Long-range signal transmission in autocrine relays

Quantitative analyses of EGFR localization and trafficking dynamics in the follicular epithelium

To bridge the gap between qualitative and quantitative analyses of the epidermal growth factor receptor (EGFR) in tissues, we generated an sfGFP-tagged EGF receptor (EGFR-sfGFP) in Drosophila The homozygous fly appears similar to wild type with EGFR expression and activation patterns that are consistent with previous reports in the ovary, early embryo, and imaginal discs. Using ELISA, we quantified an average of 1100, 6200 and 2500 receptors per follicle cell (FC) at stages 8/9, 10 and ≥11 of oogenesis, respectively. Interestingly, the spatial localization of the EGFR to the apical side of the FCs at early stages depended on the TGFα-like ligand Gurken. At later stages, EGFR localized to basolateral positions of the FCs. Finally, we followed the endosomal localization of EGFR in the FCs. The EGFR colocalized with the late endosome, but no significant colocalization of the receptor was found with the early endosome. The EGFR-sfGFP fly is an exciting new resource for studying cellular localization and regulation of EGFR in tissues.

Spherical Caps in Cell Polarization

Intracellular symmetry breaking plays a key role in wide range of biological processes, both in single cells and in multicellular organisms. An important class of symmetry-breaking mechanisms relies on the cytoplasm/membrane redistribution of proteins that can autocatalytically promote their own recruitment to the plasma membrane. We present an analytical construction and a comprehensive parametric analysis of stable localized patterns in a reaction-diffusion model of such a mechanism in a spherical cell. The constructed patterns take the form of high-concentration patches localized into spherical caps, similar to the patterns observed in the studies of symmetry breaking in single cells and early embryos.

Dynamics and control of the ERK signaling pathway: Sensitivity, bistability, and oscillations

Cell signaling is the process by which extracellular information is transmitted into the cell to perform useful biological functions. The ERK (extracellular-signal-regulated kinase) signaling controls several cellular processes such as cell growth, proliferation, differentiation and apoptosis. The ERK signaling pathway considered in this work starts with an extracellular stimulus and ends with activated (double phosphorylated) ERK which gets translocated into the nucleus. We model and analyze this complex pathway by decomposing it into three functional subsystems. The first subsystem spans the initial part of the pathway from the extracellular growth factor to the formation of the SOS complex, ShC-Grb2-SOS. The second subsystem includes the activation of Ras which is mediated by the SOS complex. This is followed by the MAPK subsystem (or the Raf-MEK-ERK pathway) which produces the double phosphorylated ERK upon being activated by Ras. Although separate models exist in the literature at the subsystems level, a comprehensive model for the complete system including the important regulatory feedback loops is missing. Our dynamic model combines the existing subsystem models and studies their steady-state and dynamic interactions under feedback. We establish conditions under which bistability and oscillations exist for this important pathway. In particular, we show how the negative and positive feedback loops affect the dynamic characteristics that determine the cellular outcome.

Paracrine communication maximizes cellular response fidelity in wound signaling

Population averaging due to paracrine communication can arbitrarily reduce cellular response variability. Yet, variability is ubiquitously observed, suggesting limits to paracrine averaging. It remains unclear whether and how biological systems may be affected by such limits of paracrine signaling. To address this question, we quantify the signal and noise of Ca(2+) and ERK spatial gradients in response to an in vitro wound within a novel microfluidics-based device. We find that while paracrine communication reduces gradient noise, it also reduces the gradient magnitude. Accordingly we predict the existence of a maximum gradient signal to noise ratio. Direct in vitro measurement of paracrine communication verifies these predictions and reveals that cells utilize optimal levels of paracrine signaling to maximize the accuracy of gradient-based positional information. Our results demonstrate the limits of population averaging and show the inherent tradeoff in utilizing paracrine communication to regulate cellular response fidelity.

