Biotechnol. Prog. 1992, 8, 132-743
132
Mathematical Model for the Effects of Epidermal Growth Factor Receptor Trafficking Dynamics on Fibroblast Proliferation Responses Cindy Starbuck Department of Chemical Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104
Douglas A. Lauffenburger* Departments of Chemical Engineering and Cell & Structural Biology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
We apply a mathematical model for receptor-mediated cell uptake and processing of epidermal growth factor (EGF) to analyze and predict proliferation responses to fibroblastic cells transfected with various forms of the EGF receptor (EGFR) to EGF. The underlying conceptual hypothesis is that the mitogenic signal generated by EGF/ EGFR binding on the cell surface, via stimulation of receptor tyrosine kinase activity, is attenuated when the receptors are downregulated and growth factor is depleted by endocytic internalization and subsequent intracellular degradation. Hence, the cell proliferation rate ought to depend on receptodligand binding and trafficking parameters as well as on intrinsic receptor signal transduction properties. The goal of our modeling efforts is to formulate this hypothesis in quantitative terms. The mathematical model consists of kinetic equations for binding, internalization, degradation, and recycling of EGF and EGFR, along with an expression relating DNA synthesis rate to EGF/EGFR complex levels. Parameter values have been previously determined from independent binding and trafficking kinetic experiments on B82 fibroblasts transfected with wildtype and mutant EGFR. We show that this model can successfully interpret literature data for EGF-dependent growth of NR6 fibroblasts transfected with wild-type EGFR. Moreover, it successfully predicts the literature observation that NR6 cells transfected with a A973 truncation mutant EGFR, which is kinase-active but intemalization-deficient, require an order of magnitude lower EGF concentration than cells with wild-type EGFR for half-maximal proliferation rate. This result demonstrates that it may be feasible to genetically engineer mammalian cell lines with reduced growth factor requirements by a rational, nonempirical approach. We explore by further model computations the possibility of exploiting other varieties of EGFR mutants to alter growth properties of fibroblastic cells, based on relationships between changes in the primary structure of the EGF receptor and the rates of specific receptodligand binding and trafficking processes. Our studies show that the ability to predict cell proliferation as a function of serum growth factors such as EGF could lead to the designed development of cells with optimized growth responses. This approach may also aid in elucidation of mechanisms underlying loss of normal cell proliferation control in malignant transformation, by demonstrating that receptor trafficking dynamics may in some cases play as important a role as intrinsic signal transduction in determining the overall resulting mitogenic response.
Introduction Only a few years ago it was stated, quite correctly, in this journal that a basic function of the biochemical engineer is to provide given biological systems with an optimal environment for the production of a product (Bader, 1986). In the meantime, an additional new role for the biochemical engineer has emerged the rational development of optimized cells, rather than merely their environments. Our focus is on regulation of key mammalian cell functions, such as proliferation, adhesion, migration, and differentiation, via signals initiated by receptor/ligand interactions. The goal is to construct and validate molecular-levelmathematical models for receptormediated cell processes,which will enable analysis and/or design of purposeful alterations in the underlying mechanisms. In philosophy our approach is related to the emerging field termed metabolic engineering [as outlined, 8756-7938/92/3008-0132$03.00/0
for example, by Bailey (1991)1,except that our central interest isin re&latoqheceptor/ligand interactionsrather than in pathways of energy generation or product formation. The growing importance of manipulating receptor/ ligand interactions for control of mammalian cell function, whether for bioprocessing or health care applications, is a clear motivation for this effort. Mammalian cells offer great potential for the production of vaccines and other useful biochemicals. Among the fundamental challenges in the large-scale culture of mammalian cells is the definition of medium components required for growth and maintenance. Development of serum-free media has been the goal of many laboratories, not only because defined media formulations can be used to select for the growth of a particular cell type but also because serum proteins present difficulties during the product recovery stage of most bioprocessing operations.
0 1992 American Chemical Society and American Instltute of Chemical Engineers
B&technol, Rog, 1992, Vol. 8, No. 2
The transition to serum-free conditions, however, is not without its own host of problems [e.g., see Mather (1984)l. Different cell types require different formulations and certain constituents of serum-free media are not commercially available, requiring that they be purified in the lab. Further, many cell types grow slower in serum-free medium and a considerable adaptation period is often required. A key to rational design of improved media is quantitative information regarding the effects of serum growth factors that control cell proliferation. At the same time, increased understanding of physiological cell growth control has extremely important implications for health care problems such as wound healing, cancer diagnosis and therapy, organism development, and tissue engineering. Quantitative data concerning the dependence of cell proliferation on growth factors will again by extremely useful for developing strategies for these applications. Despite the substantial progress made by cell biologists and biochemists in elucidating the molecular basis of cell growth regulation, surprisingly little effort has been devoted toward integrating this information to better control proliferation of mammalian cells in culture from an engineering perspective. Our research in recent years has aimed to do precisely this: to develop quantitative understanding of the dependence of cell growth on growth factor concentrations by analyzing growth factor uptake, processing, and signaling dynamics (Lauffenburger et al., 1987;Starbuck et al., 1990; Lund et al., 1990; Wiley et al., 1991;Starbucketal., 1992). In this manuscript, we attempt to demonstrate how our current model of growth factor binding and trafficking can be used to develop strategies for genetic alteration of cells to respond optimally to a culture environment. The particular system we focus on here is regulation of the proliferation of fibroblastic cells by epidermal growth factor (EGF) via its dynamic interaction with the cell epidermal growth factor receptor (EGFR).
Background Serum contains a number of polypeptide mitogens, termed growth factors, which are characterized by their ability to induce cell division, or mitogenesis (Mather, 1984). Growth factors are taken up by cells when they bind reversibly to specific receptors on the cell surface. Althoughit was originally postulated that the sole purpose of growth factor receptors was to shuttle their ligands to an appropriate destination inside the cell where the ligand could transmit the mitogenic signal, a much more complicated mechanism has been revealed. To understand and exploit the cell’s ability to regulate its proliferation response to serum growth factors, an enhanced appreciation of growth factor receptors and the cellular machinery with which they interact must fist be developed. Excellent recent reviews of general growth factor/receptor concepts are provided by Gill (1989) and Czech et al. (1990). The focus of our modeling efforts has been on cellularlevel activities involved in binding and trafficking of epidermal growth factor in an attempt to dissect the role that growth factor receptors play in receiving and transmitting the signal for cell growth. We have chosen EGF as a particular example because it is currently the best characterized growth factor in terms of its physical, chemical, and biological properties. Useful summaries of information on EGF and its receptor can by found in reviews by Gill et al. (1987)and Carpenter and Wahl(1990). The external message that the EGFR receives when EGF binds is translated into conformational changes in receptor structure. The net result is that a tyrosine kinase
133
enzymatic site within the receptor’s cytoplasmic tail becomes activated. This kinase generates an intracellular signal by catalyzing phosphorylation of tyrosine residues on other proteins as well as the EGFR itself, followed by a cascade of biochemical events resulting ultimately in DNA synthesis. As noted above, EGF does not function directly in transmitting the growth signal; it functions indirectly by triggering the conformational change in the EGFR which, in turn, activates the receptor tyrosine kinase enzyme. It should be noted that the precise molecular mechanism stimulating EGFR kinase activity is not well-understood. Controversy exists over whether it is intramolecular, occurring within an individual EGFR, or alternatively is intermolecular, requiring dimeric interaction between two EGFRs. Our model does not explicitly involve EGFR dimerization, as kinetic evidence argues against it being a rate-limiting event (Waters et al., 1990; Lund et al., 1990). Once activated, EGF/EGFR complexes are internalized by the cell by a process termed endocytosis and are then routed-or “trafficked”-within the cell to various possible destinations including lysosomal degradation or recycling to the cell surface. Recent experiments (Chen et al., 1989; Wells et al., 1990)indicate that endocytic trafficking serves to attenuate EGFR signaling, thus making the rates of binding and trafficking events crucial to the cell proliferation response. This attenuation is due to two related but distinct phenomena arising from endocytic trafficking. First, receptors are lost from the cell surface by the combination of endocytosis and degradation, so that smaller numbers are available for continued signaling; this is called receptor downregulation. Second, ligand is depleted from the extracellular medium by the same combination of endocytosis and degradation. I t is ligand depletion which causes growth factors to act effectively as nutrients rather than as the catalysts that they really are. These attenuation phenomena likely have physiological purpose as homeostatic mechanisms preventing unregulated cell proliferation. In vitro, though, they may be disadvantageous from the perspective of a biochemical engineer desiring to maximize cell productivity in a given growth medium. Clearly, understanding proliferation at the cellular level requires not only the identification of molecular components and the mechanisms by which they interact but also an integrated picture of the dynamics of these interactions. It is our belief that a quantitative understanding of the complex reaction network involved in binding and intracellular trafficking of growth factor receptors, developed through mathematical modeling and experimental analysis, can be used to understand and manipulate the process of growth factor-induced cell growth.
