Cancer Cell: Linking Oncogenic Signaling to Molecular Structure

Summary

A multiscale strategy is presented for constructing models of intracellular signaling networks in which the oncogenic behavior of the network is encoded through alternate parameterization of the kinetic and structural properties of mutant oncoproteins. The approach uses molecular dynamics and docking simulations to quantify altered topologies of interactions as well as to provide the missing parameters for network models of both wild-type and oncogenic signaling. Through simulation of the resulting signaling networks, the global behavior of these networks may then be compared and functional roles may be assigned to the mutant oncoproteins. An example of this approach is presented in which structural alterations found in a mutant form of the epidermal growth factor receptor are represented as kinetic perturbations in a model of growth factor signaling. Based on network parameters estimated from molecular-level simulations, simulations at the network level show that small perturbations in molecular structure can lead to profoundly altered cellular phenotype.

1 Introduction

The cancer phenotype may be viewed as a pathological dysregulation of cellular signals that control growth, survival, motility, cell-cell connectivity, and DNA synthesis and repair (Hanahan and Weinberg 2000). Generally speaking, the sources of dysregulation are an accumulated set of mutations that produce altered gene products. The interaction of these mutant oncoproteins with normal host signaling mechanisms perturbs proper signaling and confers the oncogenic behavior. For example, mutations affecting the catalytic activity, binding specificity, translation efficiency, or rate of degradation of an enzyme involved in DNA repair can predispose a cell to genomic instability by allowing replication of damaged genomic sequence (Zhivotovsky and Kroemer 2004). The specific identities and combinations of these cancer-causing mutations are known to vary considerably according to tissue and cell type and are strongly interdependent on the cellular/tumor micro-environment (Sjoblom, Jones et al. 2006). In light of these complexities, mathematical models of cellular signaling networks have become indispensible tools for explaining oncogenic behaviors, predicting resistance mechanisms, and designing molecular therapies to attenuate defective signaling.

How can the altered activities of mutant oncoproteins be represented in a mathematical model? In many cases, wild-type and oncogenic signaling pathways share similar network structures but differ in the kinetic behavior and interaction topologies of only a few oncoproteins (Sharma and Settleman 2007). Unless these differences are resolved quantitatively, one cannot distinguish between normal and cancerous signaling networks in a mathematical model. Moreover, when attempting to resolve such crucial but subtle differences, it may be necessary to switch from a systems perspective of protein interaction networks to a molecular perspective of enzyme activation and protein-protein interaction. This chapter describes an approach for constructing models of intracellular signaling networks in which the oncogenic behavior of the network is encoded through calculations of altered kinetic and structural properties of mutant oncoproteins. Using molecular dynamics and docking simulations, atomistic models are exploited to quantify altered topologies of interactions as well as to provide the missing parameters for network models of both wild-type and oncogenic signaling. The global behavior of these networks may then be compared and functional roles may be assigned to the mutant oncoproteins. An application of this multiscale, multiresolution approach is presented in which structural alterations found in a mutant form of the epidermal growth factor receptor are represented as kinetic perturbations in a model of growth factor signaling. Based on network parameters estimated from molecular-level simulations, simulations at the network level show how small perturbations in molecular structure can lead to profoundly altered cellular phenotype.

2 Model

A multiscale-multiresolution approach can be devised by encompassing four distinct length/time scales:

• Molecular modeling using Newton’s equations: based on a Hamiltonian H(r₁,r₂,…)=K+U; r_i=atomic coordinates, K=kinetic energy, U=Potential energy, we solve the system of equations (where F_i=Force, m_i=mass, t=time),

  $${\mathrm{F}}_{\mathrm{i}}=-\nabla \mathrm{U}={\mathrm{m}}_{\mathrm{i}}{\mathrm{d}}^2{\mathrm{r}}_{\mathrm{i}}∕\mathrm{d}{\mathrm{t}}^2.$$ (1)
• Electronic structure using mixed quantum mechanics molecular mechanics simulations: we variationally minimize the energy function E,

  $$\mathrm{E}=\langle \varphi \mid \mathrm{H}\mid \varphi \rangle \text{and}\langle \varphi \mid \varphi \rangle =1,$$ (2)

  where, the bra-ket (Dirac) notation ⟨ϕ|ϕ⟩ represents vector dot product and ⟨ϕ|H|ϕ⟩ represents the expectation value (Szabo and Ostlund 1996). In (2), ϕ is the electronic wave function satisfying the Pauli’s exclusion principle and H=H_electronic, i.e., the electronic Hamiltonian. We then solve Newton’s equations given by equation (1) for the nuclear degrees of freedom with some forces derived from H_electronic.
• Coarse-grained models: using a coarse grained Hamiltonian, H[λ(r₁, r₂)]=F[λ(r₁, r₂)], where F=free energy, λ=generalized/collective coordinate, we solve the generalized Langevin equation (Agrawal, Weinstein et al. 2008),

  $$\mathrm{d}\lambda ∕\mathrm{d}\mathrm{t}=-\mathrm{M}\delta \mathrm{F}∕\delta \lambda +\xi .$$ (3)

