Computational

Now we can calculate the force by deriving our potential energy function, the acceleration by deriving the

force (Newton equation), the velocity by

integrating the acceleration, the movement and

the position by integrating the velocity.

6. Schematic description

of a computer-aided →

drug discovery pipeline.

QSAR: quantitative structure-

activity relationship

ADMET: pharmacokinetic studies

1. Ligand-protein docking. Description, scoring functions, challenges. How side chain flexibility is

treated in docking programs?

In docking, predictions are made on how intermolecular complexes are formed between a target and a

ligand. These algorithms search for the best target–ligand poses with the right conformational state and

relative orientation. The algorithms also crudely estimate the binding affinities of the target–ligand

complexes in terms of scoring. The docking algorithms therefore comprise a search algorithm that searches

the conformational space to find docking poses and a scoring function to predict the affinity of the ligand in

that pose. Computationally docking a target structure to a molecule is a challenging process. Even when

target flexibility is ignored there are still a huge number of ways a molecule can be docked. The total

number of possible modes increases exponentially as the size of the two docked molecules increases.

Therefore efficient search methods that are fast and effective, and reliable scoring functions are critical

components of docking algorithms. The scoring functions can be categorized into knowledge-based, force-

field based, empirical and consensus. Knowledge-based scoring functions are statistical potentials and are

derived from experimentally determined protein–ligand information. The frequency of occurrence of

interactions of a large number of target–ligand complexes are used to generate these potentials. The basis

of these potentials is the Boltzmann distribution. The frequency of occurrence of atom pairs is converted

into a potential using Boltzmann’s distribution of states. Since these potentials use target–ligand complex

data already available, they are highly dependent on the dataset used to create them.

Force-field based scoring functions are developed using classical molecular mechanics. Electrostatic

(coulombic) interactions and van der Waals interactions (Lennard-Jones potential) contribute to the

interaction energy between a target–ligand complex. Empirical scoring functions are obtained by using

data from experimentally determined structures and fitting this information to parameters. The scoring

functions descripted above are not perfect and no one scoring function can do well in every docking

complex studied so, consensus scoring was introduced to combine different scoring functions in the hope

that it can balance out errors and improve accuracy.

Challenges. In order to allow the flexibility of the ligand to be considered within the docking program we

need to explore relative position, relative orientation and the number of rotatable bonds of the ligand.

While relative position and orientation are 3 degrees of freedom for each, for the rotatable bonds this will

strongly depends on the characteristics of the ligand, so the bigger amount of rotatable bonds will increase

the number of degrees of freedom. There is another challenge that will take a bit more faithful from a

computational point of view for the resources: this regards the flexibility of the side chains of the amino

acids in the binding cavity. This will increase a lot the degrees of freedom, because for each of the amino

acids in the binding cavity, we will have a number of rotatable bonds that will allow the side chains to move.

Two approaches that can be taken to account target flexibility are induced fit docking methods and

ensemble-based screening methods: • in induced fit docking the target protein structures are modeled as

flexible, not rigid, and they are able to accommodate induced fit that is caused by the ligand molecule

binding to it; • ensemble-based docking is an alternative method to induced fit docking, with ensemble-

based screening methods there is no need to choose flexible residues of interest to binding. The relaxed

complex scheme (RCS) method uses structure dynamics and docking algorithms in combination to account

for target flexibility. There is another problem, which is the large-scale movements of the protein, but for

the moment this is a problem that we cannot tackle with our available docking programs. For this reason we

need to use a combination of molecular dynamics simulations with dockings and so on…

2. Differences between the "Molecular Mechanics" energetic functions and "empirical" functions.

What about the knowledge-based energetic functions in docking?

While in molecular dynamic simulations, Molecular Mechanics force fields parameters are calculated using

advanced quantum chemistry calculations, in empirical docking approaches we extract the parameters

from real experiment data; therefore these values are measured and not calculated as in the molecular

mechanic force fields. As we are using empirical force fields, in Autodock docking we will have some terms

regarding hydrogen bonding.