Kinetic Model for Receptor/Ligand Binding and Trafficking A brief summary of our previously-developed model for EGF/EGFR binding and trafficking by fibroblastic cells will be presented here before we examine how various intracellular pathways can be changed to optimize cell growth. Detailed presentations of various aspects of this model along with experimental validation and parameter measurement can be found in Starbuck et al. (1990,1992), Lundetal. (1990),Wileyetal. (1991),andStarbuck (1991). A very brief summary is given in the Appendix. Support for this model is also provided in excellent work by Waters et al. (1990) on a similar scheme. Figure 1illustrates the surface and intracellular events which are included in the model. Extracellular ligand, to EGF (LO),binds to its receptor on the cell surface (9)
134
Biotechnol. P q . , 1992, Vol. 8, No. 2
Table I. Model Equations for EGF Binding and Trafficking.
Figure 1. Events involved in whole-cell kinetic model for binding and trafficking of the EGF receptor. Model parameters are described in the text.
form a ligand receptor complex (C,), with forward and reverse rate constants kf and k,, respectively. Ligand binding induces a conformational change in the receptor polypeptide, resulting in activation of the receptor tyrosine kinase enzyme to yield signaling receptor complexes (C,*) (Bertics and Gill, 1985). Since the time scale of receptor activation is short (seconds) relative to binding and trafficking events (minutes) (Cohen et al., 1980), we assume that all ligandheceptor complexes on the surface are active (Le., C, = C,*). These complexes migrate in the lateral plane of the membrane and cluster in specialized regions of the membrane known as clathrin-coated pits (Anderson and Kaplan, 1983). Experiments indicate that this clustering process may be mediated by the binding of ligandheceptor complexes to coated-pit proteins (P,) to form ternary complexes (T,) (Mayo et al., 1989; Lund et al., 1990). These coated-pit proteins with which the ligand/receptor complexes couple are not the pit’s coat (clathrin) moleculesthemselves but other proteins (termed endonexins or adaptors) that are associated with the clathrin coat (Pearse & Robinson, 1990). Possible participation of receptor dimerization is not explicitly included in our model, as mentioned earlier, since it appears to not be a rate-limiting event (Waters et al., 1990;Lund et al., 1990). Two pathways appear to exist for internalization of receptors from the cell surface: a low-affinity/highcapacity constitutive, or smooth-pit, pathway and a highaffinity/low-capacity induced, or coated-pit, pathway (van Duers et al., 1989; Lund et al., 1990). The coated-pit pathway differs from the smooth-pit pathway for the EGFR system in that the former requires EGF binding, EGFR tyrosine kinase activation, and ternary complex formation of the EGF/EGFR binary complex with a coated-pit protein (Wiley et al., 1991). The saturability of coated-pit, but not smooth-pit, internalization suggests that the two pathways are mechanistically distinct (Lund et al., 1990; Wiley et al., 1991). We depict the coated-pit pathway as a second-order process involving the following parameters: the coated-pit internalization rate (A), the number of internalization components (Pa),and the receptor/coated-pit couplingand uncoupling rate constants (kc, ku). Constitutive, smooth-pit internalization is depictedas a simple, first-order process, defined as the default pathway for the internalization of all receptors or complexes which are not localized in coated pits. The rate constant for constitutive internalization is designated kt. Once internalized, complexes (Ti,Ci), receptors (Ri), and free ligand (Li) are found in intracellular organelles known as endosomes, with total intracellular volume V a e . In this compartment receptors and ligands are sorted to one of two fates: recycling (with rate constant k,) or degradation. It appears that the coated-pit and smoothpit pathways merge at the endosome (Tran et al., 1987;
Surface Species dR$dt = -kfR&, + krC, - k& + kxRi + k, (MU dC$dt kfRsLo - krCn - kcCJ‘s + kuTn - ktCa + kxCi (M2) dT$dt = k & P 8 - k,T, - AT, 043) dP$dt -kcCJ‘, + k,T, + k,& 044) (Navlp)dLddt = -kfR&o + krC8 045) Intracellular Species dRildt -kfRiLi + k’,Ci + kJ1, - kbRi - kxRi 046) dCildt = kfRiLi - k’rCi + AT8 + ktC, - kbCi - k,Ci (M7) dPJdt AT, - k,& (Ma) (M9) (V&&av)dLildt = -kfRiLi + k’rCi - kM(V&JVav)Li Degraded Species dLddt = k d i + (VeNJVav)khlLi (M10) a Notation used in these equations is described in the text and in Table 11, with the exception of Nav,which is Avogadro’s number (mol-’.). Units are as follows: R,, C,, T,, Pa,Rip ci,Pi, and Ld, in cell-l; Loand Li, in mol/L.
Hansen et al., 1991). On the basis of experimental evidence that receptor and ligand have different half-lives (Wiley et al., 1991; Starbuck, 1991) we assign different rate ) comconstants to the degradation of soluble ( k ~ and plexed ( k h )ligand. Acid-enhanced dissociation in the endosome is indicated by an increased dissociation rate constant, Fr,for endosomal binary complexes while the endosomalforward rate constant remainsunchanged (K.H. Mayo, private communication). Coated-pit proteins are assumed to be immediately uncoupled from internalized complexes, due to rapid coated-pit uncoating (Pearse & Crowther, 1987). Though a rate constant for uncoating and return of coated-pit proteins is formally designated k,, we assume that this process occurs essentially instantaneously so that coated-pit protein levels remain constant. New receptor synthesis takes place with rate k,, completing the trafficking cycle. The other essential parameter is the cell density, p, which can have a significant influence on the depletion of ligand from the medium when it is sufficiently great. Equations representing the dynamics of the surface and intracellular processes illustrated in Figure 1are contained in Table I. Our formal whole-cell kinetic model consists of ten coupled, nonlinear ordinary differential equations. However, the assumption of instantaneous coated-pit protein uncoupling from internalized complexes removes eq M8 and the last term of eq M4, replaced by the conservation relation for total surface coated-pit proteins, PT:PT= P,+ T,.Further simplification can also be gained by assuming that receptor interactions with cell surface coated-pit proteins are fast relative to competing rate processes, so that ternary complex formation is at quasisteady state. This eliminates eqs M3 and M4, which are replaced by the relation T,= KcpP,C,, where Kcp is a coated-pit affinity constant, Kcp = k,J(k, + A). Note that this also simplifies eq M2. To generate concentration-dependent time plots from the model, these equations were integrated numerically using ~som-an initial value ordinary differential equation solver which employs a variable-order Adams predictorcorrector method (Hindmarsh, 1980). Initial conditions for the cell receptor species numbers were those characteristic of a steady state in the absence of growth factor, prior to incubation in growth factor at a specified concentration LOat time t = 0. Most of the parameter values listed in Table I1 were obtained from independent experiments designed to follow individual processes or well-defined subsets, using B82 fibroblasts, which can grow independently of EGF (Star-
Biotechnol. Rw., 1992, Vol. 8, NO. 2
135
Table 11. B82 Cell Parameter Values
model parameter
kx khr kt,I VY, P
B82 EGFR definition Surface Binding Parameters forward rate constant,ligand binding reverse rate constant,ligand binding equilibrium dissociation constant,C complex (k,/kf) coated-pit coupling rate constant coated-pit uncoupling rate constant equilibrium dissociation constant, T complex (k,/kc) coated pit affinity constant [kJ(X + k,)] total number receptors per cell total number coated pit proteins per cell ratio of no. of pit proteins to no. of receptors
WT 7.2 X lo7 M-' min-l 0.34 min-l 4.7 X 104 M 2.0 X 10-6min-1 0.10 min-1 5.0 x 103 1.8x 10-5 1.8 X 105 cell-l 8.1 X 104 cell-' 0.45
A973/Kin-
0 (0)
Internalization/IntracellularTrafficking Parameters coated-pit internalization rate constant 1.0 min-1 coated-pit uncoating rate constant (instantaneous) constitutive internalization rate constant 0.03 min-l receptor synthesis rate 130 cell-' min-l 10kr endosomal binary complex dissociation rate constant endosomal ternarv comdex dissociation rate constant (instantaneous) recycling rate conitant receptor degradation rate constant ligand degradation rate constant total endosomal volume cell density
