Pepperberg plot: Modeling flash response saturation in retinal rods of mouse.

Retinal rods evolved to be able to detect single photons. Despite their exquisite sensitivity, rods operate over many log units of light intensity. Several processes inside photoreceptor cells make this incredible light adaptation possible. Here, we added to our previously developed, fully space resolved biophysical model of rod phototransduction, some of the mechanisms that play significant roles in shaping the rod response under high illumination levels: the function of RGS9 in shutting off G protein transducin, and calcium dependences of the phosphorylation rates of activated rhodopsin, of the binding of cGMP to the light-regulated ion channel, and of two membrane guanylate cyclase activities. A well stirred version of this model captured the responses to bright, saturating flashes in WT and mutant mouse rods and was used to explain "Pepperberg plots," that graph the time during which the response is saturated against the natural logarithm of flash strength for bright flashes. At the lower end of the range, saturation time increases linearly with the natural logarithm of flash strength. The slope of the relation (τD) is dictated by the time constant of the rate-limiting (slowest) step in the shutoff of the phototransduction cascade, which is the hydrolysis of GTP by transducin. We characterized mathematically the X-intercept ( Φ o ) which is the number of photoisomerizations that just saturates the rod response. It has been observed that for flash strengths exceeding a few thousand photoisomerizations, the curves depart from linearity. Modeling showed that the "upward bend" for very bright flash intensities could be explained by the dynamics of RGS9 complex and further predicted that there would be a plateau at flash strengths giving rise to more than ~107 photoisomerizations due to activation of all available PDE. The model accurately described alterations in saturation behavior of mutant murine rods resulting from transgenic perturbations of the cascade targeting membrane guanylate cyclase activity, and expression levels of GRK, RGS9, and PDE. Experimental results from rods expressing a mutant light-regulated channel purported to lack calmodulin regulation deviated from model predictions, suggesting that there were other factors at play.

Effects of cell size and bicarbonate on single photon response variability in retinal rods.

Accurate photon counting requires that rods generate highly amplified, reproducible single photon responses (SPRs). The SPR is generated within the rod outer segment (ROS), a multilayered structure built from membranous disks that house rhodopsin. Photoisomerization of rhodopsin at the disk rim causes a local depletion of cGMP that closes ion channels in the plasmalemma located nearby with relative rapidity. In contrast, a photoisomerization at the disk center, distant from the plasmalemma, has a delayed impact on the ion channels due to the time required for cGMP redistribution. Radial differences should be greatest in large diameter rods. By affecting membrane guanylate cyclase activity, bicarbonate could impact spatial inhomogeneity in cGMP content. It was previously known that in the absence of bicarbonate, SPRs are larger and faster at the base of a toad ROS (where the ROS attaches to the rest of the cell) than at the distal tip. Given that bicarbonate enters the ROS at the base and diffuses to the tip and that it expedites flash response recovery, there should be an axial concentration gradient for bicarbonate that would accentuate the base-to-tip SPR differences. Seeking to understand how ROS geometry and bicarbonate affect SPR variability, we used mathematical modeling and made electrophysiological recordings of single rods. Modeling predicted and our experiments confirmed minor radial SPR variability in large diameter, salamander rods that was essentially unchanged by bicarbonate. SPRs elicited at the base and tip of salamander rods were similar in the absence of bicarbonate, but when treated with 30 mM bicarbonate, SPRs at the base became slightly faster than those at the tip, verifying the existence of an axial gradient for bicarbonate. The differences were small and unlikely to undermine visual signaling. However, in toad rods with longer ROSs, bicarbonate somehow suppressed the substantial, axial SPR variability that is naturally present in the absence of bicarbonate. Modeling suggested that the axial gradient of bicarbonate might dampen the primary phototransduction cascade at the base of the ROS. This novel effect of bicarbonate solves a mystery as to how toad vision is able to function effectively in extremely dim light.

