Why kinase binding is dynamic

By Connor Bybee, Research Scientist

A kinase switching from inactive to active

The landscape behind Movie 1

View tICADFG distances (KinCore)Distance to end states Switches with each loop of Movie 1. Click to choose.

• MSM state, DFG-out
• MSM state, DFG-inter
• MSM state, DFG-in
• Transition path
• Current frame of Movie 1

DFG-out · committor 0.00

Protein kinases are therapeutic targets whose conformations change dynamically. Kinase binding depends on how the kinase changes shape, how long binding takes, and whether the inhibitor forms a covalent bond. All three affect how results are interpreted and how assays and designs are planned, and a single measured affinity value cannot tell them apart. Movie 1 and Fig. 1 illustrate a kinase transitioning between inactive and active conformations via intermediate states.

Binding is a property of ensembles

Binding affinity is a property of conformational ensembles. A ligand can select and stabilize conformations that the protein already visits, including rare ones¹, and the binding free energy integrates over all bound and unbound states². In protein kinases, the activation loop and the DFG motif influence which binding modes are open^3,4. Movie 2 shows two type I inhibitors, which bind a DFG-in kinase, and two type II inhibitors, which bind a DFG-out kinase, each in a molecular-dynamics simulation.

Kinase–inhibitor complexes in motion

Measured affinity includes the cost of reshaping the kinase

A type II inhibitor’s measured binding free energy includes both the binding free energy for a compatible kinase conformation and the free energy of reorganizing the kinase into it⁴. When only one state contributes to binding, we can write

$$\Delta G_\mathrm{exp} = \Delta G_{\mathrm{bind},s} + \Delta G_{\mathrm{reorg},s}$$

Here, $\Delta G_{\mathrm{bind},s}$ is the standard binding free energy for the inhibitor binding to state $s$, such as a DFG-out conformation. The reorganization term depends on how populated state $s$ is in the unbound kinase’s equilibrium ensemble. If its probability is $p_s$, then

$$\Delta G_{\mathrm{reorg},s} = -RT \ln p_s$$

A rare binding-compatible state pays a larger population penalty than a common one. Combining the two terms gives the following for a single binding state.

$$\begin{aligned} \Delta G_\mathrm{exp} &= -RT \ln\left[p_s\, e^{-\Delta G_{\mathrm{bind},s}/RT}\right] \\ &= \Delta G_{\mathrm{bind},s} - RT \ln p_s \\ &= \Delta G_{\mathrm{bind},s} + \Delta G_{\mathrm{reorg},s} \end{aligned}$$

Two kinases can therefore bind the same inhibitor equally well within a compatible state yet differ a hundredfold in overall equilibrium affinity if that state’s unbound population differs a hundredfold.

When several states can bind, their contributions add inside the same logarithm.

$$\Delta G_\mathrm{exp} = -RT \ln \sum_s p_s\, e^{-\Delta G_{\mathrm{bind},s}/RT}$$

This equation includes both the unbound populations $p_s$ and the state-specific binding strengths $\Delta G_{\mathrm{bind},s}$. It assumes a partition into distinct unbound states, equilibrium binding, and a common standard state for all binding free energies (here, 1 M).

In a public panel on ABL1, paired measurements favor the non-phosphorylated kinase, so phosphorylation may shift the conformational balance⁴. Protonation states also change the balance of kinase active and inactive states^6,7.

Sampling kinase dynamics with adaptive simulations

Conformational changes such as the DFG flip happen on microsecond-to-millisecond timescales, longer than one unbiased simulation can affordably cover. Binding-compatible states may be rare, and kinetic barriers can keep a simulation from reaching them. Estimating a state’s free energy needs many samples that cover the whole ensemble, so sampling has to be efficient. Adaptive Markov state models (MSMs) are one efficient approach. Instead of running one long trajectory, adaptive MSMs run many short simulations in parallel⁸. After each round, the trajectories are described by the positions of the DFG motif, the αC helix, and the activation loop. These values are reduced to their slowest-changing combinations by time-lagged independent component analysis (tICA), clustered into states, and assembled into an MSM. The next round then restarts from the states visited least, so effort goes to the parts of the landscape that are still unexplored. This approach has mapped the activation pathway of Src kinase and proposed its intermediate states as drug targets⁹.

