A Reaction-Diffusion Model Explains Amplification of the PLC/PKC Pathway in Fibroblast Chemotaxis

Simulation of biochemical dynamics of [Formula: see text] and [Formula: see text] in fibroblast cell

Calcium dynamics is not only responsible for maintaining the framework and functions of the cell but also plays a role in the dynamics of other biochemical systems in the cell. Phospholipase C-[Formula: see text] l ([Formula: see text]) has a crucial role in the function of fibroblast cells. Experiments have shown that [Formula: see text] and [Formula: see text] have interdependent dynamics in fibroblast cells. However, no reaction-diffusion model exists for the two-way feedback system dynamics of [Formula: see text] and [Formula: see text] in fibroblasts till date. The computational model is designed to investigate the impact of variations in several processes, such as the [Formula: see text] pump, buffer process, source inflow, etc., on the system dynamics of [Formula: see text] and [Formula: see text] in fibroblast cells. The computational findings are obtained using finite element techniques, and the consequences of dysregulation in various processes on the spatiotemporal calcium and [Formula: see text] dynamics in fibroblasts are investigated. The results lead to the conclusion that the effects of buffer, source influx, diffusion, and [Formula: see text] pump can cause fluctuations in the dynamics of [Formula: see text] and [Formula: see text] in fibroblasts. Disruptions in these constitutive processes can result in changes in the dynamics of calcium and [Formula: see text]. Thus, the current model provides new/novel information regarding the precise dysregulatory constitutive systems that regulate calcium and [Formula: see text] kinetics, such as source inflow, diffusion, [Formula: see text], and buffer, can be responsible for excessive calcium and [Formula: see text] concentrations leading to fibrotic illnesses such as cancer and fibrosis.

Semi-autonomous wound invasion via matrix-deposited, haptotactic cues

Proper wound healing relies on invasion of fibroblasts via directed migration. While the related experimental and mathematical modeling literature has mainly focused on cell migration directed by soluble cues (chemotaxis), there is ample evidence that fibroblast migration is also directed by insoluble, matrix-bound cues (haptotaxis). Furthermore, numerous studies indicate that fibronectin (FN), a haptotactic ligand for fibroblasts, is present and dynamic in the provisional matrix throughout the proliferative phase of wound healing. In the present work, we show the plausibility of a hypothesis that fibroblasts themselves form and maintain haptotactic gradients in a semi-autonomous fashion. As a precursor to this, we examine the positive control scenario where FN is pre-deposited in the wound matrix, and fibroblasts maintain haptotaxis by removing FN at an appropriate rate. After developing conceptual and quantitative understanding of this scenario, we consider two cases in which fibroblasts activate the latent form of a matrix-loaded cytokine, TGFβ, which upregulates the fibroblasts' own secretion of FN. In the first of these, the latent cytokine is pre-patterned and released by the fibroblasts. In the second, fibroblasts in the wound produce the latent TGFβ, with the presence of the wound providing the only instruction. In all cases, wound invasion is more effective than a negative control model with haptotaxis disabled; however, there is a trade-off between the degree of fibroblast autonomy and the rate of invasion.

An integrated mechanistic and data-driven computational model predicts cell responses to high- and low-affinity EGFR ligands

The biophysical properties of ligand binding heavily influence the ability of receptors to specify cell fates. Understanding the rules by which ligand binding kinetics impact cell phenotype is challenging, however, because of the coupled information transfers that occur from receptors to downstream signaling effectors and from effectors to phenotypes. Here, we address that issue by developing an integrated mechanistic and data-driven computational modeling platform to predict cell responses to different ligands for the epidermal growth factor receptor (EGFR). Experimental data for model training and validation were generated using MCF7 human breast cancer cells treated with the high- and low-affinity ligands epidermal growth factor (EGF) and epiregulin (EREG), respectively. The integrated model captures the unintuitive, concentration-dependent abilities of EGF and EREG to drive signals and phenotypes differently, even at similar levels of receptor occupancy. For example, the model correctly predicts the dominance of EREG over EGF in driving a cell differentiation phenotype through AKT signaling at intermediate and saturating ligand concentrations and the ability of EGF and EREG to drive a broadly concentration-sensitive migration phenotype through cooperative ERK and AKT signaling. Parameter sensitivity analysis identifies EGFR endocytosis, which is differentially regulated by EGF and EREG, as one of the most important determinants of the alternative phenotypes driven by different ligands. The integrated model provides a new platform to predict how phenotypes are controlled by the earliest biophysical rate processes in signal transduction and may eventually be leveraged to understand receptor signaling system performance depends on cell context.

