that PlGF can augment the response to VEGF in pathological angiogenesis and in models of endothelial cell survival, migration, and proliferation. This synergy has been hypothesized to be due to a combination of the following: signaling by PlGF through VEGFR1 and displacement of VEGF from VEGFR1 to VEGFR2 by PlGF, causing increased signaling through VEGFR2. In this study, the relative contribution of PlGF-induced VEGF displacement to the synergy is quantified using a mathematical model of ligand-receptor binding to examine the effect on ligand-receptor complex formation of VEGF and PlGF acting together. Parameters specific to the VEGF-PlGF system are used based on existing data. The model is used to simulate in silico a specific in vitro experiment in which VEGF-PlGF synergy is observed. We show that, whereas a significant change in the formation of endothelial surface growth factor-VEGFR1 complexes is predicted in the presence of PlGF, the increase in the number of VEGFR2-containing signaling complexes is less significant; these results were shown to be robust to significant variation in the kinetic parameters of the model. Synergistic effects observed in that experiment thus appear unlikely to be due to VEGF displacement but to a shift from VEGF-VEGFR1 to PlGF-VEGFR1 complexes and an increase in total VEGFR1 complexes. These results suggest that VEGFR1 signaling can be functional in adult-derived endothelial cells.

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.

Nonequilibrium phase transition in a self-activated biological network

We present a lattice model for a two-dimensional network of self-activated biological structures with a diffusive activating agent. The model retains basic and simple properties shared by biological systems at various observation scales, so that the structures can consist of individuals, tissues, cells, or enzymes. Upon activation, a structure emits a new mobile activator and remains in a transient refractory state before it can be activated again. Varying the activation probability, the system undergoes a nonequilibrium second-order phase transition from an active state, where activators are present, to an absorbing, activator-free state, where each structure remains in the deactivated state. We study the phase transition using Monte Carlo simulations and evaluate the critical exponents. As they do not seem to correspond to known values, the results suggest the possibility of a separate universality class.

Long-range signal transmission in autocrine relays

Intracellular signaling induced by peptide growth factors can stimulate secretion of these molecules into the extracellular medium. In autocrine and paracrine networks, this can establish a positive feedback loop between ligand binding and ligand release. When coupled to intercellular communication by autocrine ligands, this positive feedback can generate constant-speed traveling waves. To demonstrate that, we propose a mechanistic model of autocrine relay systems. The model is relevant to the physiology of epithelial layers and to a number of in vitro experimental formats. Using asymptotic and numerical tools, we find that traveling waves in autocrine relays exist and have a number of unusual properties, such as an optimal ligand binding strength necessary for the maximal speed of propagation. We compare our results to recent observations of autocrine and paracrine systems and discuss the steps toward experimental tests of our predictions.

Modeling and computational analysis of EGF receptor-mediated cell communication in Drosophila oogenesis

Autocrine signaling through the Epidermal Growth Factor Receptor (EGFR) operates at various stages of development across species. A recent hypothesis suggested that a distributed network of EGFR autocrine loops was capable of spatially modulating a simple single-peaked input into a more complex two-peaked signaling pattern, specifying the formation of a pair organ in Drosophila oogenesis (two respiratory appendages on the eggshell). To test this hypothesis, we have integrated genetic and biochemical information about the EGFR network into a mechanistic model of transport and signaling. The model allows us to estimate the relative spatial ranges and time scales of the relevant feedback loops, to interpret the phenotypic transitions in eggshell morphology and to predict the effects of new genetic manipulations. We have found that the proposed mechanism with a single diffusing inhibitor is sufficient to convert a single-peaked extracellular input into a two-peaked pattern of intracellular signaling. Based on extensive computational analysis, we predict that the same mechanism is capable of generating more complex patterns. At least indirectly, this can be used to account for more complex eggshell morphologies observed in related fly species. We propose that versatility in signaling mediated by autocrine loops can be systematically explored using experiment-based mechanistic models and their analysis.

Hematologic consequences of exposure to ionizing radiation

From the early 1900s, it has been known that ionizing radiation (IR) impairs hematopoiesis through a variety of mechanisms. IR exposure directly damages hematopoietic stem cells and alters the capacity of bone marrow stromal elements to support and/or maintain hematopoiesis in vivo and in vitro. Exposure to IR induces dose-dependent declines in circulating hematopoietic cells not only through reduced bone marrow production, but also by redistribution and apoptosis of mature formed elements of the blood. Recently, the importance of using lymphocyte depletion kinetics to provide a "crude" dose estimate has been emphasized, particularly in rapid assessment of large numbers of individuals who may be exposed to IR through acts of terrorism or by accident. A practical strategy to estimate radiation dose and triage victims based upon clinical symptomatology is presented. An explosion of knowledge has occurred regarding molecular and cellular pathways that trigger and mediate hematologic responses to IR. In addition to damaging DNA, IR alters gene expression and transcription, and interferes with intracellular and intercellular signaling pathways. The clinical expression of these disturbances may be the development of leukemia, the most significant hematologic complication of IR exposure among survivors of the atomic bomb detonations over Japan. Those at greatest risk for leukemia are individuals exposed during childhood. The association of leukemia with chronic, low-dose-rate exposure from nuclear power plant accidents and/or nuclear device testing has been more difficult to establish, due in part to lack of precision and sensitivity of methods to assess doses that approach background radiation dose. Nevertheless, multiple myeloma may be associated with chronic exposure, particularly in those exposed at older ages.

Autocrine loops with positive feedback enable context-dependent cell signaling

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

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

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