Phototransduction in retinal cones: Analysis of parameter importance.

In daylight, cone photoreceptors in the retina are responsible for the bulk of visual perception, yet compared to rods, far less is known quantitatively about their biochemistry. This is partly because it is hard to isolate and purify cone proteins. The issue is also complicated by the synergistic interaction of these parameters in producing systems biology outputs, such as photoresponse. Using a 3-D resolved, finite element model of cone outer segments, here we conducted a study of parameter significance using global sensitivity analysis, by Sobol indices, which was contextualized within the uncertainty surrounding these parameters in the available literature. The analysis showed that a subset of the parameters influencing the circulating dark current, such as the turnover rate of cGMP in the dark, may be most influential for variance with experimental flash response, while the shut-off rates of photoexcited rhodopsin and phosphodiesterase also exerted sizable effect. The activation rate of transducin by rhodopsin and the light-induced hydrolysis rate of cGMP exerted measurable effects as well but were estimated as relatively less significant. The results of this study depend on experimental ranges currently described in the literature and should be revised as these become better established. To that end, these findings may be used to prioritize parameters for measurement in future investigations.

Position of rhodopsin photoisomerization on the disk surface confers variability to the rising phase of the single photon response in vertebrate rod photoreceptors.

Retinal rods function as accurate photon counters to provide for vision under very dim light. To do so, rods must generate highly amplified, reproducible responses to single photons, yet outer segment architecture and randomness in the location of rhodopsin photoisomerization on the surface of an internal disk introduce variability to the rising phase of the photon response. Soon after a photoisomerization at a disk rim, depletion of cGMP near the plasma membrane closes ion channels and hyperpolarizes the rod. But with a photoisomerization in the center of a disk, local depletion of cGMP is distant from the channels in the plasma membrane. Thus, channel closure is delayed by the time required for the reduction of cGMP concentration to reach the plasma membrane. Moreover, the local fall in cGMP dissipates over a larger volume before affecting the channels, so response amplitude is reduced. This source of variability increases with disk radius. Using a fully space-resolved biophysical model of rod phototransduction, we quantified the variability attributable to randomness in the location of photoisomerization as a function of disk structure. In mouse rods that have small disks bearing a single incisure, this variability was negligible in the absence of the incisure. Variability was increased slightly by the incisure, but randomness in the shutoff of rhodopsin emerged as the main source of single photon response variability at all but the earliest times. Variability arising from randomness in the transverse location of photoisomerization increased in magnitude and persisted over a longer period in the photon response of large salamander rods. A symmetric arrangement of multiple incisures in the disks of salamander rods greatly reduced this variability during the rising phase, but the incisures had the opposite effect on variability arising from randomness in rhodopsin shutoff at later times.

Local, nonlinear effects of cGMP and Ca2+ reduce single photon response variability in retinal rods.

The single photon response (SPR) in vertebrate photoreceptors is inherently variable due to several stochastic events in the phototransduction cascade, the main one being the shutoff of photoactivated rhodopsin. Deactivation is driven by a random number of steps, each of random duration with final quenching occurring after a random delay. Nevertheless, variability of the SPR is relatively low, making the signal highly reliable. Several biophysical and mathematical mechanisms contributing to variability suppression have been examined by the authors. Here we investigate the contribution of local depletion of cGMP by PDE*, the non linear dependence of the photocurrent on cGMP, Ca2+ feedback by making use of a fully space resolved (FSR) mathematical model, applied to two species (mouse and salamander), by varying the cGMP diffusion rate severalfold and rod outer segment diameter by an order of magnitude, and by introducing new, more refined, and time dependent variability functionals. Globally well stirred (GWS) models, and to a lesser extent transversally well stirred models (TWS), underestimate the role of nonlinearities and local cGMP depletion in quenching the variability of the circulating current with respect to fully space resolved models (FSR). These distortions minimize the true extent to which SPR is stabilized by locality in cGMP depletion, nonlinear effects linking cGMP to current, and Ca2+ feedback arising from the physical separation of E* from the ion channels located on the outer shell, and the diffusion of these second messengers in the cytoplasm.