buck et al., 1990; Lund et al., 1990; Wiley et al., 1991; Starbuck, 1991). A brief outline of the procedures is provided in the Appendix. The other parameters, standard endocytosis quantities-A, V,, and Ne-were estimated from literature sources [see Starbuck (1991)l. Table I1 also shows changes in model rate constants for an EGFR mutant which has been truncated at residue 973 (A973). Chen 'et al. (1989) termed the 49 amino acids between residues 973 and 1022 of the EGFR as the CaIn domain mutant, an acronym for the apparent Calcium ion flux andlnternalization features this region controls. The A973 truncation mutant is not internalized efficiently by the coated-pit pathway (Chen et al., 1989; Wiley et al., 1991). Our model analysis shows that Kcp 0 for the A973 EGFR. Apparently, this mutation prevents the EGF/EGFR complexes from coupling to a significant degree with coated-pit endonexin/adaptor molecules. It would not be surprising if other trafficking parameters, notably the recycling rate constant k,, were also affected by such mutations. Our current information, however, is that this does not appear to be the case (H. S. Wiley, private communication); the receptor regulatory domain for recycling may be different than that for internalization. Thus, only one of the model rate constants for the A973 EGFR mutant is specified as changed from the wild-type EGFR, the coated-pit coupling rate constant set to zero: k, = 0. Our model has been validated by excellent agreement of its predictions with our own experimental data on shortterm EGF/EGFR binding and internalization kinetics (Starbuck et al., 1990) and long-term EGFR downregulation and EGF depletion kinetics (Starbuck, 1991; Starbuck et al., 1992), using B82 fibroblasts. A couple of examples are shown in the Appendix, for the wild-type (WT) EGFR and a kinase-inactive (Kin-) mutant EGFR in which the essential lysine-721 residue is replaced by methionine (Chen et al., 1987). We have demonstrated that the trafficking parameters for the Kin- receptor are the same as for the WT receptor except that Kcp 0, because k, = 0 for this mutant. Notice that receptor downregulation is almost completely abrogated and that ligand degradation is substantially reduced for the Kin- EGFR relative to the WT EGFR. This suggests a close connection between tyrosine kinase mitogenic signaling activity and the signal attenuating trafficking-related phenomena of N
-
receptor downregulation and ligand depletion, resulting from the induced coated-pit endocytosis pathway, for normal physiological tissue cell proliferation control. For our present purposes of investigating the relationship between trafficking and proliferation, we are primarily interested in a form of EGFR that possesses normal signaling activity but lacks the signal attenuation phenomena. The A973 EGFR is just this sort of mutant receptor. The trafficking properties of the A973 receptor are highly similar to those for the Kin- EGFR (Chen et al., 1989) in that receptor downregulation and ligand degradation are abrogated, but the tyrosine kinase activity is normal. As mentioned above, mathematical analysis of trafficking data for the A973 EGFR shows that the coatedpit coupling rate constant is essentially zero, Le., k, = 0, just as for the Kin- EGFR. Thus, the two traffickingrelated phenomena by which mitogenic signaling is attenuated-receptor downregulation and ligand depletion-are diminished dramatically for the A973 mutant EGFR compared to the wild-type EGFR. This result is what portends significant predictions for different mitogenic responses to EGF by cells bearing these two actively-signaling EGFR forms.
Model for Cell Proliferation Response Mathematical models, whether phenomenological or mechanistic, for the effect of growth factors on mammalian cell proliferation are few a t present. Some investigators have applied the simple Monod model for the dependence of the specific cell growth rate, p, on serum concentration (Glacken et al., 1988). McKeehan and McKeehan (1981) offered a similar model to relate cell growth rate to the concentration of specific growth serum components in empirical fashion. The sole mechanistic model to date relating cell proliferation rate to growth factor receptor binding was presented by Knauer et al. (1984) for human fibroblasts (HF) and mouse embryo fibroblasts (MEF) exposed to EGF. Data from Knauer et al. for the dependence of H F proliferation on EGF are shown in Figure 2 (top). Percent maximum DNA synthesis rate is quantified here by uptake of 3H-thymidine. Knauer et al. find this dependence to be simple and sigmoidal, with the dose-response curves varying with the volume of medium in the culture dish.
Bbtechnol. Prog.. 1992, Vol. 8, No. 2
nalization rate, and negligible recycling, they derived an expression for the total number of occupied receptors as a function of parameters for EGF uptake, including the surface complexes
EGF Concentration
(nglml)
Percent intial receptors occupied
Total Occupied Receptors x I O J
Figure 2. Results from Knauer et al. (1984) study of the relationship between EGF receptor occupancy and the mitogenic response. (Top) Mitogenic response of cultured human fibroblasts to EGF in either a small or large volume of medium. HF cella were growthto confluencyon glass coverslipsand exposed to EGF in either 2 mL (closed circles) or 80 mL (open circles) of medium. The effect of increasing concentrations of EGF on [3H]thymidine incorporationwas then measured and quantified as percent maximum DNA synthesis rate. (Bottom) Dependence of maximum DNA synthesis rate on the number of total occupied receptors as calculated by Knauer et al., using the data in the top panel for 80 mL of medium and the steady-statemodel for EGF uptake described in the text. Parameter values used were as follows: k , = 2.4 X s-l, kt = 4.8 X lC5s-l, V , = 3.8 (cellas)-’, kf = 2.9 X 106 M-l s-l, k, = 1.2 X s-l, and k h = 2.4 X 10-4 s-1. Reprinted with permission from Knauer et al. (1984). Copyright 1984 Journal of Biological Chemistry.
This implies that the cell response to EGF is directly related to the availability of hormone in the culture medium. HF in the small volume (2 mL of medium) experiment depleted the medium of growth factor faster than cells in the large volume (80 mL of medium) experiment, a fact revealed by the 2-fold difference in EGF concentrations needed to elicit a half-maximal response. MEF exhibit an even greater medium volume effect. These data reveal the dependence of the mitogenic response on EGF uptake and degradation rates, indicating that it is not merely the concentration of EGF present in the medium which governs response characteristics but also the amount of EGF present. Knauer et al. conclude that receptor-mediated uptake and subsequent degradation of EGF are responsible for this phenomenon and, thus, include these processes in a mathematical model to analyze their data. The central tenet of the Knauer model is that the mitogenic response depends upon receptor occupancy (i.e., the total number of receptor-ligand complexes) at steady state. Assuming a simple, reversible bimolecular interaction between receptor and ligand, a first-order inter-
and the intracellular complexes
Ci+)
kh
where K, is the “apparent cellular affinity constant”: (3) Figure 2 (bottom) was generated by Knauer et al. from Figure 2 (top) (using the 80 mL of medium data), applying eqs 1-3 with the parameter values contained in the figure legend. The ordinate in Figure 2 (bottom) is still the percent maximum DNA synthesis rate while the abscissa is the total number of occupied receptors at steady state (CT= C, + Ci). This figure demonstrates two important points. First, the quantitative relationship between EGF receptor occupancy and 5% maximum DNA synthesis rate is piecewise linear. A minimum threshold may exist, a critical number of surface complexesnecessary to generate a mitogenic signal leading to DNA synthesis, followed by a linear increase in DNA synthesis rate with number of signaling complexes. The maximum threshold is the surface level of signalingcomplexes at which maximal DNA synthesis rate is achieved; above this number, further increases in the number of surface complexes do not generate any greater mitogenic response. Second, maximum proliferation rate occurs at roughly 25% EGFR occupancy, because at this EGF concentration approximately 75 % of the receptors have been lost by downregulation. This is indicated by the vertical dashed line in Figure 2 (bottom). Hence, a t the maximum proliferation rate essentially all of the surface EGFR are indeed bound by EGF. Linear dependence of cell proliferation rate on steadystate receptor occupancy may be a surprising result, given the complicated signal transduction mechanism which is probably involved between the initial binding event and the final steps leading to DNA replication and cell division. However, it is consistent with observations by Aharonov etal. (1978),whosestudyrevealed thatalthougheachround of EGF binding and trafficking takes place on the order of minutes, cells require 6-8 h of persistent EGFR occupation to invoke a full mitogenic response. This 68-h commitment period is the overall rate-limiting step in DNA synthesis, during which it is thought that key intracellular signals are generated at a rate proportional to the number of growth factor receptor complexes. A major question is left unaddressed by the Knauer model: it does not discriminate between possible signaling differences for surface complexes, C,, and internalized complexes, Ci. Some earlier investigators (e.g., Murthy et al., 1986; Lauffenburger et al., 1987) have suggested that intracellular receptor complexes might be responsible for generation of the mitogenic signal. Indeed, the majority of receptor-ligand complexesare intracellular, for example, Wiley and Cunningham (1981) report a steady-state ratio of Ci/C, = 7 for HF cells. However, recent experiments with various EGF receptor types transfected into NR6 cells (an NIH 3T3 line devoid of endogenous EGF receptors) strongly infer that surface EGF receptor complexes generate the mitogenicsignal (Wellset al., 1990).