3. Describe the molecular interactions that should be considered in docking.

In docking we have to consider the intramolecular forces (covalent): bond stretching, angle bending and

bond rotation. While the intermolecular forces (non-covalent) are described with: the Van der Waals term

(dispersion and repulsion term) that model the shape complementarity of the ligand with the receptor, the

electrostatic term, the hydrogen bonding term (not considered in MM) and the Pi-Stacking (they can be

end-to-face or the more stable face-to-face), Cation-Pi and Metal Ions interactions terms . In sum, those

specific terms give the specificity of recognition. Other important term is the desolvation term: it is

important to take into account the role of water within the binding cavity (desolvation because when the

ligand enters the binding cavity pulls out the molecules of water of the bulk solvent). Energy models often

account for changes in torsional entropy with a term related to the number of rotatable bonds in the

ligand. All of those terms are added for each of the trial poses that are done during the search and they are

used to find the best conformation and to estimate what the free energy is. These terms are very similar to

the force fields regarding molecular dynamics simulations.

4. Which is the condition that MD simulation must fulfill in order to be considered as a "virtual

microscope"?

Only if we follow a strict protocol we can consider our MD simulations as a “ virtual microscope”. So we

have to include our molecule (e.g. protein) in a box of water (to reproduce the environment); to create the

periodic boundaries conditions (to simulate a more physiological condition); to set the cut off (to prevent

the proteins to see their specular image); to set up the minimization parameters (in order to explore all the

possible conformations with different energies and to choose the one with the lower energy); to set up the

equilibration parameters (because our protein's structure comes from XRC and cryo-EM, so it's crystallized):

thermostats (NVT) and barostats (NPT); to define a force field and then parametrizing (if it has not already

been done for the molecules of interest). If we want to do the simulation for a membrane protein we have

also to select the membrane composition and to orientate the protein in the membrane slab.

5. What are the time/space scales that can be explored with molecular dynamics simulations?Which

kind of biological/chemical events can be studied with these techniques? VEDI ↑

6. Discussion about solvent treatment in MD simulations and docking.

Biomolecules should be model considering the solvent effect. The solvent in MD simulation can be

considered in two ways: Explicitly Solvent: explicit molecules of solvent (usually water) are included in the

simulation, this means that more atoms must be simulated augmenting the computational time. Explicit

solvent models treat explicitly (i.e. the coordinates and usually at least some of the molecular degrees of

freedom are included) the solvent molecules. Implicitly Solvent: in order to reduce the computational time

and cost in MD simulations but at the same time keeping a certain level of accuracy, a new approach for

solvent modeling has been developed. Implicit solvents or continuum solvents, are models in which one

accepts the assumption that explicit solvent molecules can be replaced by a homogeneously polarizable

medium as long as this medium, to a good approximation, gives equivalent properties. The main parameter

is the dielectric constant (ε), this is often supplemented with further parameters, for example solvent

surface tension.

In docking, the solvent effect is treated adding the desolvation term that takes into account enthalpic

contributions and entropic contributions of the release of water molecules that surround the ligand and fill

the binding site (when the ligand binds there will be a bunch of water molecules that must be released in

order to not prevent the binding); it also models the hydrophobicity effect so that desolvation term is going

to be favourable for burial of carbon-rich areas of the ligand and carbon-rich areas of the receptor. A big

problem with water molecules that docking programs cannot solve for the moment, at least in an

automatic way is when the waters are forming actually the binding cavity: when the waters are helping or

are considered as bridges between the ligand and the protein.

1. Description of autodock suite for docking.

The Autodock suite is a state of the art package that is used in numerous laboratories and for different

application such as docking and virtual screening. Vina uses a simple scoring function and rapid gradient-

optimization conformational search, while Autodock relies on an empirical free-energy force field and

rapid Lamarckian genetic algorithm search method. Vina is a very fast method but uses several

approximations in the scoring function. Indeed, the latter does not include any electrostatic terms,

hydrogen atoms and furthermore it uses spherically symmetric hydrogen bond potentials to model

hydrogen bond interactions. Vina has shown to give good results when ligands have typical biological size

and composition.

On the other hand, the Autodock score functions comprises physically based terms. Indeed, the latter

includes explicit polar hydrogen, a term for the electrostatic contribution and a term for the directional

hydrogen-bonding interactions. The Autodock score function is already optimized to give successful results

for different biological systems.

2. Discussion about periodic boundary conditions.

The biological system under investigation is finite so boundaries must be considered. In

principle, there are two options that can be adopted. In the first choice, the system can

be inserted in a virtual box, thus it has a sort of “walls”. Consequently, this could lead

to s