Linking biochemical and cellular efficacy of MERS coronavirus main protease inhibitors

This study demonstrates that while multiple data analysis methods can correlate biochemical inhibition with antiviral activity for MERS-CoV main protease inhibitors, an enzyme kinetics model accounting for dimerization and biphasic concentration-response curves provides the most accurate prediction of cellular efficacy.

The Gist

The Big Picture: A Viral Lock and a Broken Key

Imagine the MERS Coronavirus as a burglar trying to break into a house (your body). To get inside and steal the furniture (replicate itself), the burglar needs a specific tool: a Main Protease (MPro). Think of MPro as the "master key" or a specialized pair of scissors that cuts the virus's raw materials into usable parts so the virus can build copies of itself.

If we can jam that scissors or break the key, the virus stops growing. Scientists are trying to find the perfect "jam" (a drug) to stop MERS.

The Problem: The "Goldilocks" Curve

Usually, when scientists test a drug, they expect a simple result: More drug = Less virus. It's like turning up the volume on a radio; the more you turn it, the louder it gets.

But with MERS, the "radio" is broken. When they tested these drugs, they got a weird, biphasic curve (a two-phase reaction):

1. Low doses: The drug actually helped the virus scissors work better. (The burglar found a better tool!)
2. High doses: The drug finally stopped the scissors. (The burglar was arrested.)

This is confusing. It's like a car that speeds up when you press the gas pedal lightly, but only stops when you slam on the brakes hard. This "activation-then-inhibition" behavior made it very hard for scientists to figure out which drugs were actually good candidates for a medicine.

The Solution: Three Ways to Read the Map

The researchers in this paper asked: "How do we analyze this weird data to find the best drugs?" They tried three different methods to interpret the results:

1. The "Ignore the Start" Method: They looked only at the high doses where the drug worked (the braking phase) and ignored the weird speeding-up part.
2. The "Control" Method: They assumed the drug shouldn't speed up the virus and tried to fit the data to a standard model, ignoring the fact that the virus actually got faster at low doses.
3. The "Full Physics" Method (The Winner): They built a complex computer model that understood the whole story. They realized that the MERS scissors are actually made of two halves (a dimer).
   • At low drug levels, the drug acts like glue, sticking the two halves together, making the scissors work super fast.
   • At high drug levels, the drug covers the cutting blades, jamming the scissors completely.

This third method didn't ignore any data; it explained why the curve looked weird.

The "Cellular" Reality Check

Here is the tricky part: What works in a test tube (biochemical assay) doesn't always work in a living cell.

• Test Tube: The virus scissors are floating in a pool of water.
• Living Cell: The scissors are crowded in a busy factory, surrounded by walls and guards (cell membranes).

The researchers wanted to know: Which of our three math methods best predicts which drugs will actually kill the virus inside a living cell?

They compared their math predictions against real-life tests where they infected cells with the virus and saw which drugs stopped the infection.

The Results: Why the "Full Physics" Model Won

The study found that while all three methods gave somewhat similar results, the "Full Physics" method (Method #3) was the best predictor.

• The Analogy: Imagine you are trying to guess how fast a car will go on a race track.
  • Method 1 and 2 are like guessing based on the car's top speed on a straight road.
  • Method 3 is like building a simulation that accounts for the engine, the tires, the wind, and the driver's skill.
  • When they tested the drugs in "living cells" (the race track), the drugs that Method 3 predicted would work were the ones that actually worked.

Specifically, they found that calculating the drug's power at high concentrations (simulating the crowded environment of a real cell) was the most accurate way to rank the drugs.

The Takeaway

1. MERS is tricky: Its main enzyme behaves strangely, getting stronger before it gets weaker when exposed to drugs.
2. Don't ignore the weirdness: If you ignore the "activation" part of the curve, you lose valuable information.
3. Complex models win: By using a sophisticated computer model that understands how the enzyme pieces fit together (dimerization), scientists can better predict which drugs will actually cure a patient, not just work in a test tube.

In short: The researchers built a better "decoder ring" for confusing drug data. This new tool helps them pick the best candidates to fight MERS, saving time and money by avoiding drugs that look good on paper but fail in real life.

Technical Summary

1. Problem Statement

The Middle East Respiratory Syndrome Coronavirus (MERS-CoV) poses a significant global health threat with no approved vaccines or antiviral treatments. A primary target for drug discovery is the MERS-CoV Main Protease ($M^{pro}$), which is essential for viral replication. However, biochemical assays for $M^{pro}$ inhibitors often produce biphasic concentration-response curves (CRCs) rather than standard sigmoidal inhibition curves.

• The Phenomenon: At low inhibitor concentrations, the enzyme activity increases (activation); at high concentrations, it decreases (inhibition).
• The Cause: $M^{pro}$ functions as a dimer but has a relatively weak dissociation constant ($K_d \approx 52 \mu M$), meaning a significant fraction exists as inactive monomers at typical assay concentrations. Ligand binding can induce dimerization, stabilizing the active conformation and increasing activity at low concentrations. At high concentrations, both monomers in the dimer become occupied by the inhibitor, blocking catalysis.
• The Challenge: Traditional four-parameter Hill equations cannot fit these biphasic curves, making it difficult to extract meaningful inhibitory constants ($IC_{50}$) that correlate with cellular efficacy. Current methods often ignore the activation phase, potentially leading to inaccurate predictions of drug potency.

2. Methodology

The authors employed a multi-step Bayesian statistical approach to analyze biochemical and cellular data from a drug discovery campaign (ASAP Consortium).