137
Bbtechnol. Rog., 1992, Vol. 8, No. 2
-
1
r
30000
-
25000
A973
X
al 3
mj
Q
15000
L
8
3
-*
A
$ln
*
10000
5000
4
. I
1;-9
10.8
Concentration of EGF IM)
Figure 3. Wells et al. (1990) growth curve for NR6 cell transfectants. NR6 cella transfected with various EGF receptor mutants were plated in 20-mm-diameter wells and exposed to increasingconcentrations of EGF in MEM-a containing 2 % FBS. Forty thousand cells were initially seeded; counts were obtained after 9 days. NR6 cells expressing either the wild-type (WT; open squares) or A973 (truncated at residue 973, possessingfully active tyrosine kinase activity; filled circles) EGFR responded mitogenically to EGF, while NR6 cells expressing either the A1022K- construct (truncated at residue 1022, lacking tyrosine kinase activity due to site-directed mutagenesis of lysine 721; filled squares) or a frameshift (nonfunctional; filled triangles) EGFR did not. Notice that the A973 EGFR permits substantial cell proliferation at significantly lower EGF concentrations than does the WT EGFR. Reprinted with permission from Wells et al. (1990). Copyright 1990 American Association for the Advancement of Science.
The results of Wells et al. are shown in Figure 3. These demonstrate that NR6 cells transfected with wild-type (WT) EGF receptors are able to respond mitogenically to EGF, unlike cells transfected with either a frameshift or a kinase-negative form of the EGF receptor. More importantly, however,NR6 cells transfected with the A973 EGFR mutant, which is kinase competent but internalization deficient, respond mitogenically to a order-ofmagnitude lower concentration of EGF. Morphological observations for the growth of A973 transfectants show that these cells actually exhibit a transformed phenotype even at low EGF concentrations (Wells et al., 1990). NR6 cells transfected with the A973 EGFR mutant became refractile and overgrew the monolayer, whereas cells expressing WT receptors did not form the dense foci characteristic of transformed cells. These data suggest that this noninternalizing, kinase-active EGF receptor not only transmits the growth signal from the cell surface but may do so unremittingly. The studies by Wells et al. provide the final piece in our model for the relationship between EGFR dynamics and fibroblastic cell growth. Our central hypothesis is that the EGF/EGFR complex, with activated tyrosine kinase enzyme, is capable of mitogenic signal generation on the cell surface. This hypothesis defines processeswhich either remove the EGFR from its signaling environment or inactivate the tyrosine kinase as termination signals for mitogenic activity. Our objective is to quantitatively account for the wild-type (WT) EGFR growth curve and predict a priori the truncated mutant (A973)EGFR growth curve in Figure 3. Our procedure is to generate a relationship between DNA synthesis rate and number of surface complexes similar to that in Figure 2 (bottom) using the WT EGFR growth curve in Figure 3 and then to use that relationship to predict the A973 EGFR growth curve. A crucial assumption is that the DNA synthesis/ signaling complex relationship is dependent here only on the cell type (NR6 for both curves in Figure 3) but independent of the EGFR type. This is reasonable because Wells et al. find that the receptor tyrosine kinase activity is essentially unchanged between the two EGFR types
D10
O
10
o
-8
Concentration of EGF (M)
Figure 4. Predicted level of steady-state surface ligand-receptor complexes vs [EGF] for WT and A973 EGFR transfectants. Values for the steady-state level of active surface signaling as a function of the concentration of EGF added complexes (C,*) were calculated using our whole-cell model contained in Table I, with parameter values in Table 11. C.* levels are reported after numerical integration of model equations over the time course of 6 h, as our results show that variable concentrations do not change appreciably after that time. The only parameter change in generating profiles for WT and A973 EGFR transfectants is that the rate constant for receptor clustering, k,, is set = 0 in the A973 case.
considered here. For other EGFR mutations, the signaling activity (and hence the slope or thresholds of this relationship) might conceivably be altered. An additional key assumption is that the binding and trafficking parameter values we have measured with B82 fibroblasts can be used for the NR6 fibroblasts, which are a variant of NIH 3T3 cells. We justify this by referring to the studies of Chen et al. (19891, who found that B82 cells and NIH 3T3 cells exhibited similar binding and trafficking properties. One expected difference is in the receptor synthesis rate, It,; EGFR levels in transfected NR6 cells are typically about 10-fold lower than in transfected B82 cells, probably due to differences in promoter efficiency. However, because our empirical relationship between DNA synthesis rate and number of EGF/EGFR complexes is obtained directly for NR6 cells, the absolute receptor level is not really important as long as overall trafficking dynamics are similar. Our parameter measurements were carried out with B82 cells because their growth is EGF-independent, avoiding that clear complication of these experiments. Proliferation studies, obviously, could not be performed with the B82 cells. Hence, the B82 and NR6 lines were as well-suited as practicable. Further, because the data of Wells et al. suggest that changes in EGF receptor structure which cause significant effects on receptor trafficking can lead to dramatic changes in growth response, we theoretically investigate changes in other model parameters to predict their corresponding influence on cell growth. Data bearing on these results are not available at the present time, but experiments motivated by these predictions should be forthcoming.
Results and Discussion To begin making cell growth predictions from our model for EGF binding and trafficking (Figure 1,Tables I and 11),we generate profiles for the predicted level of active surface complexes (recall C, = C,*)as a function of EGF concentration. Model computations for both wild-type (WT) and A973 EGFR transfectants are shown in Figure 4. The values plotted are those obtained at a quasi-steady state, which is achieved after approximately 6 h for the cell density used here, lo6 cells/mL in culture dishes. Because incubation in EGF for about 6-8 h leads to a full cell mitogenic response characteristic of the EGF con-
138
centration used (Aharonov et al., 19781, this choice should reasonably correspond to the concentration governing typically observed proliferation data. It must be noted that this correspondence is likely to be sensitive to cell density, due to ligand depletion effects (Wiley and Cunningham, 1981). At any rate, the results in Figure 4 predict that cells transfected with the A973 EGFR reach a much higher level of surface signaling complexes (C,*) for any concentration of EGF added than their wild-type counterparts. One assumption we have made here is that binary surface complexes (C,) but not ternary surface complexes (T,) are able to phosphorylate substrates at the cell surface. This hypothesis is supported by data from Lund et al. (19901, who show that kinase activity is required for ternary complex formation. They speculate that the receptor/ phosphate bond in the ternary complex may be stabilized by phosphorylation of the coated-pit endonexinladaptor protein. If this is true, then it would be unlikely that an exogenous substrate of the tyrosine kinase enzyme could gain access to the catalytic domain of the EGFR in ita ternary complex form. This notion is consistent with the proposed function of receptor-mediated endocytosis, to modulate mitogenic signaling by removing active complexes from the cell surface. However, the model predictions are not substantially affected by this hypothesis, since the number of ternary surface complexes is typically only a small fraction of the total surface complexes. Another assumption implicit in these predictions is that the primary lesion in receptor trafficking caused by the truncation at EGFR residue 973 occurs at the level of receptor binding to coated-pit proteins. It may be that this mutation causes more subtle effects on intracellular routing which have not yet been detected. We must now convert these calculations of steady-state signaling complex, Cs*, levels into corresponding computations for cell growth rate. The methodology we have chosen is to use the piecewise linear plot of Knauer et al. for the relationship between steady-state occupancy and the mitogenic response (Figure 2, bottom) to calculate the percentage of maximum DNA synthesis expected for a given level of C,*. This is shown schematically in Figure 5. The HF cell data from Knauer et al. (1984) are replotted in Figure 5 after C, (C,*) was first calculated from the reported Ci/C, ratio (= 7; Wiley and Cunningham, 1981) for these cells. Next, a relationship between % maximum DNA synthesis rate and C,* is developed for NR6 cells by estimating values for C,* threshold and C,* maximum using the WT EGFR growth curve in Figure 3. One subtle point to note is that the C,* threshold corresponds here to roughly 8% of maximum DNA synthesis rate instead of zero. We do this in order to provide the most appropriate comparisons to the data of Wells et al., for which the background of 2% serum allowed for this level of cell proliferation in the absence of EGF. From the data of Knauer et al., the estimated values for HF cells are Ce*tbesh = 290 and Cs*m, = 3200, as can be seen in Figure 5. We find higher threshold (Cs*tbesh = 600) and maximum (C,*,, = 6500) values for the NR6 cells (alsoapparent in Figure 51, indicative of a requirement for greater levels of intracellular signals for these cells. Such variation of these values among different cell types is clearly not unexpected. Having now defined a relationship between % maximum DNA synthesis rate and Cs*, we can compute cell growth predictions from our binding and trafficking model. The first of these is shown in Figure 6. Here we have converted Figure 4 into a cell growth plot (as assayed by % maximum DNA synthesis rate) for NR6 cells transfected with the A973 and WTEGF receptors. This transformation enables
Bbtechnoi. Prog., 1992, Vol. 8, No. 2 120
1
0
I
4000
2000
6000
8000
surlace complexes (0.)