Multi-scale, numerical modeling of spatio-temporal signaling in cone phototransduction.

Mammals have two types of photoreceptors, rods and cones. While rods are exceptionally sensitive and mediate vision at very low illumination levels, cones operate in daylight and are responsible for the bulk of visual perception in most diurnal animals, including humans. Yet the mechanisms of phototransduction in cones is understudied, largely due to unavailability of pure cone outer segment (COS) preparations. Here we present a novel mathematical model of cone phototransduction that explicitly takes into account complex cone geometry and its multiple physical scales, faithfully reproduces features of the cone response, and is orders of magnitude more efficient than the standard 3D diffusion model. This is accomplished through the mathematical techniques of homogenization and concentrated capacity. The homogenized model is then computationally implemented by finite element method. This homogenized model permits one to analyze the effects of COS geometry on visual transduction and lends itself to performing large numbers of numerical trials, as required for parameter analysis and the stochasticity of rod and cone signal transduction. Agreement between the nonhomogenized, (i.e., standard 3D), and homogenized diffusion models is reported along with their simulation times and memory costs. Virtual expression of rod biochemistry on cone morphology is also presented for understanding some of the characteristic differences between rods and cones. These simulations evidence that 3D cone morphology and ion channel localization contribute to biphasic flash response, i.e undershoot. The 3D nonhomogenized and homogenized models are contrasted with more traditional and coarser well-stirred and 1D longitudinal diffusion models. The latter are single-scale and do not explicitly account for the multi-scale geometry of the COS, unlike the 3D homogenized model. We show that simpler models exaggerate the magnitude of the current suppression, yield accelerated time to peak, and do not predict the local concentration of cGMP at the ionic channels.

Analysis of diffusion in curved surfaces and its application to tubular membranes.

Diffusion of particles in curved surfaces is inherently complex compared with diffusion in a flat membrane, owing to the nonplanarity of the surface. The consequence of such nonplanar geometry on diffusion is poorly understood but is highly relevant in the case of cell membranes, which often adopt complex geometries. To address this question, we developed a new finite element approach to model diffusion on curved membrane surfaces based on solutions to Fick's law of diffusion and used this to study the effects of geometry on the entry of surface-bound particles into tubules by diffusion. We show that variations in tubule radius and length can distinctly alter diffusion gradients in tubules over biologically relevant timescales. In addition, we show that tubular structures tend to retain concentration gradients for a longer time compared with a comparable flat surface. These findings indicate that sorting of particles along the surfaces of tubules can arise simply as a geometric consequence of the curvature without any specific contribution from the membrane environment. Our studies provide a framework for modeling diffusion in curved surfaces and suggest that biological regulation can emerge purely from membrane geometry.

Simplified equation to extract diffusion coefficients from confocal FRAP data.

Quantitative measurements of diffusion can provide important information about how proteins and lipids interact with their environment within the cell and the effective size of the diffusing species. Confocal fluorescence recovery after photobleaching (FRAP) is one of the most widely accessible approaches to measure protein and lipid diffusion in living cells. However, straightforward approaches to quantify confocal FRAP measurements in terms of absolute diffusion coefficients are currently lacking. Here, we report a simplified equation that can be used to extract diffusion coefficients from confocal FRAP data using the half time of recovery and effective bleach radius for a circular bleach region, and validate this equation for a series of fluorescently labeled soluble and membrane-bound proteins and lipids. We show that using this approach, diffusion coefficients ranging over three orders of magnitude can be obtained from confocal FRAP measurements performed under standard imaging conditions, highlighting its broad applicability.

Rhodopsin expression level affects rod outer segment morphology and photoresponse kinetics.