Cryptochrome in sponges: a key molecule linking photoreception with phototransduction

Sponges (phylum: Porifera) react to external light or mechanical signals with contractile or metabolic reactions and are devoid of any nervous or muscular system. Furthermore, elements of a photoreception/phototransduction system exist in those animals. Recently, a cryptochrome-based photoreceptor system has been discovered in the demosponge. The assumption that in sponges the siliceous skeleton acts as a substitution for the lack of a nervous system and allows light signals to be transmitted through its glass fiber network is supported by the findings that the first spicules are efficient light waveguides and the second sponges have the enzymatic machinery for the generation of light. Now, we have identified/cloned in Suberites domuncula two additional potential molecules of the sponge cryptochrome photoreception system, the guanine nucleotide-binding protein β subunit, related to β-transducin, and the nitric oxide synthase (NOS)-interacting protein. Cryptochrome and NOSIP are light-inducible genes. The studies show that the NOS inhibitor L-NMMA impairs both morphogenesis and motility of the cells. Finally, we report that the function of primmorphs to produce reactive nitrogen species can be abolished by a NOS inhibitor. We propose that the sponge cryptochrome-based photoreception system, through which photon signals are converted into radicals, is coupled to the NOS apparatus.

Effects of convective transport on chemical signal propagation in epithelia

We study effects of convective transport on a chemical front wave representing a signal propagation at a simple (single layer) epithelium by means of mathematical modeling. Plug flow and laminar flow regimes were considered. We observed a nonmonotonous dependence of the propagation velocity on the ligand receptor binding constant under influence of the convective transport. If the signal propagates downstream, the region of high velocities becomes much broader and spreads over several orders of magnitude of the binding constant. When the convective transport is oriented against the propagating signal, either velocity of the traveling front wave is slowed down or the traveling front wave can stop or reverse the direction of propagation. More importantly, chemical signal in epithelial systems influenced by the convective transport can propagate almost independently of the ligand-receptor binding constant in a broad range of this parameter. Furthermore, we found that the effects of the convective transport becomes more significant in systems where either the characteristic dimension of the extracellular space is larger/comparable with the spatial extent of the ligand diffusion trafficking or the ligand-receptor binding/ligand diffusion rate ratio is high.

Probing embryonic stem cell autocrine and paracrine signaling using microfluidics

Although stem cell fate is traditionally manipulated by exogenously altering the cells' extracellular signaling environment, the endogenous autocrine and paracrine signals produced by the cells also contribute to their two essential processes: self-renewal and differentiation. Autocrine and/or paracrine signals are fundamental to both embryonic stem cell self-renewal and early embryonic development, but the nature and contributions of these signals are often difficult to fully define using conventional methods. Microfluidic techniques have been used to explore the effects of cell-secreted signals by controlling cell organization or by providing precise control over the spatial and temporal cellular microenvironment. Here we review how such techniques have begun to be adapted for use with embryonic stem cells, and we illustrate how many remaining questions in embryonic stem cell biology could be addressed using microfluidic technologies.

Genesis of two-dimensional patterns in cross-gradient fields

Tissue morphogenesis is controlled by the two-dimensional patterning of gene expression in epithelial layers, that determines cell fates. The mechanisms of pattern formation involve intracellular regulatory networks controlled by paracrine and autocrine signaling. We develop a general logical scheme to deduce the morphology of two-dimensional patterns in the field of two crossed morphogen gradients enriched by the action of autocrine signaling that may subdivide expression domains in nontrivial ways. A variety of persistent patterns, either stationary or oscillatory, are generated using the various interaction schemes, some of which have been generated by a special algorithm including random inputs and selected according to suitable criteria. We give the full classification of a variety of stationary and oscillatory expression patterns in the presence of a single autocrine signal based on logical arguments. These results are further confirmed by numerical computations based on reaction-diffusion equations for morphogens and ligands and the discrete (cell-level) description of intracellular dynamics. Model simulations also elucidate transient processes, in particular interaction schemes. Different internal schemes may lead to identical persistent patterns, although relaxation may proceed in distinct ways. As an illustration of the general method, we test a particular scheme suggested by genetic studies of dynamic gene expression patterns in the follicular epithelium of the Drosophila eggshell.