  In equation (3), M represents the mobility term, ξ represents random thermal force satisfying ⟨ξ⟩=0, and ⟨ξ(0)ξ(t)⟩=2k_BTMδ(t), where ⟨⟩ represents an ensemble average in the equilibrium ensemble, k_B=Boltzmann’s constant, and T=Temperature.

• Deterministic network models: As an average solution to the Langevin dynamics using F(λ=reaction coordinate) for transitions between reactant and product states of chemical species, we solve deterministic network models for signal transduction using rate laws based on mass-action kinetics.

Based on the aforementioned formulations, the linking of oncogenic signaling to molecular structure in a mathematical model can be achieved in three separate but interconnected modeling steps:

• Deterministic ordinary differential equations (ODE) models are used to represent both wild-type and oncogenic signaling networks that differ in a defined set of molecular species. The pair of networks must both contain the mutant or overexpressed oncoproteins as well as one or more “output” components that can be monitored to evaluate the oncogenic behavior of the system (e.g., a master transcriptional regulator controlling cell survival).

• Molecular docking is used to predict ligand binding in the absence of a ligand-bound crystal structure and functional affinity data. These free energy-based simulations are used to calculate a new set of mutant kinetic parameters based on altered molecular structure.

• Molecular dynamics simulations are used to characterize the structural properties of mutant gene products from an altered polypeptide sequence. These calculations rely on the availability of solved crystal structures and may involve homology modeling.

By integrating these three modeling regimes, the phenotypic differences that define mutant systems at the network level are encoded through fine-scale calculations of the structural and kinetic properties of mutant oncoproteins (Figure 1).

Figure 1.

Overview of multiscale modeling method for linking molecular structure to oncogenic signaling. The aberrant signaling behavior of oncogenic networks is captured by monitoring the behavior of altered network models, typically ODE reaction networks. Alternate parameterization for the models is provided by docking simulations of mutant oncoproteins, which relies on structural models of the mutant proteins. Structural information is ultimately connected to mutations in genomic sequence. An example of oncogenic signaling behavior caused by altered structural and kinetic properties in a mutant of the epidermal growth factor receptor is presented in the text.

The multiscale strategy portrayed in Figure 1 is illustrated through a model of dysregulated growth signaling caused by a single amino acid substitution in the epidermal growth factor receptor (EGFR). EGFR is a receptor tyrosine kinase (RTK) that is commonly mutated or overexpressed in human cancers (Mendelsohn and Baselga 2000). A mutant form of the receptor, L834R, exhibits an altered pattern of autophosphorylation caused by differences in its physical structure, binding affinities, and catalytic behavior. These perturbed phosphorylation patterns lead to constitutive activation of certain survival pathways that predispose L834R mutants to uncontrolled growth (Choi, Mendrola et al. 2007). Thus, the goal of this multiscale model will be to track changes in the cellular growth pathways as a result of structural alterations in the mutant receptor. Accomplishing this goal will require a consideration of the receptor’s biophysical properties on an atomic scale as well as its interaction with various binding partners and adaptor proteins.

2.1 Constructing Mechanistic Models of Oncogenic Signaling

Kinetic models of cellular signaling pathways represent the highest level of modeling in this approach and are used to monitor the global behavior of both wild-type and mutant systems (Figure 1). Ordinary differential equations (ODEs) are used to represent coupled kinetic reactions that describe the rates of production and consumption of species in the model (Aldridge, Burke et al. 2006). For large networks that contain species with posttranslational modifications or multiple binding partners, rules-based modeling (Hlavacek, Faeder et al. 2006) provides the best method of generating ODEs that encode these kinetic differences.

