Paper 2: Energy pentalties improve flexible receptor docking in model cavity

Problem and solution

• problem

Protein flexibility is a problem for library docking because it’s difficult to sample all relevant conformations with accurate probabilities

• Solution

Incorporate protein flexibility through through thermodynamic weighting from MD simulation

• MD allows sampling of many different conformations and estimate their weighting

• Without weights

  • High energy conformations dominate docking results because of their better ligand complementarity

  • not realistic because they’re harder to access

Challenges of MD Simulations

1. Weighting states by their relative energies

2. Insufficient sampling

   1. Free energy minima are often separated by large energy barriers that are rarely overcome on the timescale of conventional MD (cMD)

   2. aMD = accelerated MD
      introduces a bias potential that lowers the energybarrier between conformations allowing more diverse sampling including high energy states

      1. However it’s approximations and assumptions might prevent it from accurately weighting conformations

Workflow

Use the cavity of T4 lysozome L99A

The cavity undergoes a conformational changes as larger ligands bind and has 3 states:

1. closed

2. intermediate

3. open

Approach

1. define conformations of the apo and holo state form crystal structures

2. Sample the apo protein with MD

3. estimate the population of each state using the Markov state model (MSM)

4. These populations are converted into a conformational engery penalty (E_p) which is incorporated into the flexible docking scoreEp=-m\cdot kb\cdot T\ln p

   1. But the energyscale of the docking program does not perfectly match physical energies

   2. So E_p must be tuned for each system studied using a weighting multiplier (m)

Retrospective Testing

• Test if weights work by applying them on known ligands

Prospective Screening

• use the weights to predict how new chemotypes prefer to bind to each conformation

Thermodynamic weighting from apo MD simulations

To estimate the populations of the different states in the apo ensemble

• aMD: allows protein to explore rare conformations more easily

• cMD: regular unbiased MD, run for a longer time to capture enough transitions

The MD’s

• aMD (500ns)

  • efficiently samples rare conformational states of the apo protein and provides initial, reweighted estimates of their populations

  • In apo: 98% closed, 1.5% intermediate, 0.5% open

• cMD (7.75 µs)

  • used to accurately determine the thermodynamic weight of these conformational states and kinetcis by building a MSM

  • From cMD build the Markov State Model to estimate how often each state occurs (Thermodynamics) and how fast the transitions are between states (kinetics)

  • Thermodynamics
    Four states: S1+S2 (0.2%) = open, S3 (1.1%) = intermediate, S4(98.8%)= closed

  • Kinetics
    Transitions between closed and intermediate are fast
    Transitions from Intermediate or closed to open are slow

These probabilities are later used as weights in the flexible docking scoring fucntions so docking does not overfavor unlikely conformations

Retropesctive testing

= to test if the weights improve flexible receptor docking, they docked known ligands and measured how well docking scores enriched known ligands over property matched decoys

Decoys are chosen to match the ligands in basic properties but ar not known to bind. They are used to see if the method can rank true ligands higher than decoys)

Approaches:

1. Standard docking
   = docking each receptor conformation individually

   1. without penalties of course because the weights are for multiple conformations

2. Flexible receptor docking
   = docking all 3 conformations at the same time: with or without E_p

Retrospective testing: findings

standard docking

To open state alone without an E_p

• Allows many decoys to fit and score better than known ligands

Flexible receptor docking

without E_p:

• also favors the open state and has a poor enrichment

With E_p, directly from MD without weighting multiplier (m)

• slightly better enrichment

With E_p but now scaled to match the energy scale of the Dock3.7 scoring function

• improves enrichment significantly

• balances the distribution of molecules docked to each conformation (less dominated by open)

But:

Flexible receptor docking with energy penalties still does not outperform standard docking to the closed states
This is not unexpected since most of the known ligands naturally bind to the closed state

However, using flexible receptor docking includes high energy conformations allowing discovery of new ligands that bind to less populated states

Prospective screening

Now method works, do a real docking screen to identify new ligands that bind to each conformational state

3 key findings

1. MD can succesfully sample and weight different conformations of the binding site

2. Energy weighting conformations substantially improves hit rates

3. Most docking hits predicted for each state actually bind to that state

—> combining aMD for sampling and cMD based MSMs for accurate weighting and kinetics provides a reliable approach for flexible receptor docking

Observations for the open state

• Open state is larger and more solvent exposed

• Ligands binding to the open state contain polar groups that form new hydrogen bonds with the receptor and benefit from the solvent exposure

  • Because keeping polar groups exposed to solvent reduces the energetic cost of removing water (desolvation) that would have to occur when binding to the intermediate or closed state, making binding more favorable in this case

• Fewer compounds were predicted to bind to the open state

  • it’s less selective so it allows many molecules that don’t bind well

  • ligands that bind are typically larger and less soluble and therefore show weaker binding affinity