Quantitative understanding of cell signaling: the importance of membrane organization

Systems biology modeling of signal transduction pathways traditionally employs ordinary differential equations, deterministic models based on the assumptions of spatial homogeneity. However, this can be a poor approximation for certain aspects of signal transduction, especially its initial steps: the cell membrane exhibits significant spatial organization, with diffusion rates approximately two orders of magnitude slower than those in the cytosol. Thus, to unravel the complexities of signaling pathways, quantitative models must consider spatial organization as an important feature of cell signaling. Furthermore, spatial separation limits the number of molecules that can physically interact, requiring stochastic simulation methods that account for individual molecules. Herein, we discuss the need for mathematical models and experiments that appreciate the importance of spatial organization in the membrane.

Beyond the wiring diagram: signalling through complex neuromodulator networks

During the computations performed by the nervous system, its 'wiring diagram'--the map of its neurons and synaptic connections--is dynamically modified and supplemented by multiple actions of neuromodulators that can be so complex that they can be thought of as constituting a biochemical network that combines with the neuronal network to perform the computation. Thus, the neuronal wiring diagram alone is not sufficient to specify, and permit us to understand, the computation that underlies behaviour. Here I review how such modulatory networks operate, the problems that their existence poses for the experimental study and conceptual understanding of the computations performed by the nervous system, and how these problems may perhaps be solved and the computations understood by considering the structural and functional 'logic' of the modulatory networks.

A mathematical model of intercellular signaling during epithelial wound healing

Recent experiments monitoring the healing process of wounded epithelial monolayers have demonstrated the necessity of MAPK activation for coordinated cell movement after damage. This MAPK activity is characterized by two wave-like phenomena. One MAPK "wave" that originates immediately after injury, propagates deep into the cell sheet, away from the edge, and then rebounds back to the wound interface. After this initial MAPK activity has largely disappeared, a second MAPK front propagates slowly from the wound interface and also continues into the cell sheet, maintaining a sustained level of MAPK activity throughout the cell sheet. It has been suggested that the first wave is initiated by Reactive Oxygen Species (ROS) generated at the time of injury. In this work, we develop a minimal mathematical model that reproduces the observed behavior. The main ingredients of our model are a competition between ligand (e.g., Epithelial Growth Factor) and ROS for the activation of Epithelial Growth Factor Receptor, and a feedback loop between receptor occupancy and MAPK activation. We explore the mathematical properties of the model and look for traveling wave solutions consistent with the experimentally observed MAPK activity patterns.

Autocrine signal transmission with extracellular ligand degradation

Traveling waves of cell signaling in epithelial layers orchestrate a number of important processes in developing and adult tissues. These waves can be mediated by positive feedback autocrine loops, a mode of cell signaling where binding of a diffusible extracellular ligand to a cell surface receptor can lead to further ligand release. We formulate and analyze a biophysical model that accounts for ligand-induced ligand release, extracellular ligand diffusion and ligand-receptor interaction. We focus on the case when the main mode for ligand degradation is extracellular and analyze the problem with the sharp threshold positive feedback nonlinearity. We derive expressions that link the speed of propagation and other characteristics of traveling waves to the parameters of the biophysical processes, such as diffusion rates, receptor expression level, etc. Analyzing the derived expressions we found that traveling waves in such systems can exhibit a number of unusual properties, e.g. non-monotonic dependence of the speed of propagation on ligand diffusivity. Our results for the fully developed traveling fronts can be used to analyze wave initiation from localized perturbations, a scenario that frequently arises in the in vitro models of epithelial wound healing, and guide future modeling studies of cell communication in epithelial layers.

Compensated optimal grids for elliptic boundary-value problems

A method is proposed which allows to efficiently treat elliptic problems on unbounded domains in two and three spatial dimensions in which one is only interested in obtaining accurate solutions at the domain boundary. The method is an extension of the optimal grid approach for elliptic problems, based on optimal rational approximation of the associated Neumann-to-Dirichlet map in Fourier space. It is shown that, using certain types of boundary discretization, one can go from second-order accurate schemes to essentially spectrally accurate schemes in two-dimensional problems, and to fourth-order accurate schemes in three-dimensional problems without any increase in the computational complexity. The main idea of the method is to modify the impedance function being approximated to compensate for the numerical dispersion introduced by a small finite-difference stencil discretizing the differential operator on the boundary. We illustrate how the method can be efficiently applied to nonlinear problems arising in modeling of cell communication.

