(C) PLOS One
This story was originally published by PLOS One and is unaltered.
 . . . . . . . . . .



Spatial models of pattern formation during phagocytosis [1]

['John Cody Herron', 'Curriculum In Bioinformatics', 'Computational Biology', 'University Of North Carolina At Chapel Hill', 'Chapel Hill', 'North Carolina', 'United States Of America', 'Computational Medicine Program', 'Shiqiong Hu', 'Department Of Pharmacology']

Date: 2022-11 

Phagocytosis, the biological process in which cells ingest large particles such as bacteria, is a key component of the innate immune response. Fcγ receptor (FcγR)-mediated phagocytosis is initiated when these receptors are activated after binding immunoglobulin G (IgG). Receptor activation initiates a signaling cascade that leads to the formation of the phagocytic cup and culminates with ingestion of the foreign particle. In the experimental system termed “frustrated phagocytosis”, cells attempt to internalize micropatterned disks of IgG. Cells that engage in frustrated phagocytosis form “rosettes” of actin-enriched structures called podosomes around the IgG disk. The mechanism that generates the rosette pattern is unknown. We present data that supports the involvement of Cdc42, a member of the Rho family of GTPases, in pattern formation. Cdc42 acts downstream of receptor activation, upstream of actin polymerization, and is known to play a role in polarity establishment. Reaction-diffusion models for GTPase spatiotemporal dynamics exist. We demonstrate how the addition of negative feedback and minor changes to these models can generate the experimentally observed rosette pattern of podosomes. We show that this pattern formation can occur through two general mechanisms. In the first mechanism, an intermediate species forms a ring of high activity around the IgG disk, which then promotes rosette organization. The second mechanism does not require initial ring formation but relies on spatial gradients of intermediate chemical species that are selectively activated over the IgG patch. Finally, we analyze the models to suggest experiments to test their validity.

Phagocytosis, the process by which cells ingest foreign bodies, plays an important role in innate immunity. Phagocytosis is initiated when antibodies coating the surface of a foreign body are recognized by immune cells, such as macrophages. To study early events in phagocytosis, we used “frustrated phagocytosis”, an experimental system in which antibodies are micropatterned in disks on a cover slip. The cytoskeleton of cells attempting to phagocytose these disks organizes into “rosette” patterns around the disks. To investigate mechanisms that underlie rosette formation we turned to mathematical modeling based on reaction-diffusion equations. Building on existing models for polarity establishment, our analysis revealed two mechanisms for rosette formation. In the first scenario an initial ring of an intermediate signaling molecule forms around the disk, while in the second scenario rosette formation is driven by gradients of positive and negative pathway regulators that are activated over the disk. Finally, we analyze our models to suggest experiments for testing these mechanisms.

Funding: This work was supported by grants from the National Institute of General Medical Sciences (NIGMS) to TCE (R35GM127145) and to KMH (R35GM122596), as well as from the National Institute of Biomedical Imaging and Bioengineering to TCE (U01 EB018816). JCH received support from the NIGMS (5T32 GM067553). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Here, we expanded upon existing reaction-diffusion models for GTPase activity to demonstrate how these systems can generate the “rosette” pattern of podosomes observed during frustrated phagocytosis. We explore the behavior of a recent model for GTPase activity that includes a negative feedback loop formed through the activation of a GAP [ 9 , 10 ]. Depending on the choice of parameter values, this model generates a range of patterns including spots, mazes, and inverse spots [ 10 ]. We use the model to identify two distinct mechanisms for generating a rosette pattern. In the first scenario, an intermediate species forms a ring of activity that promotes the formation of active GTPase spots in the ring. Next, we use a parameterization approach involving an evolutionary algorithm followed by Markov chain Monte Carlo to evolve systems that do not rely on initial ring formation to generate the rosette pattern. A common theme that emerges from this analysis is that rosette formation requires the activation of both a positive and negative regulator of GTPase activity over the IgG disk. This creates spatial gradients of these regulators, which in turn are sufficient to drive the formation of the rosette pattern. Finally, we analyzed the behavior of the models to suggest experiments to test our proposed mechanisms.

There are now many reaction-diffusion models that describe how GTPases can generate cell polarity and patterning in various systems [ 8 – 11 ]. One of the best characterized cases is in yeast (Saccharomyces cerevisiae) budding, in which the GTPase Cdc42 generates a single, active site to determine the location of a bud site or mating projection. In yeast, autocatalysis is well-defined: active Cdc42 binds to the scaffold protein Bem1, which also binds to the GEF Cdc24 that locally activates more GTPase [ 25 , 26 , 28 , 29 ]. Other examples of Rho GTPase-driven pattern formation include single-cell wound healing, in which Rho and Cdc42 form distinct rings through regulation by the dual GAP-GEF Abr [ 32 , 33 ], actin waves observed during cytokinesis that are driven by RhoA and its GAP RGA-3/4 and GEF Ect2 [ 34 , 35 ], RhoA driven pulsed contractions observed during embryonic development in C. elegans [ 34 ], and tip growth in pollen tubes and fungal hyphae [ 10 ].