The transition in Movie 1 and the landscape in Fig. 1 come from our simulations run this way, using constant-pH molecular dynamics so that the protonation state of the DFG aspartate, which is coupled to the flip⁶, changes with the conditions and the conformation¹⁰. The landscape shows more than one transition path between states. In the tICA view of Fig. 1, the trajectory in Movie 1 crosses the middle of the landscape through DFG-in and intermediate states, while a second path is not visited by that trajectory.

Binding takes time, so assay timing matters

Affinity does not depend on time. A Kd, or a Ki measured at equilibrium, is an intrinsic property of a compound and its target at fixed conditions. An IC₅₀ is an assay readout. It depends on substrate concentration, incubation time, and the mechanism of inhibition, and it reflects the equilibrium value only once the assay has reached equilibrium. In a simple reversible two-state model, association and dissociation have rate constants $k_\mathrm{on}$ and $k_\mathrm{off}$, with Kd = $k_\mathrm{off}/k_\mathrm{on}$. Two compounds with the same Kd can stay bound for very different lengths of time. The residence time, $1/k_\mathrm{off}$, can track how long a drug works in the body better than its affinity does^11,12.

Type II kinase inhibitors stabilize DFG-out conformations, and imatinib binds c-Src by both conformational selection and induced fit¹³. Some type II inhibitors bind slowly. BIRB-796 binds p38 MAP kinase with slow association and slow dissociation^14,15. A type II VEGFR2 (KDR) inhibitor leaves the non-phosphorylated enzyme with a half-life longer than four hours¹⁶. For slow binders like these, an assay read before equilibrium distorts the IC₅₀. Given enough time the IC₅₀ converges to its equilibrium value, but assays read at different times can give different IC₅₀ values for the same compound.

In our enzymatic assays, we measured each compound’s IC₅₀ after both 20 and 240 minutes of enzyme–inhibitor pre-incubation. Fig. 2 shows one example from each binding class. The type I example shifted 1.1×, the type II example 5.7×, and the covalent example 6.0×. A compound that binds and releases quickly gives the same IC₅₀ either way. A compound that binds more slowly looks more potent after the longer pre-incubation. Covalent compounds can also show a time-dependent shift in IC₅₀.

IC₅₀ shift with longer pre-incubation, by binding class

• Example compound, IC₅₀ measured at both times

Benchmarks inherit this problem. Public affinity datasets often record a single IC₅₀, Ki, or Kd, without the incubation time or any rate constants, and affinity-prediction models typically predict a single equilibrium number. Unbinding simulations are one way to recover $k_\mathrm{off}$. Repeated exit simulations of eight p38α inhibitors gave relative residence times that tracked the measured kinetics¹⁷, and metadynamics has estimated the off-rate of a p38 type II inhibitor to within a factor of ten¹⁸. Movie 3 shows four steered unbinding simulations.

Inhibitors leaving the kinase pocket

Covalent inhibitor potency is a rate

Many targeted covalent inhibitors act in two steps. The inhibitor first forms a reversible complex, with dissociation constant Kd. The $K_\mathrm{I}$ in the equations below is an effective kinetic parameter, $K_\mathrm{I} = (k_\mathrm{off} + k_\mathrm{inact})/k_\mathrm{on}$; it approximates Kd only when bond formation is slow compared with dissociation of the reversible complex. In the second step, the inhibitor’s reactive group forms a bond with a nearby residue, usually a cysteine, with a first-order rate constant $k_\mathrm{inact}$:

$$\mathrm{E} + \mathrm{I} \;\rightleftharpoons\; \mathrm{E{\cdot}I} \;\rightarrow\; \mathrm{E{-}I}$$