Figure 5. Relationship between steady-state surface EGFR occupancy and the mitogenic response for NR6 cells. The HF cell data (0;Knauer et al., 1984)contained in Figure 2 (bottom) are replotted here after first converting the abscissa was first converted from the total number of occupied receptors to the number of surface complexes (C, = C,*). The NR6 cell data (0; Wells et al., 1990)-for WT EGFR only-contained in Figure 3 are replotted here after a similar conversion. The relationship between steady-state EGF receptor occupancy and the % maximum DNA synthesis rate is piecewiselinear with an apparent threshold ( c s * h h = 290 and 600 #/cell for HF and NR6 cells, over which respectively) and an estimated maximum (C,*,) further receptor occupancy fails to elicit any greater response. = 3200 and 6500 #/cell for HF and NR6 The values for C,*, cells, respectively. The threshold is set at 8% of the maximum DNA synthesis rate, correspondingto the proliferation rate found for the background level of 2% serum in the experiments by Wells et al. (1990). Surface complex threshold and maximum values are assumed to be cell-typespecific;thus, the relationship between % maximum DNA synthesisrate and surface occupancy establishedhere for NR6 cells, using the Wells et al. (1990) WT EGFR proliferation data, is used to convert model predictions for C,* levels vs [EGF] into growth curves in all remainingfigures; the same relationship between % max and C,* is assumed regardless of the mutant EGF receptor being investigated. 120
1
/------71
1004
10 .”
10
-10
10
10
Concentration of EGF (M)
Figure 6. Predictedgrowth curve for WT and A973 EGF receptor transfectants. The ordinate (C,*) in Figure 4 is converted into the % maximum DNA synthesis rate using the relationship between % maximum DNA synthesis rate and C,* which was established for NR6 cells in Figure 5. Compare to the data of Wells et al. (1990)for these EGF receptor transfectanta in Figure 3.
us to quantitatively account for the WT EGFR data of Wells et al. shown in Figure 3. I t also allows excellent prediction of the 973 EGFR data in the same figure; cells transfected with this noninternalizing, kinase-active EGFR mutant require approximately 10-fold less EGF for halfmaximal mitogenic response. This successful prediction for A973 transfectants arises by changing the value of only a single rate constant in our whole cell kinetic model-the rate constant for coated-pit clustering. This provides mechanistic support for the speculation by Wells et al. that mutations in growth factor receptors which disable them from the endocytic pathway may result in neoplastic transformation. Our model suggests that the mutation
139
Blotechnol. PrGg., 1992, Vol. 8, No. 2 I
ni \
1
E
I
-kc 10
80
(A973)
-
_ _ _ _ kr = 0.001 min-1 -volume
-volume
-
----
S .-
I
\
'
60.
m
5 )
- kr= 2'WT
' I
'
400
'
E : e 20-
.c
5 e
2
. 0-
..
/
\
,o-ll
lo-lo
10.9
10-8
10-7
W F I (M)
Figure 7. Growth advantage conferred by A973 EGF receptor. The change in growth (Agrowth) is calculated from the results in Figure 6 by subtracting the % maximum DNA synthesis rate for cells transfected with the WT EGFR from the % maximum DNA synthesisrate for cells transfected with the A973 EGFR at any given [EGFI. The dashed line shows the growth advantage which could be achieved simply by maintaining a constant EGF
concentration for the WT EGFR transfectants. This graphical method highlights the EGF concentration range over which the growth advantage is being conferred (in this case 3 X 10-11-1 X 10-8M)and the magnitude of the growth advantage.
uncouples the receptor from endocytic machinery at the level of binding to proteins in the coated pit. Notice that we have also presumed that the A973 receptor mutant obeys the same relationship between % maximum DNA synthesis rate and CB*,implying that intrinsic signal transduction on a per complex basis is unaffected by this truncation. It has been established that the receptor tyrosine kinase activity is not noticeably affected (Wells et al., 1990). However, it is not clear a t this point what intracellular biochemical process(es) govern critical signal levels, so this point must remain unresolved for now. Equipped with a mathematical model which not only has previously made accurate predictions of EGF receptor binding and trafficking characteristics (Starbuck et al., 1990, 1992; Starbuck, 1991) but also now can make predictions for cell growth outside the experimental data base, we can proceed to use the model to investigate potential changes in other model parameters, in order to identify their corresponding influence on cell growth. Comments on these proposed changes and how each might be produced by genetic manipulation of either the EGF ligand or the EGF receptor are also provided. In each case, we effectively "subtract off" the effect of having a nondepleted supply of EGF so that the advantage conferred by the parameter change can be assessed independent of changes in the bulk medium concentration of growth factor. That is, a given parameter value change may have two separate effects: (1) at a specified bulk ligand concentration, the cellular binding and trafficking dynamics may be altered, and (2) the bulk ligand concentration itself may be altered by affecting depletion. Since the latter can be ameliorated simply by using culture (or reactor) conditions in which the bulk ligand concentration stays roughly constant (by replenishment or large medium volume), the most important effects to examine are those due solely to the cellular processes per se. We accomplish this in our computations by allowing the medium volume to be effectively infinite, providing a constant bulk ligand concentration without changing any intrinsic cell property. An example plot of this type is shown in Figure 7. In
/
\
/ \
,o-ll
lo'lo
/
10-9
10.8
10-7
W F I (M)
Figure 8. Model predictions for the growth advantage conferred by EGF receptor/EGFaffinity changes. To investigatethe effect of changing the ligand dissociation rate constant (k,), methods discussed previously were used to generate growth curves from predicted levels of surface (signaling)complexes as a function of
[EGF]. The growth curve for WT receptor transfectanta (Figure
6) was subtracted from each new growth curve to calculate the
predicted growth advantage (Agrowth) conferred by increasing or decreasing ligand affinity. Changes in the dissociation rate constant, k,, are as shown; the units for k, are min-l. Decreases in the dissociation rate constant from the WT value (Table 11) reflect an increase in the affinity of EGF for its receptor. Increased affinity is shown to have a positive effect upon cell growth. this graph, we show AGrowth, i.e., the change in % maximum DNA synthesis rate due to the specified parameter change vs EGF concentration (denoted [EGFI). In this figure AGrowth = (% maximum DNA synthesis rate for A973) - (7% maximum DNA synthesis rate for WT). The greatest increase in growth response for this case is conferred at [EGF] = 4 X 10-lo M, giving 100% 20% = 80 5%. It is interesting that this EGF concentration is roughly an order of magnitude factor less than the equilibrium dissociation constant for the ligand (KD= 5 X lov9 M, Table 11). Analogous plots can be examined for other parameter changes that could be obtained by exploitation of genetic engineering methods: receptor/growth factor binding affinity, receptor synthesis rate, receptor/growth factor recycling and degradation. In each of Figures 8-11, the absolute % maximum DNA synthesis rate for the given parameter change can be found from adding the value of AGrowth to that on the baseline curve denoted WT in Figure 6. This curve corresponds to AGrowth = 0 on Figures 7-11, allowing a consistent basis for comparison among cases. ReceptorIGrowth Factor Affinity. Model predictions depicted in Figure 8 show that by greatly increasing the affinity of the ligand for ita receptor a significant growth advantage could be achieved, even compared to a constant source of EGF (without the affinity change), over the concentration range 5 X 10-11< [EGFI I10-8. The change here is in the value for the receptodligand complex dissociation rate constant, k,. Normally it is approximately 0.34 min-', and here it is decreased to 0.001 min-1, for an effective affinity increase by a factor of 340. Significant growth advantage is defined by a change in growth greater than or equal to the change in growth observed in the A973 transfectants (Figures 6 and 7). Also shown is the effect of increasing and decreasing the affinity of EGF for its receptor by a factor of 2. There are several possibilities for experimentally testing this model prediction. First, a
140
$1
1
.-
f
1: \
"I s c
60
E.
