The epidermal growth factor receptor (EGFR) is a central regulator of cell physiology that is stimulated by multiple distinct ligands. Although ligands bind to EGFR while the receptor is exposed on the plasma membrane, EGFR incorporation into endosomes following receptor internalization is an important aspect of EGFR signaling, with EGFR internalization behavior dependent upon the type of ligand bound. We develop quantitative modeling for EGFR recruitment to and internalization from clathrin domains, focusing on how internalization competes with ligand unbinding from EGFR. We develop two model versions: a kinetic model with EGFR behavior described as transitions between discrete states and a spatial model with EGFR diffusion to circular clathrin domains. We find that a combination of spatial and kinetic proofreading leads to enhanced EGFR internalization ratios in comparison to unbinding differences between ligand types. Various stages of the EGFR internalization process, including recruitment to and internalization from clathrin domains, modulate the internalization differences between receptors bound to different ligands. Our results indicate that following ligand binding, EGFR may encounter multiple clathrin domains before successful recruitment and internalization. The quantitative modeling we have developed describes competition between EGFR internalization and ligand unbinding and the resulting proofreading.

Receptor proteins on the plasma membrane enable signals, carried by extracellular molecules (ligands) that bind to the receptor, to be transduced to the cell interior [1]. The epidermal growth factor receptor (EGFR) is a receptor tyrosine kinase that mediates activation of a range of signaling pathways that regulate many aspects of cell physiology [2–4]. EGFR also plays a key role for tumor progression, representing a drug target and a drug resistance challenge for many cancers [5–7].

Ligands bind to EGFR on the plasma membrane, with recent work suggesting that EGFR ligand binding is favored for receptors localized to tetraspanin nanodomains [8]. While unliganded EGFR can form dimers, ligand-bound EGFR form distinct dimers and oligomers, which play an important role in EGFR signaling [9, 10]. Phosphorylation of intracellular EGFR domains, while EGFR is on the plasma membrane, is a key step for signal transduction [11–13].

Ligand-bound EGFR can be recruited to a clathrin domain or stabilize a nascent clathrin domain [8, 14–17]. EGFR can be endocytosed upon generation of membrane curvature to form clathrin-coated pits, a process which can lead to formation of intracellular vesicles [18, 19]. While EGFR may be internalized via other pathways, under a range of conditions clathrin-mediated endocytosis is the primary internalization pathway for epidermal growth factor (EGF) receptors at lower physiological EGF concentrations [18, 19]. EGFR signaling occurs both from EGFR on the plasma membrane and in endosomes following endocytosis [19–24]. From endosomes, receptors are either transported to lysosomes for degradation or recycled back to the plasma membrane [25].

EGFR internalization from the plasma membrane into endosomes leads to EGFR signaling modes that are distinct from EGFR signaling from the plasma membrane [18–20, 22–24]. As signaling activity of EGFR in endosomes is lost when the ligand dissociates [23], ligand binding is important for endosome-based EGFR signaling.

EGFR is stimulated by at least seven distinct ligands: high-affinity ligands EGF, heparin-binding EGF-like growth factor (HB-EGF), transforming growth factor-α (TGF-α), and betacellulin (BTC), which bind the cell surface with affinities of apparent dissociation constant –1 nM; and low-affinity ligands epiregulin (EREG), epigen (EPGN), and amphiregulin (AREG), which bind 10- to 100-fold more weakly [26, 27]. Although all bind to EGFR, these different ligands stimulate distinct responses, differentially activating various signaling pathways [28–31]. There are many examples of specific cellular responses to different ligands [30], such as EGF leading to an epithelial to mesenchymal transition while AREG causes proliferation of colon cancer cells [32]; and AREG and TGF-α stimulation both inducing kidney cell mitosis, but only AREG impacting E-cadherin distribution [33]. While the extracellular signal-regulated kinase (ERK)/mitogen-activated protein kinase (MAPK) signaling pathway is readily activated at low stimulating ligand concentration by EGF, HB-EGF, TGF-α, and BTC, the Akt, phospholipase C gamma (PLCg) and signal transducer and activator of transcription 3 (STAT3) signaling pathways respond differently to EGF, HB-EGF, TGF-α, and BTC [29].

There has been substantial effort to understand the mechanistic underpinnings of how different ligands lead to different signaling pathway activation and cellular responses. For example, different ligands lead to distinct EGFR dimers with varying interaction strength and lifetime [26] and different degrees of EGFR trafficking to the nucleus [34]. We will focus on ligand-specific differences in receptor internalization into endosomes. HB-EGF and BTC lead to high internalization, EGF and TGF-α to somewhat lower internalization, and EPGN and AREG to the lowest internalization [25]. Internalized EGFR can be recycled to the plasma membrane or lysosomally degraded, with different ligands more likely to induce EGFR degradation: EGF, HB-EGF, and BTC cause substantial degradation and TGF-α, EREG, and AREG largely induce recycling to the plasma membrane [25, 29]. Degradation and intracellular retention of EGFR align with signaling persistence: TGF-α, EPGN, and AREG cause persistent signaling as the receptors to which they bind are typically recycled to the plasma membrane, while EGF, HB-EGF, and BTC cause more transient signaling as they lead to EGFR degradation, lowering plasma membrane EGFR levels until replenished by protein synthesis [25]. The likelihood of receptor degradation with different ligands also largely aligns with internalization differences [19], ligand dissociation rates at endosomal pH (slower dissociation leads to more degradation) [25, 35], and ubiquitination and phosphorylation persistence on EGFR in endosomes (persistent modification leads to more degradation) [25].