BACKGROUND: The retinal rod outer segment is a sensory cilium that is specialized for the conversion of light into an electrical signal. Within the cilium, up to several thousand membranous disks contain as many as a billion copies of rhodopsin for efficient photon capture. Disks are continually turned over, requiring the daily synthesis of a prodigious amount of rhodopsin. To promote axial diffusion in the aqueous cytoplasm, the disks have one or more incisures. Across vertebrates, the range of disk diameters spans an order of magnitude, and the number and length of the incisures vary considerably, but the mechanisms controlling disk architecture are not well understood. The finding that transgenic mice overexpressing rhodopsin have enlarged disks lacking an incisure prompted us to test whether lowered rhodopsin levels constrain disk assembly. METHODOLOGY/PRINCIPAL FINDINGS: The structure and function of rods from hemizygous rhodopsin knockout (R+/-) mice with decreased rhodopsin expression were analyzed by transmission electron microscopy and single cell recording. R+/- rods were structurally altered in three ways: disk shape changed from circular to elliptical, disk surface area decreased, and the single incisure lengthened to divide the disk into two sections. Photocurrent responses to flashes recovered more rapidly than normal. A spatially resolved model of phototransduction indicated that changes in the packing densities of rhodopsin and other transduction proteins were responsible. The decrease in aqueous outer segment volume and the lengthened incisure had only minor effects on photon response amplitude and kinetics. CONCLUSIONS/SIGNIFICANCE: Rhodopsin availability limits disk assembly and outer segment girth in normal rods. The incisure may buffer the supply of structural proteins needed to form larger disks. Decreased rhodopsin level accelerated photoresponse kinetics by increasing the rates of molecular collisions on the membrane. Faster responses, together with fewer rhodopsins, combine to lower overall sensitivity of R+/- rods to light.

Identification of key factors that reduce the variability of the single photon response.

Rod photoreceptors mediate vision in dim light. Their biological function is to discriminate between distinct, very low levels of illumination, i.e., they serve as reliable photon counters. This role requires high reproducibility of the response to a particular number of photons. Indeed, single photon responses demonstrate unexpected low variability, despite the stochastic nature of the individual steps in the transduction cascade. We analyzed individual system mechanisms to identify their contribution to variability suppression. These include: (i) cooperativity of the regulation of the second messengers; (ii) diffusion of cGMP and Ca(2+) in the cytoplasm; and (iii) the effect of highly localized cGMP hydrolysis by activated phosphodiesterase resulting in local saturation. We find that (i) the nonlinear relationships between second messengers and current at the plasma membrane, and the cGMP hydrolysis saturation effects, play a major role in stabilizing the system; (ii) the presence of a physical space where the second messengers move by Brownian motion contributes to stabilization of the photoresponse; and (iii) keeping Ca(2+) at its dark level has only a minor effect on the variability of the system. The effects of diffusion, nonlinearity, and saturation synergize in reducing variability, supporting the notion that the observed high fidelity of the photoresponse is the result of global system function of phototransduction.

Mathematical model of PAR1-mediated activation of human platelets.

Thrombin, one of the major proteases in the coagulation cascade, activates protease activated receptors 1 and 4 (PAR 1 and PAR4) to generate a network of intracellular signals that lead to stable platelet aggregation. Abnormal platelet activation could lead to either thrombosis or bleeding disorders, thus a predictive model of platelet activation would be an invaluable tool for the study of platelet function. In this work, we developed a computational model of PAR1-stimulated human platelet activation fully based on experimental observations. The model is represented by a system of ordinary differential equations (ODEs) describing the kinetics of the interacting components. The model is able to reproduce experimental dose responses and time-courses of cytosolic calcium (Ca(2+)), phosphatidylinositol 4,5-bisphosphate (PIP2), diacylglycerol (DAG), GTP-bound Ras-proximate-1 (Rap1GTP), secretion of dense-granules, and activation of integrin α2bß3 (GPIIbIIIa). Because of the inherent complexity of such a model, we also provide a simple way to identify and divide the system into interlinked functional modules to reduce the number of unknown parameters. Both the full and the reduced kinetic models are shown to predict platelet behavior in response to PAR1 activation.