Beginning with Turing’s seminal paper [ 22 ] and continuing with developments by Gierer and Meinhardt [ 23 ] and Meinhardt [ 24 ], reaction-diffusion models have been used to investigate pattern formation in biological systems. These models rely on positive feedback to amplify local fluctuations in signaling activity and some form of global inhibition or substrate depletion to keep regions of high activity localized [ 23 ]. Another key requirement of these models is that at least one of the chemical species in the system diffuses at a different rate from the others [ 22 , 23 ]. The hydrolysis cycle of GTPases satisfies the requirements for spontaneous polarization [ 7 – 10 , 25 , 26 ]. GTPases cycle between an active state when GTP-bound and an inactive state when GDP-bound. Their activation is catalyzed by guanine nucleotide exchange factors (GEFs), which promote the exchange of GDP to GTP. This exchange typically occurs at the cell membrane where diffusion is slow as compared to the cytosol [ 7 , 8 , 10 , 26 , 27 ]. When in the active state, some GTPases have been shown to recruit their own GEFs forming a positive feedback loop [ 25 , 26 , 28 – 31 ]. GTPase inactivation is accelerated by GTPase-activating proteins (GAPs) [ 3 – 6 ]. When inactive, GTPases are sequestered in the cytosol by guanine nucleotide dissociation inhibitors (GDIs) and diffuse rapidly [ 3 – 6 ].

A-C) Rosettes of actin podosomes form around IgG disks in RAW 264.7 macrophages. A micropattern of IgG disks of diameter 3.5 μm is shown in A . Actin is shown in B , in which puncta are podosomes. An overlay (IgG in blue, actin in magenta) is shown in C . D-G) Single particle tracking (SPT) of Cdc42 during frustrated phagocytosis. Actin is shown in D . SPT of Cdc42 is shown in E , with tracks colored by their mean squared displacement (MSD, distribution of MSDs is shown in S1C Fig ). An individual rosette of actin (red box in D ) is shown expanded in F . For this same actin rosette, Cdc42 SPT (red box in E ) is shown expanded in G (same MSD coloring as in E ). Rings shown in F,G are to aid in visualization of the increased track density where actin podosomes form.

Here we focus on Fcγ Receptor (FcγR)-mediated phagocytosis because of its biological importance in the innate immune response [ 12 , 13 ] and because phagocytosis provides an ideal system for studying how Rho GTPases organize the cytoskeleton into well-defined structures. Phagocytosis is initiated by the binding of the antibody immunoglobulin G (IgG) to FcγR. Upon FcγR clustering, receptor cross-linking leads to phosphorylation of activation motif domains, enabling downstream signaling [ 12 – 14 ]. To study the events that initiate phagocytosis under well-controlled conditions, IgG is micropatterned in small disks on a glass coverslip ( Fig 1A ). Because the antibody is attached to the coverslip it cannot be internalized, and the experimental system is therefore referred to as “frustrated” phagocytosis [ 15 ]. Following receptor activation, actin-enriched, adhesion-like structures termed podosomes [ 13 , 16 , 17 ] form in a circle around the IgG disk ( Fig 1B and 1C ). Podosomes classically have been considered rod or cone-like structures of dense actin [ 16 , 17 ]. However, we recently demonstrated an hourglass-like shape [ 18 ]. Podosomes recruit many additional molecules and are thought to coordinate interactions between the actin cytoskeleton and the extracellular matrix [ 16 , 17 , 19 ]. They also form the leading edge of the phagocytic cup [ 20 , 21 ], and have been referred to as “teeth” coordinating the “jaw” during phagocytosis [ 21 ]. The mechanisms responsible for podosome formation and patterning are not known. Therefore, we turned to mathematical modeling to establish sufficient conditions for pattern formation during frustrated phagocytosis.

All cells must be able to respond to changes in their environment, and often the proper response requires cells to adopt a new morphology. For example, cell shape changes occur during migration, division, and phagocytosis. Typically, these changes are initiated when receptors on the cell surface are activated by an external cue [ 1 ]. Receptor activation initiates a signaling cascade that results in spatiotemporal regulation of the actin cytoskeleton. The Rho family of GTPases are a class of signaling molecules that play key roles in this process [ 2 – 6 ]. These proteins act as molecular switches. They are in an inactive state when bound with GDP and become active when GDP is exchanged for GTP. Once active, Rho GTPases interact with effector molecules including those that regulate the actin cytoskeleton. Due to the nonlinear nature of the signaling pathways that regulate GTPase activity, understanding the molecular mechanisms that generate cell shape changes has proven challenging [ 1 ]. Therefore, many recent studies have turned to mathematical modeling to explore mechanisms capable of generating complex molecular structures [ 7 – 11 ].