In the signaling network presented here (Figure 2), EGF-induced activation of EGFR occurs through two parallel phosphorylation pathways corresponding to tyrosine 1068 (Y1068) and tyrosine 1173 (Y1173). Phosphorylated Y1068 (pY1068) binds only to the adaptor proteins Gab-1 and Grb2, while phosphorylated Y1173 (pY1173) binds only to the adaptor Shc. The major downstream pathways include EGF-ERK via the Ras-Raf MAP-kinase cascade (Citri and Yarden 2006), and the PI3K-AKT pathway, which results in the activation of the downstream protein-serine/threonine kinase AKT. In choosing the scope of a network, it is important to include one or more species that serve as indicators of the oncogenic potential of the system. Here, we include both AKT and ERK because they are well-studied indicators of EGFR-mediated growth and survival behaviors (Citri and Yarden 2006).

Figure 2.

Network model of EGFR-mediated signaling used in this study. Phosphorylation of the EGFR dimer occurs at either Y1068, which can bind GAB-1 or Grb2, or at Y1173, which binds Shc. Activation of downstream proteins AKT and ERK were used as indicators of cell survival signaling. Multiscale modeling is achieved by calculating changes in dimerization, peptide binding affinity, and phosphorylation in structural mutants of the receptor.

The critical step in distinguishing wild-type and mutant signaling models is defining kinetic differences between the systems. Differences between the wild-type EGFR and L834R models are marked in Table 1 and include reactions affecting receptor dimerization, phosphorylation, and peptide binding. Rather than write each reaction equation separately, “reaction rules” (Hlavacek, Faeder et al. 2006) are used to define general types of interactions between functional domains among the species in the model. For example, the rate constant k₇ in Table 1 that describes the catalytic turnover of Y1068 phosphorylation is applied to all forms of the receptor that participate in this phosphorylation reaction (e.g., monomer, dimer, ATP-bound). In this way, rules-based modeling ensures efficient and accurate construction of ODE-based signaling models.

Table 1.

Reaction rules for two-site phosphorylation model of the EGF receptor. The 10 rules generate 328 species and 3324 half-reactions representing all possible molecular intermediates and reaction steps. For simplicity, reaction rules for adaptor protein binding, MAP kinase cascade, and ERK/AKT activation are not shown.

Event	Reaction Rule	Forward	Reverse
Ligand/receptor binding	egfr(l) + egf(r) ↔ egfr(l!1).egf(r!1)	k 1	k −1
Ligand-induced receptor dimerization	egfr(l!1,r) + egfr(l!2,r) ↔ egfr(l!1,r!3).egfr(l!2,r!3)	k 2 *	k −2
Spontaneous receptor dimerization	egfr(r) + egfr(r) ↔ egfr(r!1).egfr(r!1)	k 3 *	k −3 †
Receptor/ATP binding	egfr(r!+,k) + ATP(r) ↔ egfr(r!+,k!1).ATP(r!1)	k 4	k −4 †
Y1068 entering active site	egfr(y1068~u) ↔ egfr(y1068~b)	k 5	k −5 †
Y1173 entering active site	egfr(y1173~u) ↔ egfr(y1173~b)	k 6	k −6 †
Autophosphorylation of Y1068	egfr(r!1,y1068~b).ATP → egfr(r!1,y1068~p) + ATP	k 7 †
Autophosphorylation of Y1173	egfr(r!1,y1173~b).ATP → egfr(r!1,y1173~p) + ATP	k 8 †
Dephosphorylation of Y1068	egfr(y1068~p) + phos → egfr(y1068~u)	V 9	K 9
Dephosphorylation of Y1173	egfr(y1173~p) + phos → egfr(y1173~u)	V 10	K 10

^*Note that k₂ = k₃ because the on-rate of dimerization is diffusion limited

^†Rate constants k₋₃, k₋₄, k₋₅, k₋₆, k₇, and k₈ are each affected by mutation L858R

^!Denotes the site of association for two molecules. For example, egfr(l!1).egf(r!1) are bound through “l” and “r” sites on egfr and egf, respectively.

2.2 Providing Alternate Parameterization through Docking Simulations

Once the network has been defined and the mutant oncoproteins identified, molecular docking is used to predict ligand binding in the absence of a ligand-bound crystal structure and functional affinity data. Thus, docking simulations provide the missing parameters that characterize the mutant system. Automated docking tools such as AutoDock (Morris, Goodsell et al. 1998) in combination with more accurate approaches such as free energy perturbation may be used to predict how small molecules, such as substrates or drug candidates, bind to a receptor of known 3-dimensional structure. The binding free energy is calculated based on the intermolecular energy between protein and ligands and changes to the solvation environment. For the EGFR/L834R model, binding modes were determined for ATP as well the C-terminal peptides Y1068 and Y1173 to the catalytic site. A global conformational search was performed using a multiple conformation docking strategy, in which the protein flexibility is taken into account implicitly. Note that rules-based modeling (Section 1.2.1) facilitates the reuse of kinetic parameters calculating through docking simulations.