A quantitative approach to analyze binding diffusion kinetics by confocal FRAP.

Most of the important types of interactions that occur in cells can be characterized as binding-diffusion type processes, and can be quantified by kinetic rate constants such as diffusion coefficients (D) and binding rate constants (k(on) and k(off)). Confocal FRAP is a potentially important tool for the quantitative analysis of intracellular binding-diffusion kinetics, but how to dependably extract accurate kinetic constants from such analyses is still an open question. To this end, in this study, we developed what we believe is a new analytical model for confocal FRAP-based measurements of intracellular binding-diffusion processes, based on a closed-form equation of the FRAP formula for a spot photobleach geometry. This approach incorporates a binding diffusion model that allows for diffusion of both the unbound and bound species, and also compensates for binding diffusion that occurs during photobleaching, a critical consideration in confocal FRAP analysis. In addition, to address the problem of parametric multiplicity, we propose a scheme to reduce the number of fitting parameters in the effective diffusion subregime when D's for the bound and unbound species are known. We validate this method by measuring kinetic rate constants for the CAAX-mediated binding of Ras to membranes of the endoplasmic reticulum, obtaining binding constants of k(on) ∼ 255/s and k(off) ∼ 31/s.

Kinetics of rhodopsin deactivation and its role in regulating recovery and reproducibility of rod photoresponse.

The single photon response (SPR) in vertebrate phototransduction is regulated by the dynamics of R* during its lifetime, including the random number of phosphorylations, the catalytic activity and the random sojourn time at each phosphorylation level. Because of this randomness the electrical responses are expected to be inherently variable. However the SPR is highly reproducible. The mechanisms that confer to the SPR such a low variability are not completely understood. The kinetics of rhodopsin deactivation is investigated by a Continuous Time Markov Chain (CTMC) based on the biochemistry of rhodopsin activation and deactivation, interfaced with a spatio-temporal model of phototransduction. The model parameters are extracted from the photoresponse data of both wild type and mutant mice, having variable numbers of phosphorylation sites and, with the same set of parameters, the model reproduces both WT and mutant responses. The sources of variability are dissected into its components, by asking whether a random number of turnoff steps, a random sojourn time between steps, or both, give rise to the known variability. The model shows that only the randomness of the sojourn times in each of the phosphorylated states contributes to the Coefficient of Variation (CV) of the response, whereas the randomness of the number of R* turnoff steps has a negligible effect. These results counter the view that the larger the number of decay steps of R*, the more stable the photoresponse is. Our results indicate that R* shutoff is responsible for the variability of the photoresponse, while the diffusion of the second messengers acts as a variability suppressor.

A generalization of theory for two-dimensional fluorescence recovery after photobleaching applicable to confocal laser scanning microscopes.

Fluorescence recovery after photobleaching (FRAP) using confocal laser scanning microscopes (confocal FRAP) has become a valuable technique for studying the diffusion of biomolecules in cells. However, two-dimensional confocal FRAP sometimes yields results that vary with experimental setups, such as different bleaching protocols and bleaching spot sizes. In addition, when confocal FRAP is used to measure diffusion coefficients (D) for fast diffusing molecules, it often yields D-values that are one or two orders-of-magnitude smaller than that predicted theoretically or measured by alternative methods such as fluorescence correlation spectroscopy. Recently, it was demonstrated that this underestimation of D can be corrected by taking diffusion during photobleaching into consideration. However, there is currently no consensus on confocal FRAP theory, and no efforts have been made to unify theories on conventional and confocal FRAP. To this end, we generalized conventional FRAP theory to incorporate diffusion during photobleaching so that analysis by conventional FRAP theory for a circular region of interest is easily applicable to confocal FRAP. Finally, we demonstrate the accuracy of these new (to our knowledge) formulae by measuring D for soluble enhanced green fluorescent protein in aqueous glycerol solution and in the cytoplasm and nucleus of COS7 cells.