One-sentence summary

Integrated kinetic and data-driven EGFR signaling model identifies the specific signaling mechanisms that dictate cell responses to EGFR activation by different ligands.

A kinetic model of phospholipase C-γ1 linking structure-based insights to dynamics of enzyme autoinhibition and activation

Phospholipase C-γ1 (PLC-γ1) is a receptor-proximal enzyme that promotes signal transduction through PKC in mammalian cells. Because of the complexity of PLC-γ1 regulation, a two-state (inactive/active) model does not account for the intricacy of activation and inactivation steps at the plasma membrane. Here, we introduce a structure-based kinetic model of PLC-γ1, considering interactions of its regulatory Src homology 2 (SH2) domains and perturbation of those dynamics upon phosphorylation of Tyr783, a hallmark of activation. For PLC-γ1 phosphorylation to dramatically enhance enzyme activation as observed, we found that high intramolecular affinity of the C-terminal SH2 (cSH2) domain-pTyr783 interaction is critical, but this affinity need not outcompete the autoinhibitory interaction of the cSH2 domain. Under conditions for which steady-state PLC-γ1 activity is sensitive to the rate of Tyr783 phosphorylation, maintenance of the active state is surprisingly insensitive to the phosphorylation rate, since pTyr783 is well protected by the cSH2 domain while the enzyme is active. In contrast, maintenance of enzyme activity is sensitive to the rate of PLC-γ1 membrane (re)binding. Accordingly, we found that hypothetical PLC-γ1 mutations that either weaken autoinhibition or strengthen membrane binding influence the activation kinetics differently, which could inform the characterization of oncogenic variants. Finally, we used this newly informed kinetic scheme to refine a spatial model of PLC/PKC polarization during chemotaxis. The refined model showed improved stability of the polarized pattern while corroborating previous qualitative predictions. As demonstrated here for PLC-γ1, this approach may be adapted to model the dynamics of other receptor- and membrane-proximal enzymes.

A metabolic reaction-diffusion model for PKCα translocation via PIP2 hydrolysis in an endothelial cell

Hydrolysis of the phospholipid phosphatidylinositol 4,5-bisphosphate (PIP2) at the cell membrane induces the release of inositol 1,4,5-trisphosphate (IP3) into the cytoplasm and diffusion of diacylglycerol (DAG) through the membrane, respectively. Release of IP3 subsequently increases Ca2+ levels in the cytoplasm, which results in activation of protein kinase C α (PKCα) by Ca2+ and DAG, and finally the translocation of PKCα from the cytoplasm to the membrane. In this study, we developed a metabolic reaction-diffusion framework to simulate PKCα translocation via PIP2 hydrolysis in an endothelial cell. A three-dimensional cell model, divided into membrane and cytoplasm domains, was reconstructed from confocal microscopy images. The associated metabolic reactions were divided into their corresponding domain; PIP2 hydrolysis at the membrane domain resulted in DAG diffusion at the membrane domain and IP3 release into the cytoplasm domain. In the cytoplasm domain, Ca2+ was released from the endoplasmic reticulum, and IP3, Ca2+, and PKCα diffused through the cytoplasm. PKCα bound Ca2+ at, and diffused through, the cytoplasm, and was finally activated by binding with DAG at the membrane. Using our model, we analyzed IP3 and DAG dynamics, Ca2+ waves, and PKCα translocation in response to a microscopic stimulus. We found a qualitative agreement between our simulation results and our experimental results obtained by live-cell imaging. Interestingly, our results suggest that PKCα translocation is dominated by DAG dynamics. This three-dimensional reaction-diffusion mathematical framework could be used to investigate the link between PKCα activation in a cell and cell function.