E
2;
n z x
Mi
4
,
40-
i
40
E
'
t 20-
8
t
0 ',;0:11
'
'
"'10~10'
'
"'li.9
'
"
10.8
10-7
'
[EGFI (M)
Figure 9. Model predictionsfor the growth advantage conferred by amplification of EGF receptor synthesisrate. To investigate the effect of amplifying EGF receptor synthesis rate, methods discussed previously were used to generate growth curves from predicted levels of surface (signaling)complexes as a function of [EGF]. The growth curve for WT receptortransfectanta (Figure 6)was subtracted from each new growth curve to calculate the predicted growth advantage (Agrowth)conferred by overexpressing the EGFR at the levels shown. Receptor overexpression by a factor of 10 (Rt X 10) is shown to confer a significant growth advantage to cells over a constant source of EGF. bank of genetically-engineered EGF molecules has been created by Campion et al. (1991) with affinities for the EGFR ranging from 4% to about 200% of the affinity of natural human EGF for the human EGFR. These could be readily used to test model predictions for small changes ink,. Another possibility is experimentation with another natural ligand for the EGFR, transforming growth factor a (TGFa). Defeo-Jones et al. (1988) have created a sitedirected mutant of human TGF-a with 250 % of the affinity of the natural human TGF-a for the human EGFR. The dramatic growth effect we predict for increasing affinity by a very large factor might be achieved by transfecting cells with chicken rather than human EGFR. It has been reported that TGF-a has a 100-foldhigher affinity for the chicken EGFR than does EGF (Laxet al., 1988). Within the realm of rational drug design, it might also be possible to synthesize defined fragments of EGF molecule or antiEGFR antibodies which might bind more tightly to the EGFR. EGFR Synthesis Rate. Model predictions depicted in Figure 9 show that by amplifying the EGFR synthesis rate so that EGFR are overexpressed by a factor of 2-10 we can achieve a significant growth advantage compared to a constant source of EGF over the range < [EGFI < 10-8. The experimental method for selecting higher receptor expressing clones in transfectanta created by our collaborators is to expose cultures to increasing concentrations of methotrexate (Glenney et al., 1988). To test these model predictions, either this strategy could be employed or a better promoter could be used in the transfection vector. These predictions are corroborated, qualitatively at least, by the experimental results of Di Fiore et al. (1987),who used a different vector to transfect EGFR into the NR6 cell line. They found that NR6 clonal lines which express EGFR at 50-100-fold levels over control NIH 3T3 cells demonstrated a marked increase in DNA synthesis in response to EGF over an intermediate concentration range. Because the EGFR gene is frequently amplified or overexpressed in human malignancies, these results indicate that receptor overexpressionmight provide a selective growth advantage to a transformed cell. Recycling/Degradation. Model predictions depicted in Figure 10A show that if degradation is prevented (i.e.,
B
80 -
t
kx = 1.O min-1
:
8 60c
5
:
Z 4
'
!2 S
40-
'
20:
8
' 0~~
lo-ll
lo.lo
10-9
10-8
10-7
WFI (M) Figure 10. Model predictions for the growth advantageconferred by enhanced EGF receptor recycling with or without blocking receptodligand degradation. To investigatethe effectof changing the recycling rate constant (kx),methods discussed previously were used to generate growth curves from predicted levels of surface (signaling)complexes as a function of [EGF] either with (A) or without (B)a degradation block imposed. The growth curve for WT receptor transfectanta (Figure 6)was subtracted from each new growth curve to calculate the predicted growth
advantage (Agrowth) conferred by increasing the recycling rate constant. In (A) the degradation rate constants (ku,kb) were set = 0 while in (B)they were kept at their WT value (Table 11). Changes in the recycling rate constant, k., are as shown; the unita for k, are min-l. A recycling rate constant of 0.19 min-* is the pinocytic rate (the rate of solute return) in B82 cells (Wiley et al., 1991). Blocking degradation is shown to have a positive effect on cell growth for all values of the recycling rate constant. k h = 0)values of the recycling rate constant greater than or equal to the wild-type EGFR value (k, = 0.058 mi&) enhance growth compared to a constant supply of EGF over the range M < [EGFI < 10-8 M. k, = 0.19 min-1 is the rate constant for so-called diacytosis of EGF, the very rapid return to the cell surface of ligand that apparently is not routed through the endosomal compartment (Wiley et al., 1991); this may be some sort of practical upper bound on the recycling rate constant, though this is not certain. The effect of changing the recycling rate without preventing degradation is also shown (Figure 10B); in this case the growth enhancement over a constant supply of EGF is not as dramatic. A possible strategy would be to knock out a retention signal for degradation which is likely to exist within the cytoplasmic tail of the receptor. To date, retention signal sequences have not been found in growth factor receptors. However, they have been identified in proteins which reside in the endoplasmic reticulum (ER); specificC-terminal retention
Bbtechnol. Rog., 1992, Vol. 8, No. 2
signals prevent ER resident proteins from passage into the secretory pathway (Pelham, 1989). A recent study by Sorkin et al. (1991) shows that site-directed mutagenesis of the three autophosphorylation sites in the EGFR tail dramatically retards EGFR degradation. Testing our model predictions by transfecting these F3 receptors (3 tyrosines 3 phenylalanines) into NR6 cells would be a logical first step. Overall, our modeling approach appears to be very promising for analysis of the possible effects of changes in growth factor/receptor binding and trafficking parameters on cell proliferation. The essential concepts are (1) that binding and traffickingparameters govern the number of Signaling receptor complexes and (2) that the rate of cell proliferation is related to the number of signaling receptor complexes. Therefore, we believe that we have elucidated two distinct mechanisms for affecting growth factor regulation of proliferation. One mechanism is the intrinsic signal generation activity of the activated receptor, which is characterized quantitatively by the slope of the linear portion of the curves in Figures 2 (bottom) and 5. The greater this slope, the greater the intrinsic signaling activity. This is the typical focus of investigators consideringpossible alterations of growth factor regulation, whether designed or pathological. However, a second mechanism is the receptodligand trafficking dynamics, which is characterized by the position on the abscissa axis of Figures 2 (bottom) and 5 for agiven EGF concentration. That is, without changing the intrinsic receptor signaling activity, the overall mitogenic response can be altered either by design or in natural pathology by changing cellular trafficking properties. We believe that this distinction may prove to be important in improving our understanding of growth factor regulation of cell proliferation. System mutations may involve either or both of these mechanisms, and it will be useful to determine which. The apparent connection between the EGFR tyrosine kinase mitogenic signaling activity and the attenuating trafficking phenomena of EGFR downregulationand EGF depletion, as seen by the effects of the Kin- EGFR mutant (see Appendix Figures 11and 121, suggest a physiological role for trafficking as a homeostatic mechanism of tissue cell growth control. Loss of this control could be related to development of some cancers (Wells et al., 1990;Masui et al., 1991). For purposes of mammalian cell bioreactors or in vitro tissue engineering, on the other hand, loss of attenuation mechanisms for actively signaling EGFR by altering receptor trafficking properties could be very useful in promoting cell growth at lower EGF concentrations. In such cases, the growth factor may be caused to act more as a catalyst than as a nutrient. Although we have confidence that the basic features of our mathematical model have been satisfactorilyvalidated for the EGF/fibroblast system, there is still room for improvements in some detailed aspects. Primarily, the intracellular mechanisms of endosomalsorting to recycling and degradation destinations are not well understood. We have lumped together what are likely to be complicated mechanisms similar to those operating on the cell surface for endocytic internalization, so we certainly anticipate more accurate representation of this process to be developed before long. In other work (Linderman & Lauffenburger, 1988)we have analyzed some possible models, but experimental data relevant to this aspect of the trafficking pathway is currently lacking. We expect that alteration of sorting by means of changes in receptor structure will be possible in an analogous fashion to what is available now for internalization. It is not clear how well this mathematical model might be generalized to other growth factor and cell types.
loo80
r
141
-
2o
1
0 4
0
'
'
I
'
I
30
15
I
'
45
I
60
'
2
'
I
90
75
time (minutes)
Figure 11. Comparisonof model computationsand experimental data for EGFR downregulation. The fraction of the initial number of cell surface EGFR is plotted as a function of time after incubation of cella in EGF at a concentration of 50 nM. Symbols are experimental data from Chen et al. (1989)for B82 cells transfected with WT (squares) and Kin- (circles) EGFR. Curves are computed results from the mathematical model of Table I with parameter values from Table 11. Both of these curves are a priori predictions because all parameter values were determined independently of the data shown here. Note that WT EGFR demonstrate substantial downregulation,while KinEGFR show very little. The essential difference in parameter values between these two receptors is that k, = 0 for the Kinform; i.e., this mutant EGFR is not efficiently internalized by the ligand-induced coated-pit endocytosis pathway. P
P
?