Overexpression of rhodopsin alters the structure and photoresponse of rod photoreceptors.

Rhodopsins are densely packed in rod outer-segment membranes to maximize photon absorption, but this arrangement interferes with transducin activation by restricting the mobility of both proteins. We attempted to explore this phenomenon in transgenic mice that overexpressed rhodopsin in their rods. Photon capture was improved, and, for a given number of photoisomerizations, bright-flash responses rose more gradually with a reduction in amplification--but not because rhodopsins were more tightly packed in the membrane. Instead, rods increased their outer-segment diameters, accommodating the extra rhodopsins without changing the rhodopsin packing density. Because the expression of other phototransduction proteins did not increase, transducin and its effector phosphodiesterase were distributed over a larger surface area. That feature, as well as an increase in cytosolic volume, was responsible for delaying the onset of the photoresponse and for attenuating its amplification.

Diffusion of the second messengers in the cytoplasm acts as a variability suppressor of the single photon response in vertebrate phototransduction.

The single photon response in vertebrate phototransduction is highly reproducible despite a number of random components of the activation cascade, including the random activation site, the random walk of an activated receptor, and its quenching in a random number of steps. Here we use a previously generated and tested spatiotemporal mathematical and computational model to identify possible mechanisms of variability reduction. The model permits one to separate the process into modules, and to analyze their impact separately. We show that the activation cascade is responsible for generation of variability, whereas diffusion of the second messengers is responsible for its suppression. Randomness of the activation site contributes at early times to the coefficient of variation of the photoresponse, whereas the Brownian path of a photoisomerized rhodopsin (Rh*) has a negligible effect. The major driver of variability is the turnoff mechanism of Rh*, which occurs essentially within the first 2-4 phosphorylated states of Rh*. Theoretically increasing the number of steps to quenching does not significantly decrease the corresponding coefficient of variation of the effector, in agreement with the biochemical limitations on the phosphorylated states of the receptor. Diffusion of the second messengers in the cytosol acts as a suppressor of the variability generated by the activation cascade. Calcium feedback has a negligible regulatory effect on the photocurrent variability. A comparative variability analysis has been conducted for the phototransduction in mouse and salamander, including a study of the effects of their anatomical differences such as incisures and photoreceptors geometry on variability generation and suppression.

Modeling the role of incisures in vertebrate phototransduction.

Phototransduction is mediated by a G-protein-coupled receptor-mediated cascade, activated by light and localized to rod outer segment (ROS) disk membranes, which, in turn, drives a diffusion process of the second messengers cGMP and Ca2+ in the ROS cytosol. This process is hindered by disks-which, however, bear physical cracks, known as incisures, believed to favor the longitudinal diffusion of cGMP and Ca2+. This article is aimed at highlighting the biophysical functional role and significance of incisures, and their effect on the local and global response of the photocurrent. Previous work on this topic regarded the ROS as well stirred in the radial variables, lumped the diffusion mechanism on the longitudinal axis of the ROS, and replaced the cytosolic diffusion coefficients by effective ones, accounting for incisures through their total patent area only. The fully spatially resolved model recently published by our group is a natural tool to take into account other significant details of incisures, including their geometry and distribution. Using mathematical theories of homogenization and concentrated capacity, it is shown here that the complex diffusion process undergone by the second messengers cGMP and Ca2+ in the ROS bearing incisures can be modeled by a family of two-dimensional diffusion processes on the ROS cross sections, glued together by other two-dimensional diffusion processes, accounting for diffusion in the ROS outer shell and in the bladelike regions comprised by the stack of incisures. Based on this mathematical model, a code has been written, capable of incorporating an arbitrary number of incisures and activation sites, with any given arbitrary distribution within the ROS. The code is aimed at being an operational tool to perform numerical experiments of phototransduction, in rods with incisures of different geometry and structure, under a wide spectrum of operating conditions. The simulation results show that incisures have a dual biophysical function. On the one hand, since incisures line up from disk to disk, they create vertical cytoplasmic channels crossing the disks, thus facilitating diffusion of second messengers; on the other hand, at least in those species bearing multiple incisures, they divide the disks into lobes like the petals of a flower, thus confining the diffusion of activated phosphodiesterase and localizing the photon response. Accordingly, not only the total area of incisures, but their geometrical shape and distribution as well, significantly influence the global photoresponse.