Microfluidic lithography of SAMs on gold to create dynamic surfaces for directed cell migration and contiguous cell cocultures

A straightforward, flexible, and inexpensive method to create patterned self-assembled monolayers (SAMs) on gold using microfluidics-microfluidic lithography-has been developed. Using a microfluidic cassette, alkanethiols were rapidly patterned on gold surfaces to generate monolayers and mixed monolayers. The patterning methodology is flexible and, by controlling the solvent conditions and thiol concentration, permeation of alkanethiols into the surrounding PDMS microfluidic cassette can be advantageously used to create different patterned feature sizes and to generate well-defined SAM surface gradients with a single microfluidic chip. To demonstrate the utility of microfluidic lithography, multiple cell experiments were conducted. By patterning cell adhesive regions in an inert background, a combination of selective masking of the surface and centrifugation achieved spatial and temporal control of patterned cells, enabling the design of both dynamic surfaces for directed cell migration and contiguous cocultures. Cellular division and motility resulted in directed, dynamic migration, while the centrifugation-aided seeding of a second cell line produced contiguous cocultures with multiple sites for heterogeneous cell-cell interactions.

Time and length scales of autocrine signals in three dimensions

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

Noise can play an organizing role for the recurrent dynamics in excitable media

We analyze patterns of recurrent activity in a prototypical model of an excitable medium in the presence of noise. Without noise, this model robustly predicts the existence of spiral waves as the only recurrent patterns in two dimensions. With small noise, however, we found that this model is also capable of generating coherent target patterns, another type of recurrent activity that is widely observed experimentally. These patterns remain essentially deterministic despite the presence of the noise, yet their existence is impossible without it. Their degree of coherence can also be made arbitrarily high for wide ranges of the parameters, which does not require fine-tuning. Our findings demonstrate the need to reexamine current modeling approaches to active biological media.

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.

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.

Role of boundary conditions in an experimental model of epithelial wound healing

Coordinated cell movements in epithelial layers are essential for proper tissue morphogenesis and homeostasis, but our understanding of the mechanisms that coordinate the behavior of multiple cells in these processes is far from complete. Recent experiments with Madin-Darby canine kidney epithelial monolayers revealed a wave-like pattern of injury-induced MAPK activation and showed that it is essential for collective cell migration after wounding. To investigate the effects of the different aspects of wounding on cell sheet migration, we engineered a system that allowed us to dissect the classic wound healing assay. We studied Madin-Darby canine kidney sheet migration under three different conditions: 1) the classic wound healing assay, 2) empty space induction, where a confluent monolayer is grown adjacent to a slab of polydimethylsiloxane and the monolayer is not injured but allowed to migrate upon removal of the slab, and 3) injury via polydimethylsiloxane membrane peel-off, where an injured monolayer migrates onto plain tissue culture surface, as in the case of empty space induction allowing for direct comparison. By tracking the motion of individual cells within the sheet under these three conditions, we show how the dynamics of the individual cells' motion is responsible for the coordinated migration of the sheet and is coordinated with the activation of ERK1/2 MAPK. In addition, we demonstrate that the propagation of the waves of MAPK activation depends on the generation of reactive oxygen species at the wound edge.

Biological effects in unirradiated human tissue induced by radiation damage up to 1 mm away

A central tenet in understanding the biological effects of ionizing radiation has been that the initially affected cells were directly damaged by the radiation. By contrast, evidence has emerged concerning "bystander" responses involving damage to nearby cells that were not themselves directly traversed by the radiation. These long-range effects are of interest both mechanistically and for assessing risks from low-dose exposures, where only a small proportion of cells are directly hit. Bystander effects have been observed largely by using single-cell in vitro systems that do not have realistic multicellular morphology; no studies have as yet been reported in three-dimensional, normal human tissue. Given that the bystander phenomenon must involve cell-to-cell interactions, the relevance of such single-cell in vitro studies is questionable, and thus the significance of bystander responses for human health has remained unclear. Here, we describe bystander responses in a three-dimensional, normal human-tissue system. Endpoints were induction of micronucleated and apoptotic cells. A charged-particle microbeam was used, allowing irradiation of cells in defined locations in the tissue yet guaranteeing that no cells located more than a few micrometers away receive any radiation exposure. Unirradiated cells up to 1 mm distant from irradiated cells showed a significant enhancement in effect over background, with an average increase in effect of 1.7-fold for micronuclei and 2.8-fold for apoptosis. The surprisingly long range of bystander signals in human tissue suggests that bystander responses may be important in extrapolating radiation risk estimates from epidemiologically accessible doses down to very low doses where nonhit bystander cells will predominate.