At inhibitor concentration $[\mathrm{I}]$, active enzyme disappears at the rate

$$k_\mathrm{obs} = \frac{k_\mathrm{inact}[\mathrm{I}]}{K_\mathrm{I} + [\mathrm{I}]}$$

and, in this approximation, after a pre-incubation of length $t$ a fraction $e^{-k_\mathrm{obs}t}$ of the enzyme remains unmodified. Some unmodified enzyme may still be reversibly inhibited. Well below saturation, $k_\mathrm{obs} \approx (k_\mathrm{inact}/K_\mathrm{I})[\mathrm{I}]$. That makes the second-order constant $k_\mathrm{inact}/K_\mathrm{I}$ the standard measure of covalent potency¹⁹.

Because irreversible inactivation accumulates, measured IC₅₀ depends on time. In practice the IC₅₀ eventually levels off near the enzyme concentration in the assay¹⁹. This is consistent with the shift seen for the covalent example in Fig. 2, and it is why a single IC₅₀ measured at one time point cannot give the rate constants. Movie 4 shows a covalent inhibitor’s reactive group approaching a target cysteine residue until the bond forms.

A covalent kinase inhibitor reaching its cysteine

This has two consequences for design.

• Two parameters. $K_\mathrm{I}$ comes from reversible recognition, and $k_\mathrm{inact}$ from the warhead’s reactivity and its position relative to the nucleophile. Potency is their ratio, so a weakly reactive warhead can still give a potent drug if the reversible complex is tight. In a study of investigational covalent EGFR inhibitors, high reversible affinity (below 1 nM) compensated for low reactivity²⁰. Low reactivity also limits off-target reactions, which leaves more of the selectivity to the reversible step.
• Scoring needs the reaction. An affinity model that predicts an equilibrium number addresses reversible recognition, rather than the full kinetic parameter $K_\mathrm{I}$ or the reaction rate. Scoring a covalent design also needs the geometry that places the warhead next to the nucleophile, and the reactivity that sets $k_\mathrm{inact}$.

What this means for affinity models

A single measured affinity combines three things. These are how tightly a ligand binds a given conformation, how often the kinase adopts that conformation, and, for slow and covalent binders, how long binding takes and whether a bond forms. A model that predicts one equilibrium number cannot recover residence time or $k_\mathrm{inact}$, and affinity data measured at one incubation time include kinetic effects that such a model cannot represent. Residence time and the reaction rate need other tools, such as the unbinding simulations above for $k_\mathrm{off}$ and models of the reaction for covalent inhibitors.

For drug design, this means the same measured potency can come from different mechanisms, with different selectivity and duration of action. Ensembles can show which conformations a design can exploit, including intermediates that end-state structures miss. Kinetic and covalent measurements show how long and how irreversibly a compound acts. For this reason, a single affinity value should be read together with the conformational ensemble, the incubation time, and the reaction rate.

Contributions

• Conceptualization. Connor Bybee, Benjamin Rousseau, Robert A. Galemmo, and Fernando Martinez.
• Data curation. Connor Bybee and Jiaqi Zhu.
• Formal analysis. Connor Bybee and Benjamin Rousseau.
• Investigation. Connor Bybee, Jiaqi Zhu, Xiaotong Lu, Patrick Visperas, Benjamin Rousseau, and Malhar Kute.
• Methodology. Connor Bybee, Xiaotong Lu, Patrick Visperas, Benjamin Rousseau, and Anthony M. Giannetti.
• Project administration. Connor Bybee and Benjamin Rousseau.
• Resources. Connor Bybee and Jiaqi Zhu.
• Software. Connor Bybee, Benjamin Rousseau, Andre Graubner, Tomas Salgado, and Scott Leishman.
• Validation. Benjamin Rousseau.
• Visualization. Connor Bybee and Jiaqi Zhu.
• Writing – original draft. Connor Bybee.
• Writing – review & editing. Jiaqi Zhu, Robert A. Galemmo, Anne Pipathsouk, and Anthony M. Giannetti.

References

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