As EGFR internalization into endosomes facilitates important signaling modes distinct from EGFR signaling modes from the plasma membrane and different EGFR ligands induce varying degrees of EGFR internalization, we explore a possible mechanism behind the variation in EGFR internalization due to binding of different ligands.

'Kinetic proofreading' describes a class of mechanisms that use nonequilibrium conditions to reduce the error rates or enhance discrimination between stimuli for various cellular and biochemical processes. While initially envisioned to increase accuracy of 'reading' or copying processes such as DNA replication or protein synthesis [36, 37], kinetic proofreading principles are understood to apply to a broader class of phenomena, particularly signaling and recognition processes [38–41] such as those of receptors on the plasma membrane. To improve copying or signaling fidelity, these kinetic proofreading processes utilize multiple stages and repeated cycles to enhance the difference between 'right' and 'wrong' substrates. With multiple stages each discriminating between the substrate types, the combined effect is to enhance the overall difference in outcome between substrate types beyond the performance of an equilibrium process.

Recently, a distinct spatial proofreading mechanism was proposed [42], with the diffusive search time between a binding event at one location and a reaction event at another location allowing discrimination between ligands with different unbinding rates. For sufficiently distinct unbinding rates and an appropriate timescale for diffusive search, a receptor stimulated by a slower-unbinding ligand can be far more likely than a receptor stimulated by a faster-unbinding ligand to reach the final reaction location before ligand unbinding.

We propose that the EGFR internalization process following ligand binding, including distinct signaling modes due to interaction with clathrin-coated pits and endosomes, applies the principles of kinetic and spatial proofreading to improve ligand discrimination. We develop two related quantitative models for EGFR dynamics, one solely kinetic and another involving receptor diffusion on the plasma membrane. We find that the internalization probability ratio for EGFR stimulated by different EGFR ligands exceeds the unbinding rate ratio between the ligands for physiological parameters. This increased differentiation between EGFR ligands enables greater ligand specificity in EGFR signaling activity.

The kinetic EGF receptor model considers receptors immediately following ligand binding until the receptor is internalized into the cell during endocytosis of a clathrin domain or the ligand unbinds from the receptor. A kinetic version of this model is shown in figure 1(A), with kc the rate of a ligand-bound receptor RL entering a clathrin domain, the rate of a clathrin-localized receptor RC exiting a clathrin domain, ki the rate of a clathrin-localized receptor RC internalizing via endocytosis, and ku the rate of a ligand unbinding from a receptor (inside RC or outside RL a clathrin domain). Receptors are initiated in the ligand-bound state outside of clathrin domains following recent work suggesting ligands primarily bind to EGFR within tetraspanin domains [8].

Figure 1. (A) Kinetic model of EGFR. In this model receptors are initiated in the ligand-bound state outside of clathrin domains (RL). These receptors can enter a clathrin domain (state RC) with rate kc or have the ligand unbind at rate ku. Receptors in a clathrin domain can leave the domain with rate , internalize at rate ki, or have the ligand unbind at rate ku. Ligand unbinding or receptor internalization are terminal states. (B) Schematic of spatial model of EGFR. Receptors (red) begin following ligand (green) binding outside of clathrin domains (blue). Receptors diffuse to encounter clathrin domains and within clathrin domains, and cross an energy barrier to enter or exit clathrin domains. Ligand unbinding (occurring both within and outside of clathrin domains) and internalization from within clathrin domains terminate the receptor trajectory. For both models receptor internalization is irreversible.

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For a receptor beginning in state RL, the probability Pi that a receptor is internalized is (see appendix for derivation)

We estimate the clathrin entry rate , which is substantially slower than the estimated diffusion-limited entry rate [43] of (for EGFR with diffusivity [8, 9, 44–47] to clathrin domains of 50 nm radius representing of the plasma membrane surface [48]). and are estimated from clathrin domain dynamics [48]. See the appendix for the details of these parameter estimates from experimental observations.

In figure 2(A) the internalization probability Pi is shown as the ligand unbinding rate ku, which will be distinct for different ligands, is varied. Figure 2(A) shows Pi for the estimated EGFR parameters and with each parameter kc, , or ki increased or decreased relative to the estimated parameters by an order of magnitude. At low ku the internalization probability is flat at , as the unbinding rate is too small to compete with internalization. As the unbinding rate increases, the internalization probability decreases, eventually reaching a limiting power law for high ku of . This power law, reached only for sufficiently high unbinding rates, corresponds to receptors that effectively make a single attempt to enter a clathrin domain and then internalize or have the ligand unbind, without sufficient time for another internalization opportunity. EGFR internalization switches from a nearly certain event for low ku to a rare event for ku that are two to three orders of magnitude larger.

