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We modeled the kinetics of drug binding to protein kinases in the EGF signaling pathway relevant to non-small cell lung cancer and found that binding kinetics could influence therapeutic potential, that fast binding kinetics was advantageous for most targets with a couple of exceptions, that targeting some protein kinases could enhance rather than attenuate the pathway, and that IC50 could be sensitive to the kinetic parameters of drug binding.
Computer-aided drug design has mostly focused on considering binding strength or thermodynamics rather than kinetics. Yet, there is already evidence that drug binding kinetics can also play a role. In a recent paper, Tummino and Copeland proposed that the residence time, rather than the binding affinity, determined the therapeutic potential of drug candidates.1 They defined the residence time to be the inverse of koff.
One study supporting this proposal concerned the design of peptide mimics to bind to the extracellular domain of the receptor tyrosine kinase Human Epidermal growth factor Receptor 2 (HER2), a protein kinase in the same family as Epidermal Growth Factor Receptor (EGFR).2 In this work, the authors found that the desired cellular interference correlated better with the dissociation constant than with the binding affinity of the peptide mimics. Another example came from studies correlating the response of T cells with the types of MHC/peptide complexes with which they interacted. Whether the presented peptide by MHC was an agonist, partial agonist, antagonist, or one that did not trigger any T-cell response appeared to correlate with the duration of interaction between a T cell and an MHC/peptide complex.3-8
On the other hand, some studies found that kon, rather than koff, associated better with therapeutic potential. For example, Wu et al showed that kon of engineered antibodies linked better with the ability of the antibodies to neutralize the respiratory syncytial virus.9
To gain further insights into the role of drug-binding kinetics in drug discovery, we performed kinetic modeling on the Epidermal Growth Factor (EGF) signaling pathway, which is overly active in non-small cell lung cancer, for example. Modeling has the advantage that it can study theoretical compounds that may be difficult to make experimentally to help test a concept of drug design. For example, it is not easy to synthesize compounds with exactly the same binding affinity but different rate constants of drug-receptor association and dissociation to examine whether kinetics, in addition to thermodynamics, can be an important factor to consider in drug discovery. However, one can do this easily with a kinetic model.
In kinetic modeling, it is also useful to examine a larger pathway instead of only analyzing the impact of a drug candidate on its direct target. In this work, we studied the effects of applying theoretical drugs to different protein kinases in the EGF signaling pathway constructed previously by Wang et al.10 We modified their pathway only slightly to include drug interactions. Fig.1 shows an example in which a drug is applied to the EGF-EGFR dimer denoted by (EGF:EGFR)2.
In order to study whether drug-binding kinetics could attenuate the production of the doubly phosphorylated form of MAP kinase (ERK-PP depicted in Fig. 1) differently, we prepared theoretical drugs with exactly the same binding affinity (KI) to its protein kinase target but with different kinetic constants of binding (ka) and unbinding (kd) such that KI=kd/ka remained constant. If these drugs with exactly the same binding affinity Ki affected the activity of ERK-PP differently, one could conclude that binding kinetics indeed played a role in drug design. (We monitored the concentration of ERK-PP because its level of activity is believed to control cell proliferation.)
We performed kinetics modeling by using Copasi 4.5 (build 30).11 The model consisted of twenty-two molecules and involved solving twenty-two coupled differential equations. We used the same rate laws, kinetic constants and initial concentrations as in Wang et al’s work,10 except when we modeled an over-activated EGF-EGFR dimer or when we mimicked an over-expression of EGFR. On the other hand, because our model introduced drug binding, we modified one kinetic equation accordingly and added one equation for drug binding (step R3 in Fig. 1). The equations and parameters of the kinetic model are reported in Tables S1 and S2 of Supplementary Materials.
Fig. 2 gives an example of the time course of the concentration of ERK-PP. The concentration rose to a maximum before decaying to zero. In this study, we monitored the change in the maximum concentration when different theoretical drugs were applied in order to calculate percent inhibition of ERK-PP, which was obtained by using the maximum concentration of ERK-PP before and after a drug was applied.
