FLEX* - REVIEW

Agenda

Introduction

Main concepts

FlexE

FlexS

Evaluation and Discussion

Introduction

Methods for the prediction of binding properties of molecules to proteins.

Classification by the amount of information available about the target protein

The general schema

Incremental construction

Scoring function

Receptor-ligand interactions

Ligand conformational flexibility

Modeling

Algorithm

Base selection

Base placement

The Ligand conformational flexibility

Approximated by a discrete set of conformations. rotatable single bond - modeled by a

discrete set of preferred torsion angles from the MIMUMBA DB.

Ring system - A set of ring conformations is computed with the program CORINA.

The model of receptor-ligand interactions

Modeled by a few special types of interactions

hydrogen bondsmetal acceptors bondshydrophobic contacts

The model of protein-ligand interactions – Cont.

To each interaction group, we assign: Interaction types Interaction geometry ( center + surface)

Two groups interact if : The centers of the groups lie approximately on the surface of

the counter group. The interaction types are compatible

The intermolecular interactions can be classified by the strength of their geometric constrains

Scoring function Estimates the free binding energy in the complex

The function is additive in the ligand atoms.

match score

contact score

Overall docking algorithm

1. Ligand fragmentation

2. Select & Place a set of base fragments

3. Construct the ligand by linking the remaining fragments.

Ligand fragmentation

The ligand is decomposed into components by cutting at each acyclic bond.

Fragmentation is a partition of the components of the molecule, such that every part, called fragment, is connected in the component tree.

Ligand fragmentation

Good results are produced if the added fragments are small

Every fragment, except for the base fragment consist of only one component.

Selecting a base fragment

The problem: Find a fragment which leads to low energy docking solution.

Good base fragment properties:PlaceabilitySpecificity

Selecting a base fragment –Cont.

We look for fragments maximizing the function:

Rules for selecting a set of fragments

No base fragment is fully contained in another base fragment

Each component occurs in at most two base fragments

Each component in a base fragment must be either necessary for the connectivity of the fragment or it must have interaction centers.

The base placement algorithm

Goal: find positions of the base fragment in the active site such that sufficient number of favorable interactions between the fragment and the protein can occur simultaneously.

Solution: pose clustering.

The base placement algorithm – Cont.

Preparation: Store all triangles of interaction points (IP) of the protein in a hash table.

Find all the compatible fragment IP’s triangles.

Clustering of the legal transformations

The incremental construction algorithm

Input: solution set - set of partial placements with the ligands with the ligands constructed up to and including fragment i-1

Output: set of partial placements with the ligands with the ligands constructed up to and including fragment i

The complex construction algorithm – cont.

Adding the next fragment in all the possible conformations

Reject extended placements that have strong overlap with the receptor or internal overlap with the ligand.

Searching for new interactions Optimizing the positions of the partial ligand Selecting a new solution set Clustering the solution set

Optimizing the positions of the partial ligand

The placement is optimized when:New interactions are found.The placement contains slightly

overlapping atoms between the receptor and the ligand.

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Selecting a new solution set

Select k best-scoring solution

Problem: the scoring values cannot be compared directly when different fragments are involved.

Solution: estimate the score of the whole ligand, given a partial placement.

Clustering partial solutions

If no placement contains the other, the distance is infinity

Otherwise, the distance is defined to be the RMSD of the intersecting atoms.

A cluster is reduced to a single placement.

Protein flexibility - motivation

Induced fit – side chain or even backbone adjustments upon docking of different ligands to the same protein.

Even small conformational changes are critical for docking applications e.g. if a rotate able bond prevents a ligand from binding in the correct position.

Protein flexibelity

Main idea: describe the protein structure variations with a set of protein structures representing the flexibility, mutation or alternative models of a protein.

The variability considered by flexE is defined by the differences within the given input structures.

United protein description

Data structure that administers the protein structures variations.