Figure 2. Internalization probability and fidelity with kinetic model. (A) Internalization probability Pi (equation (1)) as ligand unbinding rate ku is varied. Thick solid black curve shows Pi with estimated EGFR parameters (see text). Other curves have one parameter value changed compared to thick black curve, as indicated. Black circle shows Pi for and orange circle shows Pi for . Black dashed line is the high ku limiting power law . (B) EGFR internalization fidelity (equation (4)) between a fast and slow unbinding ligand with ratio as the unbinding rate of the slow unbinding ligand ku is varied. Black circle shows the fidelity for slow unbinding rate . (C) Fidelity vs internalization probability as ku is parametrically varied. Curves in (B) and (C) take parameter values indicated by legend in (A). (D) Limits of fidelity vs internalization probability relationship as ku is parametrically varied. The high fidelity limit (black dashed curve) is equation (6) and the low fidelity limit (black dotted curve) is equation (5). Random parameter combinations (grey) is 104 random, logarithmically-distributed, and independent samples for kc, ki, , and ku from the range .

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The unbinding rate ku varies between EGFR ligands. EGF has an unbinding rate experimentally measured as 0.02–0.04 [49], 0.04 [50], 0.055 [51], 0.06 [52], 0.062 [53], and 0.066 [54]. Selecting an intermediate value of EGF unbinding from EGF receptors of , the internalization probability of EGFR following EGF binding is approximately 29 (black circle in figure 2(A)).

EGFR binding affinity varies for other ligands. EREG has a weak EGFR affinity compared to other ligands [27], with at least 10× weaker affinity for EGFR compared to EGF [26, 27]. As EGFR ligands have the same binding motif [55], use similar binding modes [56], and ligand affinities can be accurately ranked by ligand-receptor interaction energies [56], we assume that binding rate constants are similar for different EGFR ligands and that unbinding rate differences are proportional to the affinity differences. Thus we take the EREG unbinding rate to be 10× faster than that of EGF, . This corresponds to a receptor internalization probability of approximately 1.4 (orange circle in figure 2(A)), which is approximately 20× less internalization than receptors bound to EGF.

Proofreading often describes the ratio between a 'right' and a 'wrong' product or signal. However, distinctions in EGFR response to stimulation by different ligands such as EGF and EREG do not clearly fit into categories of 'right' and 'wrong' as these EGFR ligands each send meaningful signals to a cell via EGFR. We will instead treat EGFR internalization as a signaling aspect with a propensity that differs between ligand types. Variation of internalization propensity between ligands, combined with distinct EGFR signaling from endosomes following receptor internalization compared to EGFR signaling from the plasma membrane [18–20, 22–24], could serve as one mode to assist cells to distinguish between the signals mediated by different EGFR ligands and initiate the appropriate response. In this way EGFR internalization proofreading is similar to proofreading during chromatin remodeling, which involves targeting of nucleosomes with particular characteristics by different remodeler families and lacks clear categories of 'right' and 'wrong' targets [57].

We calculate the fidelity [42], or ratio of receptor internalization probabilities for different ligand types, as a measure of the degree to which EGFR internalization can distinguish between stimulation by different ligand types. The EGFR internalization fidelity between a ligand with unbinding rate ku and a ligand with unbinding rate is then

If the ratio between the unbinding rates is , then

In figure 2(B) the fidelity is shown as the unbinding rate ku is varied for unbinding rate ratio A = 10, corresponding to the estimated ratio between unbinding rates of EGF and EREG ligands. For low ku, the fidelity approaches unity, as binding of both ligand types leads to near-certain receptor internalization. As the unbinding rate ku increases, the fidelity also increases, as the receptor with lower unbinding rate ku becomes internalized more frequently than the receptor with higher unbinding rate . The fidelity in equation (4) saturates at as the unbinding rate becomes high, corresponding to the internalization probability for both ligands described by the limiting power law in figure 2(A). The discrimination between different ligands, as quantified by the fidelity, is bounded from above by .

With and , the fidelity of EGF binding and internalization relative to EREG is approximately 20 (black circle in figure 2(B)), well below the saturated fidelity of 100. Receptors bound to EGF are approximately 20× more likely to be internalized than receptors bound to EREG. This fidelity range leaves ligand internalization sensitive to changes in EGFR dynamics, as illustrated in figure 2(B). Adjusting the rate of clathrin recruitment kc or internalization ki will modestly change fidelity, with an order of magnitude decrease in either of these parameters nearly doubling the fidelity to approximately 35 and an order of magnitude increase in either of these parameters reducing the fidelity by almost two-thirds to approximately 8. The fidelity is less sensitive to the clathrin domain exit rate of receptors, , with an order of magnitude increase in reducing the fidelity by approximately one-quarter, and an order of magnitude decrease in