Table I shows that binding kinetics did affect ERK-PP production when we applied theoretical drugs with different kinetic, but same thermodynamic, parameters to the EGF-EGFR dimer. When we used a drug concentration of 1 nM (equaled to KI), there was no inhibition. But as we increased the concentration to 100 nM, appreciable inhibition appeared and the degree of inhibition depended on binding kinetics. Percent inhibition was low at slow binding kinetics but approached a maximum value with faster binding kinetics (note that as we increased the dissociation constant kd, the association constant increased accordingly so as to keep KI constant.) The last column in Table I gives the results for a truncated pathway in which only steps R1 to R5 in Fig. 1 were included. The purpose of this computational experiment was to examine whether a simpler assay could predict the behavior of a more complex assay including more downstream steps. We found that this truncated pathway gave similar results as the larger pathway in Fig. 1. The percent inhibition was nearly the same for the full and truncated pathways. (For the truncated pathway, we monitored the concentration of (EGF:EGFR)-P in Fig. 1 instead of ERK-PP.)
Fig. 3 shows similar qualitative dependence of percent inhibition on kd when we decreased the binding affinity (KI) of the drug to the EGF-EGFR dimer by a factor of ten, when we decreased the concentration of EGFR to 1 nM, when we increased the concentration of EGFR by a factor of ten to mimick an over-expression of the protein, and when we increased the rate constant of the phosphorylation of the EGF-EGFR dimer by twenty times to mimick an over-activated protein resulting from a diseased mutation, for example. (In this last case, we used a higher-affinity drug, with KI = 0.1 nM, in order to obtain observable percent inhibition.)
Although applying drugs to most protein kinases in this pathway gave similar qualitative dependence of percent inhibition on kd as those shown in Fig. 3, there were exceptions. For example, when we applied a drug to the activated form of Raf – denoted by Raf* in Fig. 1 - we observed that the percent inhibition peaked at an intermediate kd approximately around 1 × 10-3 s-1 and decreased afterwards, instead of increasing monotonously with kd to an asymptotic value as the cases illustrated in Fig. 3. (Fig. 4) On the other hand, applying drug to the un-activated form of Raf showed the common behavior discussed earlier. The larger percent inhibition observed for the un-activated form of Raf also suggested that targeting the un-activated form of Raf might be more effective in attenuating ERK-PP production than targeting the activated form, according to this kinetic model.
Fig. 5 shows yet another behavior when we applied drugs to the three different forms of MAP kinase kinase. Applying a drug to the un-phosphorylated form, MEK, increased the production of ERK-PP rather than attenuating it. On the other hand, applying drugs to either the mono- or doubly-phosphorylated forms of MEK both reduced ERK-PP production.
Using the singly phosphorylated form of MAP kinase kinase, MEK-P, as an example, Fig. 6 shows that IC50 obtained from a kinetic assay could depend on the kinetic constants of drug binding. The IC50 varied by about a factor of four for the range of kd covered in the figure. Computational drug designers need to be aware of this as they often compare computed binding affinity – a thermodynamic rather than a kinetic quantity - with experimental ln(IC50).
In summary, our kinetic modeling of drug interference with protein kinases in the EGF signaling pathway showed that drug-binding kinetics could play a role in attenuating this pathway. Thus, tuning the kinetic parameters of drug binding can also be important in drug discovery. Although fast-binding kinetics seemed to be favored for most protein kinase targets in this pathway, there were exceptions. In the case of activated Raf, drug with intermediate kinetic constants appeared best. On the other hand, we found that applying a drug to a protein kinase such as the unphosphorylated form of MEK could activate rather than attenuate signaling. In addition, we found that IC50 could depend on drug binding kinetics when measured by kinetic assays. Although the reliability of our predictions on EGF signaling depends on how well this kinetic model reflects reality, the principles that drug-binding kinetics can play a role in drug discovery should be general. As kinetic models are continually being refined to fit experimental observations for specific pathways and networks, these models can play an important role in guiding drug discovery.
This research is supported in part by the National Institutes of Health.