2.3 Resolving the Structure of Mutant Oncoproteins through Molecular Dynamics

In order to perform docking simulations it is necessary to acquire accurate structural information about the molecules involved. In the EGFR/L834R model, we model the receptor activation characteristics (whether active as a monomer or requires dimerization) of the EGFR receptor tyrosine kinase using molecular dynamics simulations. 10–30 ns trajectories of atomistic and explicitly solvated systems of wild-type and mutant EGFR kinase monomers and dimers are obtained and analyzed for specific stabilizing interactions such as hydrogen bonds and salt-bridges, hydrophobic interactions, and conformational changes.

3 Results

Modeling the EGFR at the network, molecular, and structural levels allows one to determine how point-mutations in the EGFR receptor can alter signaling characteristics leading to the onset of oncogenic transformations. The model was constructed in ‘top-down’ fashion, beginning with identical signaling networks that were differentiated by a defined set of mutant oncoproteins. We now examine the effects of these differences in reverse order, beginning with structural alterations in the tyrosine kinase domain and proceeding to observe how these perturbations affect both receptor kinetics and network behavior.

3.1 Activation of Wildtype EGFRTK and L834R Mutant RTK

Crystal structures of the EGFRTK suggest that the conformational switching from an inactive to an active conformation involves a rotation of the αC-helix and the shifting of the activation loop (A-loop) to make way for substrate peptide (harboring the tyrosine residue) and ATP binding. To assess the structural requirements for such a conformational shift, analyses of bond patterns and hydrophobic interactions were performed to identify specific interactions (H-bonds and salt-bridges) between residues of the αC-helix and those of the A-loop needed to reorganize the enzyme and allow conformational switching from inactive to active states. Most of the stabilizing interactions holding the kinase in the inactive conformation are influenced by the dimer-interface residues, supporting an allosteric activation mechanism proposed for the wild type (Zhang, Gureasko et al. 2006). Many of these interactions overlap with the residues associated with several clinically relevant mutations, including L834R. The R substitution of L at 834 destabilizes the specific (external H-bonds) interactions associated with A-loop and αC-helix in the inactive but not the active conformations. Thus, our analysis of stabilizing interactions presented in Figure 3a-b serves as a platform for unifying the effects of these mutations at a structural level. An important outcome of these simulations is the notion that the mutant receptor can be active (and thus mediate signaling) even as a monomer, i.e., in the absence of any growth factor binding. This establishes a small but crucial variation in network topology between the wildtype and the mutant systems.

Figure 3.

Structural, kinetic, and network analysis of the effect of L834R mutation in the EGFRTK. Visualization of the stabilizing residues external to A-loop and αC-helix (blue), dimer interface residues (red) and clinical mutations (green) of both the active (a) and inactive (b) EGFR tyrosine kinases. (c) Binding modes for ATP (cyan) and the optimal peptide sequence (yellow) in the EGFRTK domain. (d) Calculated ERK and AKT phosphorylation levels in units of nM (peak-levels over an 1800 s time course) under serum starved (EGF−) and serum cultured (EGF+) conditions for cell types with normal EGFR expression and EGFR overexpression. x- and y-axes represent log changes in the binding affinity (K_D) of the peptide relative to the wild-type.

3.2 Ligand and Substrate Binding Affinities for EGFRTK

The structural basis for the context-specific kinetics of the C-terminal tyrosine substrates is provided by our computational docking calculations (Liu, Purvis et al. 2007). Substrate peptides derived from tyrosine sites of the EGFR C-terminal tail — Y1068 (VPEYINQ) and Y1173 (NAEYLRV) — bound to the wild-type and the L834R mutant EGFR kinase revealed how the structure of the bound peptide–protein complex is altered at the catalytic site due to the arginine substitution of leucine in L834R (Figure 3c). By employing this method, we computed the binding affinities for wildtype and L834R mutant RTK binding to two peptide sequences consisting of Y1068 and Y1173. These calculations, reported in Table 1, are used to parameterize the reactions involving inhibitor binding and substrate phosphorylation in the systems model.

3.3 Differential Signaling through EGFRTK

To examine the effects of signaling through Y1068 and Y1173 on the downstream response, a series of 15 min simulations were performed for wild-type and mutants under different initial conditions (varying [EGF] and [EGFR]) and monitoring the resulting total phosphorylated ERK and AKT responses (Figure 3d). A 2-dimensional scan over K_D values associated with Y1068 and Y1173 phosphorylation in which the respective K_D values are allowed to deviate from their default (wildtype) value over a logarithmic range of 5 log units. This was achieved by adjusting k₋₅ and k₋₆ from Table 1. The result is a 2-dimensional matrix in which each element represents the total ERK or AKT levels from a single simulation involving a unique pair of parameters. In Figure 3d,e each output state is quantified according to the peak level of phosphorylation over the simulated time of 1800 s.

