# Free Energy Function Auto Dock 4 2 Biology Essay

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MD involves the calculation of solutions to Newtons equations of motions. To find the global minimum energy of a docked complex is difficult since traversing the rugged hyper surface of a biological problem is problematic. (Kaapro et al)

## Monte Carlo methods (MCM):

The Monte Carlo simulation method occupies a special place in the history of molecular modelling, as it was the technique used to perform the 1st computer simulation of a molecular system. The expression Monte Carlo simulation seems to be extremely general and many algorithms are called by that whenever they contain a stochastic process or some kind of random sampling. For those interested, in molecular docking the expression Monte Carlo usually means importance sampling or Metropolis method. The Metropolis method, which is actually a Markov chain Monte Carlo method, generates random moves to the system and then accepts or rejects the move based on a Boltzmann probability. The Monte Carlo methods play an important role in molecular docking but the variety of different kinds of algorithms is too large be considered. Programs using MC methods include Auto Dock, Pro Dock, ICM, MCDOCK, Dock Vision, QXP and Affinity.

## Genetic algorithms (GA):

Genetic algorithms and evolutionary programming are quite suitable for solving docking problems because of their usefulness in solving complex optimization problems. The essential idea of genetic algorithms is the evolution of a population of possible solutions via genetic operators (mutation, crossovers, and migrations) to a final population, optimizing a predentness function. The process of applying genetic algorithms starts with encoding the variables (i.e., the degrees of freedom) into a "genetic code", e.g. binary strings. Then a random initial population of solutions is created. Genetic operators are then applied to this population leading to a new population. This new population is then scored and ranked, and using "the survival of the fittest", their probabilities of getting to the next iteration round depends on their score.

## Fragment-based methods:

Fragment based methods can be described as dividing the ligand into separate portions or fragments, docking the fragments, and finally linking these fragments together. These methods require subjective decisions on the importance of the various functional groups in the ligand, because a good choice of base fragment is essential for these methods. A poor choice can significantly act the quality of the results. The base fragment must contain the predominant interactions with the receptor. Early algorithms required manual selection of base fragment, but this has been automated in newer implementations. Some well known programs using fragment based methods are FlexX and DOCK

## Point complementary methods:

Point complementary methods are based on evaluating the shape and/or chemical complementarity between interacting molecules.

## Distance geometry methods:

Many types of structural information can be expressed as intra- or intermolecular distances. The distance geometry formalism allows these distances to be assembled and three-dimensional structures consistent with them to be calculated.

## Tabu searches:

Tabu searches are based on stochastic processes, in which new states are randomly generated from an initial state (referred to as the current solution). These new solutions are then scored and ranked in ascending order. The best new solution is then chosen as the new current solution and the same process is then repeated again. To avoid loops and ensure diversity of the current solution, a Tabu list is used. This list acts as a memory. It contains information about previous current solutions and a new solution is rejected if it reminds a previous solution too much. An example of docking algorithm using Tabu search is PRO LEADS.

## Systematic searches:

These methods systematically go through all possible conformations and represent the brute force solution to the docking problem. All molecules are usually assumed to be rigid and interaction energy is evaluated from a force field model. Some constraints and restraints can be used to reduce the dimensionality of the problem.

## Common scoring functions:

Force-field methods

Empirical free energy scoring functions

Knowledge-based potential of mean force

## Force-field methods:

Geometry of a molecule can be approximated effectively by taking all the interacting forces into account. Bonded interactions are described by spring forces and non-bonded interactions are usually approximated by potentials resembling van-der Waals interaction. The desired parameters are determined by experimental observations. Geometry is further optimized by binding the energy minimum. Total energy is represented by a set of potential energy functions. In addition to these functions, a set of parameters is also needed to compute the total energy. It is worthwhile to notice, that force field parameters have no meaning unless they are considered together with the potential energy functions. Thus a comparison between force field models is very difficult. In addition to these two parts, information about atom types and atom charges are also required. We also usually need - a set of rules to type atoms, generate parameters not explicitly defined and to assign functional forms and parameters. These methods together form a force field.

- Potential energy functions

- Parameters for function terms

- List of atoms and atom charges

- Rules for atom-typing, parameter generation and

functional form assigning.

Force fields are usually employed to generate accurate predictions to complex problems by interpolating and extrapolating from relatively simple experimental set of molecules. There are generally two approaches to force fields. They are either very accurate with small set of molecules and compounds. They also may be more general, in which case the accuracy is often compromised.

#Auto Dock

#DOCK

#FlexX

#Gold

#Glide

#Slide

## DOCK:

DOCK is one of the oldest and best known ligand-protein docking programs. The initial version used rigid ligands; flexibility was later incorporated via incremental construction of the ligand in the binding pocket. DOCK is a fragment-based method using shape and chemical complementary methods for creating possible orientations for the ligand. These orientations can be scored using three different scoring functions; however none of them contain explicit hydrogen-bonding terms, salvation/desolvation terms, or hydrophobicity terms thus limiting serious use. DOCK seems to handle well a polar binding site and is useful for fast docking, but it is not the most accurate software available.