Mechanistic models of PLC/PKC signaling implicate phosphatidic acid as a key amplifier of chemotactic gradient sensing

Chemotaxis of fibroblasts and other mesenchymal cells is critical for embryonic development and wound healing. Fibroblast chemotaxis directed by a gradient of platelet-derived growth factor (PDGF) requires signaling through the phospholipase C (PLC)/protein kinase C (PKC) pathway. Diacylglycerol (DAG), the lipid product of PLC that activates conventional PKCs, is focally enriched at the up-gradient leading edge of fibroblasts responding to a shallow gradient of PDGF, signifying polarization. To explain the underlying mechanisms, we formulated reaction-diffusion models including as many as three putative feedback loops based on known biochemistry. These include the previously analyzed mechanism of substrate-buffering by myristoylated alanine-rich C kinase substrate (MARCKS) and two newly considered feedback loops involving the lipid, phosphatidic acid (PA). DAG kinases and phospholipase D, the enzymes that produce PA, are identified as key regulators in the models. Paradoxically, increasing DAG kinase activity can enhance the robustness of DAG/active PKC polarization with respect to chemoattractant concentration while decreasing their whole-cell levels. Finally, in simulations of wound invasion, efficient collective migration is achieved with thresholds for chemotaxis matching those of polarization in the reaction-diffusion models. This multi-scale modeling framework offers testable predictions to guide further study of signal transduction and cell behavior that affect mesenchymal chemotaxis.

Cell movement directed by external gradients of chemical composition is critical for immune responses, wound healing, and development. Although theoretical concepts explaining how shallow external gradients might definitively polarize a cell’s motility have been offered over the past two decades, mathematical models cast in terms of defined molecules and mechanisms are uncommon in this context. Based on both recent and older insights from the literature, we offer mechanistic models that are able to explain experimentally observed polarization of signal transduction elicited by shallow attractant gradients. A novel insight of our models is the implicated role of phosphatidic acid, a membrane lipid produced by at least two enzymatic pathways, in two positive feedback loops that amplify signal transduction locally. In separate simulations, we explored the implications of polarization for efficient cell invasion during wound healing. We expected that the ability to polarize in response to shallow gradients would enhance the speed of wound invasion, but an unexpected finding is that this property can promote intermittent polarization throughout the wound.

A PKC-MARCKS-PI3K regulatory module links Ca2+ and PIP3 signals at the leading edge of polarized macrophages

The leukocyte chemosensory pathway detects attractant gradients and directs cell migration to sites of inflammation, infection, tissue damage, and carcinogenesis. Previous studies have revealed that local Ca²⁺ and PIP₃ signals at the leading edge of polarized leukocytes play central roles in positive feedback loop essential to cell polarization and chemotaxis. These prior studies showed that stimulation of the leading edge Ca²⁺ signal can strongly activate PI3K, thereby triggering a larger PIP₃ signal, but did not elucidate the mechanistic link between Ca²⁺ and PIP₃ signaling. A hypothesis explaining this link emerged, postulating that Ca²⁺-activated PKC displaces the MARCKS protein from plasma membrane PIP₂, thereby releasing sequestered PIP₂ to serve as the target and substrate lipid of PI3K in PIP₃ production. In vitro single molecule studies of the reconstituted pathway on lipid bilayers demonstrated the feasibility of this PKC-MARCKS-PI3K regulatory module linking Ca²⁺ and PIP₃ signals in the reconstituted system. The present study tests the model predictions in live macrophages by quantifying the effects of: (a) two pathway activators—PDGF and ATP that stimulate chemoreceptors and Ca²⁺ influx, respectively; and (b) three pathway inhibitors—wortmannin, EGTA, and Go6976 that inhibit PI3K, Ca²⁺ influx, and PKC, respectively; on (c) four leading edge activity sensors—AKT-PH-mRFP, CKAR, MARCKSp-mRFP, and leading edge area that report on PIP₃ density, PKC activity, MARCKS membrane binding, and leading edge expansion/contraction, respectively. The results provide additional evidence that PKC and PI3K are both essential elements of the leading edge positive feedback loop, and strongly support the existence of a PKC-MARCKS-PI3K regulatory module linking the leading edge Ca²⁺ and PIP₃ signals. As predicted, activators stimulate leading edge PKC activity, displacement of MARCKS from the leading edge membrane and increased leading edge PIP₃ levels, while inhibitors trigger the opposite effects. Comparison of the findings for the ameboid chemotaxis of leukocytes with recently published findings for the mesenchymal chemotaxis of fibroblasts suggests that some features of the emerging leukocyte leading edge core pathway (PLC-DAG-Ca²⁺-PKC-MARCKS-PIP₂-PI3K-PIP₃) may well be shared by all chemotaxing eukaryotic cells, while other elements of the leukocyte pathway may be specialized features of these highly optimized, professional gradient-seeking cells. More broadly, the findings suggest a molecular mechanism for the strong links between phospho-MARCKS and many human cancers.