As indicated by the color maps in these scans, the effect of altered affinities of the Y1068 and Y1173 sites to the catalytic domain of the EGFR is that the L834R under normal EGFR expression exhibits differential downstream response, i.e., a pronounced decrease in ERK activation (5-fold) and relatively much smaller decrease AKT activation (15% decrease). Our calculated responses for ERK short-term signaling for normal EGFR expression (Figure 3d,e) agree with the experimental observations of Sordella et al. (Sordella, Bell et al. 2004) and Tracy et al. (Tracy, Mukohara et al. 2004), who have also reported a pronounced decrease in activated ERK to AKT ratio for the L834R mutant. These results suggest that preferential activation of AKT in L834R could be one of the factors leading to enhanced AKT activation observed in non-small-cell lung cancer cell lines.

4. Discussion

While the genetic basis of cancer is well appreciated, the resulting complexity in intracellular signaling mechanisms relevant for the conquest of this disease resides at multiple levels of organization, ranging from the subatomic realm involving mutations in individual protein domains to the cellular level of macromolecular assemblies and membrane processes. Relating cancer genotypes to disease phenotypes will be aided by the development of specialized modeling tools to treat the hierarchy of interactions ranging from molecular (nm, ns) to signaling (μm, ms) length and time scales. By introducing increased resolution in phosphorylation kinetics at the receptor level, the network model of EGFR-mediated signaling in wildtype and mutant cells showed how mutant forms of the receptor use an irregular pattern of tyrosine phosphorylation that preferentially activates the survival oncoprotein, AKT.

Recently, this type of multiscale analysis was used to explain why certain networks respond to anti-tumor tyrosine kinase inhibitors (TKIs) such as erlotinib and gefitinib (Purvis, Ilango et al. 2008; Shih, Purvis et al. 2008). Specifically, the branched signaling model was employed to analyze the inhibitory effects of the TKI erlotinib on EGFR phosphorylation and downstream ERK and Akt activation. The results provided a mechanistic basis for the enhanced inhibitor efficacy in mutant cell lines.

Thus, collectively, our results suggest that the clinically identified mutations of the EGFR kinase induce fragility in the stabilizing interactions of the inactive kinase conformation, providing a persistent stimulus for kinase activation even in the absence of any growth factor. At a cellular level, perturbations driving network hypersensitivity through the enhancement of phosphorylated ERK and AKT levels show a striking correlation with observed mutations of specific proteins in oncogenic cell lines as well as the observed mechanisms of drug resistance to EGFR inhibition. Therefore, we suggest that cascading mechanisms of network hypersensitivity/fragility at multiple scales enable molecular-level perturbations (clinical mutations) to induce oncogenic signaling. Moreover, our results describe a possible mechanism for preferential AKT activation in non-small-cell lung cancer lines harboring EGFR activating mutations. This preferential activation of a survival factor makes theses cell-lines conducive to pathway addiction, i.e. reliance on the L834R EGFR-mediated generation phosphorylated AKT for survival signals. The survival pathway addiction also results in a remarkable sensitivity to TKIs targeting the EGFR kinase.

The computational tools described here are ideal for assessing the likely effect of novel EGFR and HER2 mutations and determining whether the drug-sensitizing mutations implicated in non-small-cell lung cancer also occur in other cancers. Such approaches can also be employed effectively to address the issue of drug resistance to TKI therapy, which in the case of non-small-cell lung cancers is either mediated by point mutations in EGFR kinase (T790M) or the over-expression of HER3 and Met receptors and to investigate other molecular therapeutics targeting for e.g., VEGF and c-Met. Ultimately, these approaches could be used to optimize the development of small molecule inhibitor therapies.

The multiscale modeling approach illustrated in this chapter enables the incorporation of the molecular context and variability and their impact on intracellular signaling pathways of oncogenic relevance and subsequent cell-fate decisions. This approach also enables the rationalization and prediction of the role and nature of molecular variability in malignant transformed cells as well as drug-sensitive/drug-resistant cells by bridging the gap between molecular resolution/context and intracellular signaling. The approach employed here can be seamlessly integrated with sub-cellular resolution modeling in agent-based models emphasized in other chapters (see Wang et al. in this book).