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.

The constant on the right-hand side incorporates Avogadro's number and the conversion of volume units from L to µm 3 , which is done automatically in Virtual Cell.
For each membrane species i, conservation equations have the following form: Here, ci is the local area density of membrane species i (#/µm 2 ), Di is the molecular diffusivity of membrane species i (µm 2 /s), and ri is the production rate of membrane species i.

Molecular diffusivities and initial concentrations
The assigned diffusivity of receptor-bound PLC is 0.01 µm 2 /s, which is typical of transmembrane receptors and effectively immobile. We assigned diffusivities for PIP2, DAG, PA, DAG-PKC, and DAG-PKC* equal to 0.5 µm 2 /s, a value typical for plasma membrane lipids. Diffusivities of cytosolic species vary modestly according to hydrodynamic radius, scaling approximately with molecular weight (MW) as D ∝ MW -1/3 and are of the order of magnitude estimated from photobleaching measurements in cytoplasm. These diffusivity values are the same as those assumed in Mohan et al. [1]. Initial conditions are also the same as in Mohan et al., except for the initial concentration of inactive PLC enzyme, which was modestly reduced from 0.03 to 0.02 µM. As explained previously [1], the initial abundance of membrane-bound MARCKS, together with its affinity for PIP2, was chosen such that 90% of the PIP2 molecules and 90% of the MARCKS molecules in the cell are initially in complex.

Rate law expressions
All rate laws are listed in Table S2. As explained in Mohan et al. [1], most of them are based on simplified kinetic principles (mass-action binding, pseudo-first-order and pseudo-second-order reactions). For VMARCKS (binding of unphosphorylated MARCKS to the membrane), we assume that MARCKS initially associates with the membrane via reversible insertion of its myristoyl lipid, and is stabilized by quasi-equilibrium binding to PIP2; the polybasic motif of MARCKS is modeled as three equivalent binding sites for PIP2. As previously derived [1], these assumptions allow one to calculate p, the density of free (unbound) PIP2 from pT, mT, and the single-site equilibrium constant of MARCKS-PIP2 binding, KPIP2.
The rate laws involving p, including VMARCKS, are given in Table S2.
The net rate of PLC binding to the membrane, VPLC, is also given in Eqn. 2 of the main text and has been modified in the following ways relative to the model presented in Mohan

Specification of rate parameters
Where reasonable, we kept values of rate constants the same as in the previous modeling study [1]. Exceptions and new rate parameters are discussed below.
In the Mohan model, parameters kon,e and koff,e in VPLC were chosen to yield fast kinetics and a dissociation constant (koff,e/kon,e) of 10 nM. To achieve that, the previous value of kon,e (10 µM -1 s -1 , or 10 7 M -1 s -1 ) was at the high end of the observed range for protein-protein interactions.
Furthermore, those kinetics did not account for enhancement of PLC recruitment by PA.
Therefore, we reduced the value of kon,e by two logs, to 0. Collectively these changes bring the effects of MARCKS regulation on the PKC pathway in line with those characterized in Mohan et al. [1].
In the modeling by Mohan et al., PA was an implicit variable, as the phosphorylation of DAG by DAGKs was considered irreversible. As stated above, the present models consider the reverse reaction, with rate VPAP and pseudo-first-order rate constant kPAP. As a base case, we chose kPAP = kDAGK = 1 s -1 . The effect of this parameter on the relative densities of DAG and PA are elucidated in the following section. PA is also generated by a newly considered reaction: hydrolysis of phosphatidylcholine catalyzed by PLD. In the associated rate expression, VPLD, the phosphatidylcholine concentration does not appear, as it is assumed relatively abundant and approximately constant. To simplify the analysis, we chose an extremely low value of the basal synthesis rate (Vsynth,dp), such that the effect of this reaction is negligible in the absence of PFL 7 2. In effect, the rate constant for PLD is the product, RSTUV,GH , and that is why it is stated that way in the caption of Fig. 5. As explained in the main text, extensive parameter sweeps of KPLD and were run to determine optimal values for amplification by PFL 2 in conjunction with MARCKS, PFL 1, or both MARCKS and PFL 1.

Steady state analysis of DAG and PA levels (no PFL 2)
A steady-state analysis, assuming negligible spatial gradients of the lipid species, predicts a consistent proportional relationship between the concentrations of DAG and PA, dependent on just four parameters (kDAGK, kbasal,dp, kPAP, and Vsynth,dp). The derivation for this relationship follows, starting with the reaction-diffusion equation for PA: Assuming a steady state has been reached and neglecting the diffusion term, Substituting in the rate expressions, with no PFL 2 (VPLD = Vsynth,dp) and rearranging, Incorporating the approximately proportional relationship between dp and d derived above, the DAG-nullcline is, approximately, The local densities of free PIP2, p, at the front and back of the cell were obtained from the corresponding simulation.