## FlexX:

FlexX is another fragment based method using flexible ligands and rigid proteins. It uses MIMUMBA torsion angle database for the creation of conformers. The MIMUMBA is an interaction geometry database used to exactly describe intermolecular interaction patterns. For scoring, the Boehm function (with minor adaptions necessary for docking) is applied. FlexX is introduced here to pronounce the importance of scoring functions. Although FlexX and DOCK both are fragment based methods, they produce quite different results. On the contrary to DOCK which performs well with a polar binding sites, FlexX shows totally opposite behaviour. It has a bit lower hit rate than DOCK but provides better estimates of Root Mean Square Distance for compounds with correctly predicted binding mode. There is an extension of FlexX called FlexE with flexible receptors which has shown to produce better results with significantly lower running times.

## Gold:

Gold has won a lot of new users during the last few years because of its good results in impartial tests. It has a good hit rate overall, however it somewhat suffers when dealing with hydrophobic binding pockets. Gold uses genetic algorithm to provide docking of flexible ligand and a protein with flexible hydroxyl groups. Otherwise the protein is considered to be rigid. This makes it a good choice when the binding pocket contains amino acids that form hydrogen bonds with the ligand. Gold uses a scoring function that is based on favourable conformations found in Cambridge Structural Database and on empirical results on weak chemical interactions. The development of GOLD is currently focused on improving the computational algorithm and adding a support for parallel processing.

This dissertation utilizes Auto Dock version 4.2 for the in-silico investigation of AchE Inhibition

## AUTO DOCK:

Auto Dock uses Monte Carlo simulated annealing and Lamarckian genetic algorithm (LGA) to create a set of possible conformations. LGA is used as a global optimizer and energy minimization as a local search method. Possible orientations are evaluated with AMBER force field model in conjunction with free energy scoring functions and a large set of protein-ligand complexes with known protein-ligand constants.

Auto Dock is an automated procedure for predicting the interaction of ligands with bio macromolecular targets. The motivation for this work arises from problems in the design of bioactive compounds, and in particular the field of computer-aided drug design. Progress in bio molecular x-ray crystallography continues to provide important protein and nucleic acid structures. These structures could be targets for bioactive agents in the control of animal and plant diseases, or simply key to the understanding of fundamental aspects of biology. The precise interaction of such agents or candidate molecules with their targets is important in the development process. Our goal has been to provide a computational tool to assist researchers in the determination of bio molecular complexes.

In any docking scheme, two conflicting requirements must be balanced: "The desire for a robust and accurate procedure and the desire to keep the computational demands at a reasonable level". The ideal procedure would find the global minimum in the interaction energy between the substrate and the target protein, exploring all available degrees of freedom (DOF) for the system. However, it must also run on a laboratory workstation within an amount of time comparable to other computations that a structural researcher may undertake, such as a crystallographic refinement. In order to meet these demands a number of docking techniques simplify the docking procedure. Auto Dock combines two methods to achieve these goals: rapid grid-based energy evaluation and efficient search of torsional freedom.

Auto Dock 3.0

Auto Dock 4.0

Auto Dock 4.2

## Getting Started with Auto Dock:

Auto dock and Auto dock Tools, the graphical user interface for Auto Dock are available on the WWW at: http://autodock.scripps.edu/

Auto Dock calculations are performed in several steps:

1) Preparation of coordinate files using AutoDockTools,

2) Pre calculation of atomic affinities using Auto Grid,

3) Docking of ligands using Auto Dock, and

4) Analysis of results using AutoDockTools.

Step 1: Coordinate File Preparation.

AutoDock4.2 is parameterized to use a model of the protein and ligand that includes polar hydrogen atoms, but not hydrogen atoms bonded to carbon atoms. An extended PDB format, termed PDBQT, is used for coordinate files, which includes atomic partial charges and atom types. The current Auto Dock force field uses several atom types for the most common atoms, including separate types for aliphatic and aromatic carbon atoms, and separate types for polar atoms that form hydrogen bonds and those that do not. PDBQT files also include information on the torsional degrees of freedom. In cases where specific side chains in the protein are treated as flexible, a separate PDBQT file is also created for the side chain coordinates. In most cases, AutoDockTools will be used for creating PDBQT files from traditional PDB files.

Step2: Auto Grid Calculation.

Rapid energy evaluation is achieved by pre-calculating atomic affinity potentials for each atom type in the ligand molecule being docked. In the Auto Grid procedure the protein is embedded in a three-dimensional grid and a probe atom is placed at each grid point. The energy of interaction of this single atom with the protein is assigned to the grid point. Auto Grid affinity grids are calculated for each type of atom in the ligand, typically carbon, oxygen, nitrogen and hydrogen, as well as grids of electrostatic and desolvation potentials. Then, during the Auto Dock calculation, the energetics of a particular ligand configuration is evaluated using the values from the grids.

Step 3: Docking using Auto Dock.