0
30
60
90
120
Incubation time (min)
Figure 12. Comparison of model computationsand experimental data for EGF degradation. The number of degraded EGF molecules is plotted as a function of time after incubation of cella in EGF at a concentration of 1.7 nM. Symbols are experimental data from Wiley et al. (1991)for B82 cells transfected with WT (squares) and Kin- (circles)EGFR. Curves are computed results from the mathematical model of Table I with parameter values from Table 11. The Kin- curve is an a priori prediction because all parameter values were determined independently of that data shown here, while the WT curve represents the means by which a value for the EGF degradation rate constant, kH, was determined. Note that WT EGFR demonstrate substantial ligand degradation, while Kin- EGFR show very little. The essential difference in parameter values between these two receptors is that k, = 0 for the Kin- form; Le., this mutant EGFR is not efficiently internalized by the ligand-induced coated-pit endocytosis pathway.
Trafficking effects such as receptor downregulation and ligand depletion seem to be ubiquitous, however, so we suggest that the general conceptual framework-that of quantitatively relating trafficking effects to mitogenic behavior via effects on signaling receptor dynamics-could serve examination of cell proliferation responses in other systems productively.
Conclusions We have demonstrated the ability of our mathematical model for EGFR binding and trafficking dynamics to
142
Biotechnol. Prog., 1992, Vol. 8, No. 2
account for the experimentally-observed EGF concentration dependence of the proliferation of NR6 fibroblasts transfected with the wild-type EGFR, as reported by Wells et al. (1990). We have then gone on to show that this model can predict the observed shift of proliferation dependence to lower EGF concentrations for NR6 fibroblasts transfected with a truncated EGFR, A973, for which the ligand-induced coated-pit internalization pathway does not operate efficiently. Thus, we have been able to account for a dramatic improvement in cell growth efficiency on a serum growth factor in terms of a genetically-engineered alteration in growth factor receptor structure. Given this encouraging foundation, we have further generated a number of additional predictions for how proliferation dependence on this growth factor might be altered by specific modifications of the growth factor and/or its receptor. We believe that the potential implications of this approach for rational design of cell growth control in culture may be great. It may also have implications for elucidation of mechanisms underlying loss of normal cell proliferation control in malignant transformation, by demonstrating that receptor trafficking dynamics may in some cases play as important a role as intrinsic signal transduction in determining the overall resulting mitogenic response.
Acknowledgment We express deep appreciation to Dr. G. N. Gill (University of California, San Diego) for allowing us to participate on work with the cell lines. Also, we are indebted to Dr. H. Steve Wiley (University of Utah)and Dr. Alan Wells (University of Alabama, Birmingham) for providing figures from their manuscripts and for many helpful discussions. Financial support from the NSF Biotechnology Program is gratefully acknowledged.
Appendix We wish to provide a concise overview summary of the procedures used to validate the receptodligand binding and trafficking model for the EGF/EGFR system for B82 fibroblasts. Details of both experimental methods and mathematical analyses can be found in Starbuck (1991), and various aspects of this model development, validation, and parameter determination work have been previously presented (Starbuck et al., 1990,1992; Lund et al., 1990; Wiley et al., 1991). Briefly, the cell-surface parameters kf,kr, k,, k,, RT,and PT were determined together at 37 “C by experiments following the kinetics of 12%labeled EGF cell-surface binding and dissociation (using phenylarsineoxide-treated cells to prevent internalization), along with saturationof-internalization (“satin”) plots of EGF/EGFR internalization rate constants as a function of the number of surface complexes, C,. Satin plots use values of the overall endocytic internalization rate constant, k, [which combines parameters of the induced (coated-pit) and constitutive (smooth-pit) internalization pathways], obtained from kinetic inside-vs-surface (“insur”)plots of ‘Wlabeled EGF during endocytosis. The constitutive internalization rate constant, kt,was found by using an 12%labeledanti-EGFR monoclonal antibody instead of 12SI-labeledEGF to follow endocytosis. The recycling rate constant, k,, was determined from pulse/chase experiments using 12SI-labeled EGF. The liganddegradation rate constant, kH,was found from kinetic measurements of labeled EGF degradation products in the medium. The receptor degradation rate constant, khr, and synthesis rate, k,, were determined together from measurements of labeled EGFR loss in the presence and absence of EGF. The coated-pit internal-
ization rate constant, A, as well as the total cell endosomal volume, VJVe (combining individual endosomal volume and number of endosome5 per cell), were estimated from literature sources. The EGF/EGFR dissociation rate constant in the endosomal compartment was assumed to be enhanced by a factor of 10 due to lower pH, based on surface binding experiments at various pH levels by K. H. Mayo (private communication). The cell density, p, is specified in a given experiment by the cell number and medium volume. Computations using the model equations in Table I along with the parameter values in Table I1 were performed to generate predictions of long-time (hours) dynamic behavior of cell receptor number of medium ligand concentration. Results were obtained and compared to experimental data for B82 cells transfected with either the wild-type (WT) EGFR or a mutant (Kin-) EGFR lacking tyrosine kinase activity (because of replacement of the key lysine-721 residue by methionine). For the Kin- EGFR, all parameter values remained the same as for the WT EGFR except that the coated-pit coupling rate constant, k,, was determined to be essentially zero. Example plots showing such comparisons between model computations and experimental data are given in Figures 11 and 12, illustrating receptor downregulation and ligand degradation results. In Figure 11,curves for both WT and Kin- EGFR are a priori predictions. In Figure 12, the Kin- curve is also an a priori prediction, while the WT EGFR data was in fact used originally to determine the ligand degradation rate constant, k ~ .In each case, the data are accounted for satisfactorily by the model predictions. Notice that receptor downregulation and ligand degradation are both substantially diminished for the Kin- EGFR compared to the WT EGFR, because the Kin- EGFR are unable to be internalized effectively via the induced, coated-pit pathway.
Literature Cited Aharonov, A. M.; Pruss, R. M.; Herschman, H. R. Epidermal growth factor: relationship between receptor regulation and mitogenesisin 3T3 cells. J.Biol. Chem. 1978,253,3970-3977. Anderson, R. G. W.; Kaplan, J. Receptor-mediated endocytosis. Mod. Cell Biol. 1983,1, 1-52. Bader, F. G. Meeting the challenge of understanding biological systems. Biotechnol. h o g . 1986,2,J3. Bailey, J. E. Toward a scienceof metabolic engineering. Science 1991,252,1668-1675. Bertics, P. J.; Gill, G. N. Self-phosphorylation enhances the protein-tyrosine kinase activity of the epidermal growth factor receptor. J. Biol. Chem. 1985,260,14642-14647. Campion, S. R.; Matsunami, R. K.; Engler, D. A.; Niyogi, S. K. Biochemical properties of site-directed mutants of human epidermal growth factor: Importance of solvent-exposed hydrophobicresiduesof the amino-terminaldomain in receptor binding. Biochemistry 1990,29,9988-9993. Carpenter, G.; Wahl, M. I. The epidermal growth factor family. In Peptide Growth Factors and Their Receptors Sporn, M. B., Roberts, A. B., Eds.; Springer-Verlag: New York, 1990;pp 69-171. Chen, W.S.; Lazar, C. S.; Poenie, M.; Tsien, R. Y.; Gill, G. N.; Rosenfeld, M. G. Requirement for intrinsic protein tyrosine kinase in the immediate and late actions of the EGF receptor. Nature 1987,328,820-823. Chen, W. S.;Lazar, C. S.; Lund, K. A.; Welsh, J. B.; Chang, C. P.; Walton, G. M.; Der, C. J.; Wiley, H. S.; Gill, G. N.; Rosenfeld, M. G. Functional independence of the epidermal growth factor receptor from a domain required for ligand-induced internalization and calcium regulation. Cell 1989,59,33-43. Cohen, S.; Carpenter, G.; King, L., Jr. Epidermal growth factorreceptor kinase interactions. Co-purification of receptor and epidermal growth factor-enhanced phosphorylation activity. J. Biol. Chem. 1980,255,4834-4842.