Results

Experimental observations suggest Cdc42, but not myosin, is required for rosette patterning Macrophages (RAW 264.7 cells) were observed during frustrated Fcγ receptor IIa (FcγR) mediated phagocytosis, where cells attempt to phagocytose fixed, micropatterned disks of immunoglobulin G (IgG). Actin, a major downstream effector during FcγR-mediated phagocytic signaling, formed in rings of small puncta, just outside of the IgG disks (Fig 1A–1C). These puncta were podosomes: actin-rich, adhesion-like structures observed during phagocytosis but more commonly known for their roles in motility and extracellular matrix interactions [16,19]. This superstructural organization of podosomes in a circular arrangement has previously been termed a podosome “rosette” [36–38]. Due to the dynamic nature of phagocytosis, actomyosin contractility is known to play an integral role during the engulfment process [12,13,21,39] and myosin II has been observed to localize to phagocytic podosomes and podosome rosettes [17,21]. Therefore, we wondered whether actomyosin contractility was important for podosome rosette formation. To test this possibility, we treated cells with the Rho kinase inhibitor Y27632. Inhibition of Rho kinase during frustrated phagocytosis led to the complete disassembly of myosin II filaments, demonstrating that myosin II contractility was inhibited (S1A and S1B Fig). However, podosome rosettes still formed (S1A and S1B Fig), which suggested that the formation and maintenance of podosomes during phagocytosis is independent of actomyosin contractility and that a biochemical mechanism may underlie rosette formation. Rho family GTPases, including Cdc42, are known to be activated during FcγR-mediated phagocytic signaling [2,12,13,40,41]. Cdc42 is a regulator of the actin cytoskeleton, so we next examined its localization during frustrated phagocytosis. We recently developed tools for observing and analyzing single molecule conformational changes in living cells [42]. We made use of these techniques to visualize Cdc42 during frustrated phagocytosis (Figs 1D–1G and S1C). Cdc42 localized to the podosome rosette, with individual molecule tracks clustered near podosomes (Fig 1D–1G). Taken together these results suggest podosome rosette organization involves localized Cdc42 activity but does not require active myosin-mediated force generation. The involvement of Cdc42 in rosette formation is also supported by other studies; Cdc42 levels are reduced when actin is reduced at the phagocytic site [43], and Cdc42 is recruited to the tips of pseudopodia early in phagocytosis [40,44]. Therefore, we decided to investigate if a mechanism involving Cdc42 might underlie formation of the podosome rosette.

A two-step model for rosette formation We next sought to determine if the WPGAP model could be modified to enable rosette formation. One possible explanation for how a rosette could form is if two distinct steps occur: 1) an initial ring of high or low concentration of some species (M) forms and 2) this species modulates a key parameter in the pattern forming, WPGAP model. To test this model, we assumed a preexisting ring in the concertation profile of M. We note that rings of high GTPase activity have been observed and modeled in other contexts, such as in wound healing, in which a chemical gradient and modulation of a bistable GTPase resulted in distinct rings of activity [32,33]. For our initial investigations, we assumed that a modulator M affected a rate in the WPGAP model through the functional form: where ω 1 is the basal rate, ω 2 models the effect of M on ω ± and r measures the radial distance from the center of an IgG disk. In our simulations, we consider a single IgG disk and use polar coordinates with the origin located at the center of the disk. The computational domain consists of a disk of radius of R with reflective boundaries at r = 0 to r = R (see Methods). Unless otherwise noted R = 4 μm. M(r) was modeled as a Gaussian-shaped function centered at r = 2 μm with variable variance. This form of ω ± allowed us to tune model parameters so that spot formation was only promoted within the ring. For parameters that increase GTPase activity (GTPase activation b, GAP inactivation d, and the maximum self-positive feedback rate γ), the WPGAP model was coupled to a ring of high M concentration ω + (Fig 2C and 2D, three leftmost columns). For parameters that decrease GTPase activity (GAP activation c, GTPase inactivation σ, and GAP-mediated GTPase inactivation e), the WPGAP model was coupled to an inverted ring of M, ω - (Fig 2C and 2D, three rightmost columns). For each model parameter, ω 1 and ω 2 were varied to determine if the system could generate rosette organization. As an initial guess, the parameter values were chosen based on the results from the parameter sweeps (Fig 2B). As expected from the parameter sweep results, modulating the basal GTPase activation rate b did not appear sufficient to form a rosette pattern, because this produced spot formation throughout the entire domain. However, modulating the other rate constants, such as the positive feedback rate γ, all resulted in a rosette forming (Fig 2C and 2D). Interestingly, when we modulated the rates for GTPase inactivation σ and the GAP-mediated negative feedback e, we found that the rates required to form rosettes were higher than expected (Fig 2C and 2D). For example, to form a rosette, the rate required for the GTPase inactivation σ within the ring was ~15 s-1, which resulted in no patterning when used as the global rate in the isolated WPGAP model (Fig 2B–2D).

[END]
---
[1] Url: https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1010092

Published and (C) by PLOS One
Content appears here under this condition or license: Creative Commons - Attribution BY 4.0.

via Magical.Fish Gopher News Feeds:
gopher://magical.fish/1/feeds/news/plosone/