The DNA binding activity of p53 displays reaction-diffusion kinetics.

The tumor suppressor protein p53 plays a key role in maintaining the genomic stability of mammalian cells and preventing malignant transformation. In this study, we investigated the intracellular diffusion of a p53-GFP fusion protein using confocal fluorescence recovery after photobleaching. We show that the diffusion of p53-GFP within the nucleus is well described by a mathematical model for diffusion of particles that bind temporarily to a spatially homogeneous immobile structure with binding and release rates k1 and k2, respectively. The diffusion constant of p53-GFP was estimated to be Dp53-GFP=15.4 microm2 s-1, significantly slower than that of GFP alone, DGFP=41.6 microm2 s-1. The reaction rates of the binding and unbinding of p53-GFP were estimated as k1=0.3 s-1 and k2=0.4 s-1, respectively, values suggestive of nonspecific binding. Consistent with this finding, the diffusional mobilities of tumor-derived sequence-specific DNA binding mutants of p53 were indistinguishable from that of the wild-type protein. These data are consistent with a model in which, under steady-state conditions, p53 is latent and continuously scans DNA, requiring activation for sequence-specific DNA binding.

Functional selectivity of G protein signaling by agonist peptides and thrombin for the protease-activated receptor-1.

Thrombin activates protease-activated receptor-1 (PAR-1) by cleavage of the amino terminus to unmask a tethered ligand. Although peptide analogs can activate PAR-1, we show that the functional responses mediated via PAR-1 differ between the agonists. Thrombin caused endothelial monolayer permeability and mobilized intracellular calcium with EC(50) values of 0.1 and 1.7 nm, respectively. The opposite order of activation was observed for agonist peptide (SFLLRN-CONH(2) or TFLLRNKPDK) activation. The addition of inactivated thrombin did not affect agonist peptide signaling, suggesting that the differences in activation mechanisms are intramolecular in origin. Although activation of PAR-1 or PAR-2 by agonist peptides induced calcium mobilization, only PAR-1 activation affected barrier function. Induced barrier permeability is likely to be Galpha(12/13)-mediated as chelation of Galpha(q)-mediated intracellular calcium with BAPTA-AM, pertussis toxin inhibition of Galpha(i/o), or GM6001 inhibition of matrix metalloproteinase had no effect, whereas Y-27632 inhibition of the Galpha(12/13)-mediated Rho kinase abrogated the response. Similarly, calcium mobilization is Galpha(q)-mediated and independent of Galpha(i/o) and Galpha(12/13) because pertussis toxin Y-27632 and had no effect, whereas U-73122 inhibition of phospholipase C-beta blocked the response. It is therefore likely that changes in permeability reflect Galpha(12/13) activation, and changes in calcium reflect Galpha(q) activation, implying that the pharmacological differences between agonists are likely caused by the ability of the receptor to activate Galpha(12/13) or Galpha(q). This functional selectivity was characterized quantitatively by a mathematical model describing each step leading to Rho activation and/or calcium mobilization. This model provides an estimate that peptide activation alters receptor/G protein binding to favor Galpha(q) activation over Galpha(12/13) by approximately 800-fold.