143
Blotechnol. Prog., 1992, Vol. 8, No. 2
Czech, M. P.; Clairmont, K. B.; Yagaloff, K. A.; Corvera, S. Properties and regulation of receptors for growth factors. In Peptide Growth Factors and Their ReceptorsI; Sporn, M. B., Roberts, A. B., Eds.; Springer-Verlag: New York, 1990; pp 37-65. Defeo-Jones,D.; Tai, J. Y.; Wegrzyn, R. J.; Vuocolo, G. A.; Baker, A. E.; Payne, L. S.; Garsky, V. M.; Oliff, A,; Riemen, R. W. Structure-function analysis of synthetic and recombinant derivatives of transforming growth factor a. Mol. Cell. Biol. 1988,8, 2999-3007. DiFiore, P. P.; Pierce, J. H.; Fleming, T. P.; Hazan, R.; Ullrich, A.; King, C. R.; Schlessinger, J.; Aronson, S. A. Overexpression of the human EGF receptor confers and EGF-dependent transformed phenotype to NIH 3T3 cells. Cell 1987,51,10631070. Gill, G. N. Growth factors and their receptors. In Oncogenes and the Molecular Origins of Cancer;Weinberg, R., Ed.; Cold Spring Harbor Laboratory Press: Cold Spring - Harbor, NY, 1989;p p 67-96. Gill, G. N.; Bertics, P. J.; Stanton, J. B. Epidermal growth factor and its receptor. Mol. Cell. Endocrinol. 1987, 51, 169-186. Glacken. M. W.: Adema. E.: Sinskev. A. J. Mathematical descriptionsof hybridoma c u b e k i n k s : I. Initial metabolic rates. Biotechnol. Bioeng. 1988, 32, 491-506. Glenny, J. R., Jr.; Chen, W. S.; Lazar, C. S.; Walton, G. M.; Zokas, L. M.; Rosenfeld, M. G.; Gill, G. N. Ligand-induced endocytosis of the EGF receptor is blocked by mutational inactivation and by microinjection of anti-phosphotyrosineantibodies. Cell 1988,52,675-684. Hansen, S. H.; Sandvig, K.; van Deurs, B. The preendosomal compartment comprises distinct coated and noncoated endocytic vesicle populations. J . Cell Biol. 1991,113,731-741. Hindmarsh, A. C. LSODE and LSODI,two initial value ordinary differential equation solvers. ACM-Signum Newsl. 1980,15, 10-11. Knauer, D. J.; Wiley, H. S.; Cunningham, D. D. Relationship between epidermal growth factor receptor occupancy and mitogenic response. Quantitative analysis using a steady-state model system. J . Biol. Chem. 1984,259, 5623-5631. Lauffenburger, D. A.; Linderman, J.; Berkowitz, L. Analysis of mammalian cell growth factor receptor dynamics. Ann. N . Y . Acad. Sci. 1987,506, 147-162. Lax, I.; Johnson, A.; Hawk, R.; Snap, J.; Bellot, F.; Winkler, M.; Ullrich, A.; Vennstrom, B.; Schlessinger,J.; Givol, D. Chicken epidermal growth factor (EGF) receptor: cDNA cloning, expression in mouse cells, and differential binding of EGF and transforming growth factor a. Mol. Cell. Biol. 1988, 8, 1970-1978. Linderman, J.; Lauffenburger, D. A. Analysis of intracellular receptor/ligand sorting in endosomes. J . Theor. Biol. 1988, 132, 203-245. Lund, K. A.; Opresko, L. K.; Starbuck, C.; Walsh, B. J.; Wiley, H. S. Quantitative analysis of the endocytic system involved in hormone-induced receptor internalization. J . Biol. Chem. 1990,265, 15713-15723. Masui, H.; Wells, A.; Lazar, C. S.; Rosenfeld, M. G.; Gill, G. N. Enhanced tumorigenesisof NR6 cells which express non-downregulating epidermal growth factor receptors. Cancer Res. 1991,51,6170-6175. Mather, J. P., Ed. Mammalian Cell Culture: The Use of SerumFree Hormone-Supplemented Media. Plenum Press: New York, 1984. Mayo, K. H.; Nunez, M.; Burke, C.; Starbuck, C.; Lauffenburger, D.; Savage,C. R., Jr. Epidermalgrowthfactor receptor binding is not a simple one-step process. J . Biol. Chem. 1989, 264, 17838-17844.
McKeehan, W. L.; McKeehan, K. A. Extracellular regulation of fibroblast multiplication. A direct kinetic approach to analysis of role of low molecular weight nutrients and serum growth factors. J . Supramol. Struct. Cell. Biochem. 1981, 15, 83110. Murthy, U.; Basu, M.; Sen-Majumdar, A.; Das, M. Perinuclear location and recycling of epidermal growth factor receptor kinase: Immunofluorescent visualization using antibodies directed to kinase and extracellular domains. J . Cell Biol. 1986, 103, 333-342. Pearse, B. M. F.; Crowther, R. A. Structure and assembly of coated vesicles. Annu. Rev. Biophys. Biophys. Chem. 1987, 16,49-68. Pearse, B. M. F.; Robinson, M. S. Clathrin, adaptors, and sorting. Annu. Rev. Cell Biol. 1990, 6, 151-171. Pelham, H. R. B. Control of protein exit form the endoplasmic reticulum. Annu. Rev. Cell Biol. 1989, 5, 1-23. Schlessinger, J. Allosteric regulation of the epidermal growth factor receptor kinase. J . Cell Biol. 1986, 103, 2067-2072. Sorkin, A.; Waters, C.; Overholser,K. A.; Carpenter, G. Multiple autophosphorylation site mutations of the epidermal growth factor receptor: Analysis of kinase activity and endocytosis. J . Biol. Chem. 1991,266, 8355-8362. Starbuck, C. Quantitative studies of epidermal growth factor receptor binding and trafficking dynamics: relationship to cell proliferation. Ph.D. Thesis, University of Pennsylvania, Philadelphia, PA, 1991. Starbuck,C.; Wiley, H. S.; Lauffenburger,D. A. Epidermalgrowth factor binding and trafficking dynamics in fibroblasts: relationship to cell proliferation. Chem. Eng. Sci. 1990,45,23672373. Starbuck, C.; Wiley, H. S.; Lauffenburger, D. A. Engineering growth factor/receptor processes: an approach for optimizing mammalian cell proliferation responses. Proceedings of 1991 U.S./JapanConferenceon Biotechnology; Tanner, R. D., Ed.; Springer-Verlag: New York, 1992; in press. Tran, D.; Carpentier, J.-L.; Sawano, F.; Gorden, P.; Orci, L. Ligands internalized through coated or noncoated invaginations follow a common intracellular pathway. Proc. Natl. Acad. Sci. U.S.A. 1987,84, 7957-7961. van Deurs, B.; Petersen, 0. W.; Olsnes, S.; Sandvig, K. The ways of endocytosis. Znt. Rev. Cytol. 1989, 117, 131-177. Waters, C. M.; Oberg, K. C.; Carpenter, G.; Overholser, K. A. Rate constants for binding, dissociation, and internalization of EGF: effect of receptor occupancy and ligand concentration. Biochemistry 1990, 29, 3563-3569. Wells, A.; Welsh, J. B.; Lazar, C. S.; Wiley, H. S.; Gill, G. N.; Rosenfeld, M. G. Ligand-induced transformation by a noninternalizing epidermal growth factor receptor. Science 1990, 247,962-964. Wiley, H. S.; Cunningham, D. D. A steady-state model for analyzing the cellular binding, internalization, and degradation of polypeptide ligands. Cell 1981, 25, 433-440. Wiley, H. S.; Herbst, J. J.; Walsh, B. J.; Lauffenburger, D. A.; Rosenfeld,M. G.; Gill, G. N. The role of tyrosine kinase activity in endocytosis,compartmentation, and down-regulationof the epidermal growth factor receptor. J . Biol. Chem. 1991,266, 11083-11094. Accepted January 16, 1992. Registry No. EGF, 62229-50-9;EGF receptor kinase, 7907906-4.