A model of cytokine shedding induced by low doses of gamma radiation

A model for sustained shedding of epidermal growth factor (EGF) in response to low doses of gamma radiation was developed based on a time delay in the feedback from mitogen-activated protein kinase (MAPK) activation to metalloprotease activity in an autocrine signaling process. We determined the kinetic parameters of our model using the data available for MAPK activation by gamma irradiation in the 1-2-Gy dose range and then showed that predictions of the model were consistent with experimental results for the kinetics of EGF shedding into the growth medium after exposure of human mammary epithelial cells to 1-5 cGy of gamma radiation in the presence of antibodies that block ligand binding to EGF receptors. The model allowed us to estimate the rate of radiation-induced cytokine release per cell from measurements of EGF concentration in the growth medium and to assess the effectiveness of EGF shedding and subsequent diffusion through the medium as a mechanism for signal transmission between hit cells and bystanders.

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.

Spatial analysis of 3' phosphoinositide signaling in living fibroblasts: I. Uniform stimulation model and bounds on dimensionless groups

Fluorescent protein probes now permit spatial distributions of specific intracellular signaling molecules to be observed in real time. Mathematical models have been used to simulate molecular gradients and other spatial patterns within cells, and the output of such models may be compared directly with experiments if the binding of the fluorescent probe and the physics of the imaging technique are each incorporated. Here we present a comprehensive model describing the dynamics of 3' phosphoinositides (PIs), lipid second messengers produced in the plasma membrane in response to stimulation of the PI 3-kinase signaling pathway, as monitored in the cell-substratum contact area using total internal reflection fluorescence microscopy. With this technique it was previously shown that uniform stimulation of fibroblasts with platelet-derived growth factor elicits the formation of axisymmetric 3' PI gradients, which we now characterize in the context of our model. We find that upper and lower bounds on the relevant dimensionless model parameter values for an individual cell can be calculated from four well-defined fluorescence measurements. Based on our analysis, we expect that the key dimensionless group, the ratio of 3' PI turnover and diffusion rates, can be estimated within approximately 20% or less.

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.

Signal processing underlying extrinsic control of stem cell fate

PURPOSE OF REVIEW

Strategies to manipulate stem cells for therapeutic applications are limited by our inability to control or predict stem cell fate decisions in response to exogenous stimuli. This review focuses on the mechanisms by which exogenous stimuli influence cell fate.

RECENT FINDINGS

Limitations in our ability to control cell fate arises from our primarily qualitative understanding of stem cell regulation, which proposes straightforward cue-fate relationships that appear to be the exception rather than the rule. Alternatively, consideration of the underlying quantitative, temporal, and spatial mechanisms governing extrinsic regulation of stem cell fate may enable novel approaches to control stem cell output predictively.

SUMMARY

The authors review advances in the understanding of these underlying mechanisms, and discuss experimental and analytic tools necessary to investigate and use these mechanisms to control stem cell fate.

Discrete models of autocrine cell communication in epithelial layers

Pattern formation in epithelial layers heavily relies on cell communication by secreted ligands. Whereas the experimentally observed signaling patterns can be visualized at single-cell resolution, a biophysical framework for their interpretation is currently lacking. To this end, we develop a family of discrete models of cell communication in epithelial layers. The models are based on the introduction of cell-to-cell coupling coefficients that characterize the spatial range of intercellular signaling by diffusing ligands. We derive the coupling coefficients as functions of geometric, cellular, and molecular parameters of the ligand transport problem. Using these coupling coefficients, we analyze a nonlinear model of positive feedback between ligand release and binding. In particular, we study criteria of existence of the patterns consisting of clusters of a few signaling cells, as well as the onset of signal propagation. We use our model to interpret recent experimental studies of the EGFR/Rhomboid/Spitz module in Drosophila development.