A. Data Collection

• Biochemical Assays: Fluorescence-based dose-response curves were measured for 85+ inhibitors under various conditions:
  • ES Datasets: Enzyme-substrate kinetics (varying substrate, fixed enzyme).
  • ESI Datasets: Enzyme-substrate-inhibitor kinetics (varying inhibitor, fixed enzyme/substrate).
• Cellular Assays: Live-virus antiviral screening using Vero-TMPRSS2 cells infected with MERS-CoV to determine cellular $EC_{50}$ values.

B. Modeling Approach
Instead of ignoring the activation phase, the authors fitted a mechanistic enzyme kinetics model that explicitly incorporates:

1. Dimerization: Equilibrium between monomer ($M$) and dimer ($D$).
2. Ligand Binding: Binding of substrate ($S$) and inhibitor ($I$) to monomers and dimers.
3. Catalysis: Turnover rates ($k_{cat}$) for various complexes (e.g., $M-S$, $D-S$, $D-S-I$).

C. Bayesian Inference Strategy
Due to computational complexity, the authors used a stepwise Bayesian regression approach:

1. Step 1: Fit a simplified model (no inhibitor) to ES data to constrain global thermodynamic parameters ($\Delta G_d$, $\Delta G_S$).
2. Step 2-4: Incrementally add inhibitor data (ESI4c, then ESI1c) to refine parameters. Global parameters (dimerization energy, substrate binding) were shared across datasets, while inhibitor-specific parameters were sampled locally.
3. Sampling: Used the No-U-Turn Sampler (NUTS) to sample from posterior distributions, ensuring convergence of parameters like binding free energies ($\Delta G$) and rate constants ($k_{cat}$).

D. Three Analysis Procedures for Comparison
To evaluate efficacy, the authors compared three methods for deriving inhibitory constants:

1. Inhibition pIC$_{50}$: Fitting a Hill equation only to the inhibition phase (ignoring activation).
2. Control pIC$_{50}$: Fitting a Hill equation to the inhibition phase with the top response fixed to the negative control (assuming no ligand-induced dimerization).
3. Dimer pIC$_{50}$: Using the full mechanistic model to simulate CRCs at high enzyme concentrations (mimicking cellular conditions where enzyme is abundant and fully dimerized) and fitting a Hill equation to the resulting curve.

3. Key Contributions

• Mechanistic Model Validation: Demonstrated that a complex enzyme kinetics model incorporating dimerization and ligand binding can be precisely fitted to large datasets of biphasic CRCs using Bayesian inference.
• Parameter Quantification: Successfully quantified thermodynamic and kinetic parameters, including substrate-induced dimerization and ligand binding cooperativity, which were previously difficult to resolve.
• Predictive Protocol: Established a protocol to extrapolate biochemical data to cellular conditions by simulating high enzyme concentrations, yielding the "dimer pIC$_{50}$."
• Open Science: Made all code and data freely available, integrating the workflow into an automated pipeline for the ASAP drug discovery consortium.

4. Key Results

• Model Convergence: The Bayesian posterior distributions for binding free energies and rate constant ratios converged with sufficient data. The model confirmed positive cooperativity for substrate binding to the dimer and positive cooperativity for inhibitor binding for most compounds.
• Substrate-Induced Dimerization: The model predicted strong substrate-induced dimerization under assay conditions, with an apparent dimerization free energy ($\Delta G_{d,app}$) of $\approx -10$ kcal/mol, significantly stronger than the intrinsic dimerization energy ($\approx -5.9$ kcal/mol).
• Correlation with Cellular Efficacy:
  • All three biochemical procedures showed correlation with cellular $pEC_{50}$, but the Dimer pIC$_{50}$ (derived from the mechanistic model) showed the highest rank correlation (Spearman $\rho$ and Kendall $\tau$) with cellular efficacy.
  • While Pearson $R$ values were similar across methods, the rank-order metrics (crucial for drug prioritization) favored the dimer model.
• IC$_{90}$ Superiority: The study found that pIC$_{90}$ (concentration for 90% inhibition) derived from the dimer model was an even better predictor of cellular pEC$_{90}$ than pIC$_{50}$ was for pEC$_{50}$. This suggests that high levels of inhibition are required for cellular efficacy, a nuance captured better by the mechanistic model.
• Comparison with SARS-CoV-2: The study highlighted distinct kinetic differences between MERS-CoV and SARS-CoV-2 $M^{pro}$, particularly regarding dimerization affinity and substrate binding cooperativity.

5. Significance

• Improved Drug Discovery: The study provides a robust framework for interpreting biphasic CRCs, which are common in dimeric enzymes. By using the mechanistic model to predict cellular efficacy, researchers can more accurately prioritize drug leads, reducing the failure rate in expensive cellular and animal studies.
• Methodological Advancement: The work demonstrates that complex, multi-parameter enzyme kinetics models can be solved globally for large datasets, moving beyond simple empirical fitting (Hill equations) to mechanistic understanding.
• Broad Applicability: The approach is not limited to MERS-CoV. The authors note that biphasic curves and ligand-induced dimerization occur in other serine and cysteine proteases (e.g., caspase-1), suggesting this methodology is widely applicable to antiviral and oncology drug discovery.
• Resource Availability: By releasing the code and integrating it into the CDD Vault, the authors enable the broader scientific community to apply these rigorous statistical methods to their own enzyme inhibition data.

In conclusion, this paper resolves the ambiguity of biphasic inhibition curves in MERS-CoV $M^{pro}$ by combining mechanistic modeling with Bayesian statistics, proving that extrapolating biochemical data to cellular conditions via a dimer-focused model yields the most accurate prediction of antiviral efficacy.