Contains an ensemble of up to 30 possible conformation of the protein.

Most of them are low energy conformations of the same protein.

United protein description - construction

Superposition

Clustering

Add picture - 8

Notation

Component : all the atoms which belong to the same amino acid or mutation of the amino acid. Contains a backbone part and a side chain part

Part : set of instances

Instance : one of the alternative conformations.

United protein description - clustering

The superimposed structures are combined by clustering each part separately

Complete linkage hierarchical cluster

The clustered instances can be recombined to form new valid protein structures.

Incompatibility Two instances of the united

protein description are incompatible if they cannot be realized simultaneously. Logical: two instances are

alternative to each other Geometric: two logically

compatible instances overlap Structural: two instances of

the same chain are unconnected

Incompatibility graph

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Incompatibility graph The incompatibility is

internally represented as a graph by using the instances as nodes and the connecting pairs of incompatible node by an edge.

Valid protein structures correspond to independent set in the graph.

Selection of instancesThe ligand is placed fragment by

fragment into the active site by the incremental construction algorithm.

After each construction step, all possible interactions are determined.

Apply the scoring function for each instance.

We chose the IS with the highest score.

chose the IS with the highest score.

The IS can be assembled from IS of the connected components.

Apply a modified version of the Bron-Kerbosch algorithm.

Select the optimal IS

Evaluation

FlexE was evaluated with ten protein structures ensembles containing 105 crystal structure from the PDB.

The structures within the ensemble highly similar backbone traceDifferent conformations for several side

chains.

Evaluation – Cont.

FlexE finds a ligand position with RMSD below 2 A in 67% of the cases.

Average CPU time for the incremental construction algorithm is 5.5 minutes.

Discussion

The ensemble approach is able to cope with several side-chains conformations and even movements of loops.

Motions of larger backbone segments or even domains movements are not covered by this approach.

flexS - motivation

In drug design, often enough, no structural information about a particular receptor is available.

Considerable number of different ligands are known together with their binding affinities towards the receptor.

flexS - overview

A method for structurally superpositing pairs of ligands, approximating their putative binding site geometry.

Main Applications ligand superpositioning Virtual Screening

Implementation in flexS

RigFit – fast rigid-body placement using Fourier space methods.

Incremental construction

Systematic parameter study

Two Base Placement Methods

Target: Place a rigid molecule fragment onto the reference ligandCombinatorial placement procedureNumerical placement procedure

RigFit

Optimizes the common volume of two molecule expressed by various Gaussian functions associated to different physicochemical properties.

Solves the combinatorial placement problem.

Variable Sequence Construction

The sequence in which fragments are added is selected dynamically depending on the actual placement.

Effective in cases where the flexible test ligand partially extends beyond the reference ligand.

Dynamically selection of the next fragment

Each partial placement is associated with a list of candidate fragments.

Evaluation of the next fragment considers: The amount of expected

overlap with the reference The number of potential

interaction in the candidate fragment

The size of the substructure tree rooted at the candidate fragment.

Dynamically selection of the next fragment – Cont.

Nbus –number of buildup states.

Deviation from the original sequence only if a better sequence is found

If flexS exceeds Nbus upper limit, it returns to the original sequence

Evaluation

The performance of the algorithm depends on the size of the superimposed ligands.

In reproduction of 284 alignments, 60% reproduces with RMSD below A.

Questions?

Thank you!

Scoring & Selection strategy

Total score fo the partial ligand

FlexS Flow

Test ligand

Reference ligand

fragmentation

Placement of the anchor molecule

Add a fragment that adopts a

discrete set of conformations

The physicochemical model

The conformational space of the ligand

The model of protein-ligand interactions

Scoring function

United protein description - superposition

Assumption: highly similar backbone traces -> superposition by fitting the backbone atoms of the particular structures.

This procedure emphasizes the differences and improves the fitting in conserved regions of structures. [why ???]

Surface and interaction geometries