Docking is carried out using one of several search methods. The most efficient method is a Lamarckian genetic algorithm (LGA), but traditional genetic algorithms and simulated annealing are also available. For typical systems, Auto Dock is run several times to give several docked conformations, and analysis of the predicted energy and the consistency of results is combined to identify the best solution.

Step 4: Analysis using AutoDockTools.

Auto Dock Tools includes a number of methods for analyzing the results of docking simulations, including tools for clustering results by conformational similarity, visualizing conformations, visualizing interactions between ligands and proteins, and visualizing the affinity potentials created by Auto Grid.

## Auto Dock 4.2 includes several enhancements over the methods available in Auto Dock 3.0:

Side chain Flexibility: Auto Dock 4.2 allows incorporation of limited side chain flexibility into the receptor. This is achieved by separating the receptor into two files, and treating the rigid portion with the Auto Grid energy evaluation and treating the flexible portion with the same methods as the flexible ligand.

Force Field: The Auto Dock 4.2 force field is designed to estimate the free energy of binding of ligands to receptors. It includes an updated charge-based desolvation term, improvements in the directionality of hydrogen bonds, and several improved models of the unbound state.

Expanded Atom Types: Parameters have been generated for an expanded set of atom types including halogens and common metal ions.

Desolvation Model : The desolvation model is now parameterized for all supported atom types instead of just carbon. Because of this, the constant function in Auto Grid is no longer used, since desolvation of polar atoms is treated explicitly. The new model requires calculation of a new map in Auto Grid which holds the charge-based desolvation information.

Unbound State: Several models are available for estimating the energetics of the unbound state, including an extended model and a model where the unbound state is assumed to be identical with the protein-bound state.

## Auto Dock 4.0, there are several changes in Auto Dock 4.2:

Default Unbound State: The default model for the unbound state has been changed from "extended" to "bound=unbound". This is in response to persistent problems sterically-crowded ligands. The "extended" unbound state model is available in Auto Dock 4.2 through use of the "unbound extended" keyword.

Backwards Compatibility: We have made every attempt to ensure that docking parameter files generated for use in Auto Dock 4.0 should be correctly run by Auto Dock 4.2.

## Theory background:

Overview of the Free Energy Function:

Auto Dock 4.2 uses a semi empirical free energy force field to evaluate conformations during docking simulations. The force field was parameterized using a large number of protein-inhibitor complexes for which both structure and inhibition constants, and Ki, are known

The force field evaluates binding in two steps. The ligand and protein start in an unbound conformation. In the first step, the intramolecular energetics are estimated for the transition from these unbound states to the conformation of the ligand and protein in the bound state. The second step then evaluates the intermolecular energetics of combining the ligand and protein in their bound conformation. The force field includes six pair-wise evaluations (V) and an estimate of the conformational entropy lost upon binding (Î”S conf):

where L refers to the "ligand" and P refers to the "protein" in a ligand-protein docking calculation. Each of the pair-wise energetic terms includes evaluations for dispersion/repulsion, hydrogen bonding, electrostatics, and desolvation:

The weighting constants 'W' have been optimized to calibrate the empirical free energy based on a set of experimentally-determined binding constants. The first term is a typical 6/12 potential for dispersion/repulsion interactions. The parameters are based on the Amber force field. The second term is a directional H-bond term based on a 10/12 potential. The parameters C and D are assigned to give a maximal well depth of 5kcal/mol at 1.9Å for hydrogen bonds with oxygen and nitrogen, and a well depth of 1 kcal/mol at 2.5Å for hydrogen bonds with sulphur. The function E (t) provides directionality based on the angle't' from ideal H-bonding geometry. The third term is a screened Coulomb potential for electrostatics. The final term is a desolvation potential based on the volume of atoms (V) that surround a given atom and shelter it from solvent, weighted by a salvation parameter (S) and exponential term with distance-weighting factor Ïƒ = 3.5Å.

By default, Auto Grid and Auto Dock use a standard set of parameters and weights for the force field. The parameter file keyword may be used, however, to use custom parameter files.

Fig: Viewing Grids in AutoDockTools

In the fig the protein is shown on the left in white bonds, and the grid box is shown on the right side. The blue contours surround areas in the box that are most favorable for binding of carbon atoms, and the red contours show areas that favor oxygen atoms.A ligand is shown inside the box at upper right.

Fig: Graph of Auto Dock Potentials:

In the graphical figure examples of the four contributions to the Auto Dock force field are shown. The dispersion/repulsion potential is for interaction between two carbon atoms. The hydrogen bond potential, which extends down to a minimum of about 2 kcal/mol, is shown for an oxygen-hydrogen interaction. The electrostatic potential is shown for interaction of two oppositely charged atoms with a full atomic charge. The desolvation potential is shown for a carbon atom, with approximately 10 atoms displacing water at each distance.

## Auto Dock has applications in:

X-ray crystallography

Structure-based drug design

Lead optimization

Virtual screening (HTS)

Combinatorial library design

Protein-protein docking

Chemical mechanism studies