Structural Biochemistry/Molecular Modeling

Molecular Modeling

Molecular Modeling Overview

Molecular modeling refers to abstract methods and techniques for finding the molecular structures and properties by using computational chemistry and graphical visualization techniques to ‘model’ or copy the behavior of the molecule. Besides computational chemistry, they can also be used in fields such as computational biology and science that studies molecular structures. These methods or techniques can be used to figure out molecules ranging from combination of a few atoms such as CH₃ to large macromolecules such as polypeptides by giving possible 3-D representation of those structures. The simplest atomic structures do not necessarily need computers to figure out the molecular model, but large molecules do; Molecular modeling helps to make it easier to understand each specific parts of the complex molecule and also allow more atoms to be considered during simulation. The two most common models that are used in molecular modeling are quantum mechanics and molecular mechanics. A method of molecular modeling, molecular docking, can be used to discover and design new molecules.

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Quantum Mechanics

Common Models

Quantum Mechanics are principles describing the physical reality at the atomic level of matter (molecules and atoms) and the subatomic (electrons, protons, and smaller particles), and it include the simultaneous wave-like and particle-like behavior of both matter and radiation. It is a mathematical description of reality, which is usually different than how humans see a set of bodies or how a system behave. The most complete description of a system is its wavefunction, which is a number varying between time and place. In quantum mechanics, quantum refers to a discrete unit that quantum theory assigns to certain physical quantities, such as the energy of an atom at rest. Particles are discrete packets of energy with wave-like properties which led to the branch of physics that deals with atomic and subatomic systems. This area of study is the quantum mechanics. The principle between classical and quantum mechanics is that all objects obey laws of quantum mechanics, and classical mechanics is just a quantum mechanics of large systems.Quantum mechanics are usually compared with classical physics, but they are not the same because they aren't defined at the same time by the Universe. Quantum theory also provides accurate descriptions for many previously unexplained phenomena such as black body radiation and the stability of electron orbitals. It has also given insight into the workings of many different biological systems, including smell receptors and protein structures.

three fundamental ways Quantum mechanics differs from classical physics:

the integration of particle and wave phenomena with the relative equivalence of mass and energy
the quantization of both wave and particle phenomena
the uncertainty involved in making physical measurements.

Quantum mechanics theory was formed by a continuation of important discoveries: 1838 discovery of cathode rays by Michael Faraday, the 1859 statement of the black body radiation problem by Gustav Kirchhoff, the 1877 suggestion by Ludwig Boltzmann that the energy states of a physical system could be discrete, the 1900 quantum hypothesis by Max Planck and then the 1905 postulation of light itself consisting of individual quanta called photons, by Albert Einstein.

Molecular Mechanics refers to the use of classical mechanics (Newtonian mechanics) to describe the physical basis behind the models. Molecular models usually describe atoms as point charges with an associated mass. The interactions between neighboring atoms are described by spring-like interactions (representing chemical bonds) and van der Waals forces. Molecular mechanics can be used to study small molecules as well as large biological systems or material assemblies with many thousands to millions of atoms. Simple energy functions can be quick to solve, can deal with large molecules, accurate for systems which are close to the models used to reproduce the force field, and can be used to specify mandatory bonds in a molecule.

Molecular mechanics force field: Simple equations to describe the energy cost of deviating from ideal geometry
- E = E_s + E_b + E_w + E_nb
  - E_s is the energy involved in the deformation of a bond either by stretching or compression; E_b is the energy involved in angle bending; E_w is the torsional angle energy; E_nb is the energy involved in interactions between atoms that are not directly bonded
- E_pot=∑V_s+∑V_a+∑V_t+∑V_v+∑V_e
  - where E_pot is the energy of the potential function; V_s the bond stretch potential of all bonds; V_a is all the bond angle bending; V_t is torsion; V_v is van der waals of all atoms; V_e is the electrostatic interactions
Molecular mechanics minimization: a method of minimizing the energy by changing the structure toward optimum geometry
Properties of molecular mechanics methods:
1. each atom is represented as a single particle
2. each particle has a radius, has polarizability, and a constant net charge
3. Bonded interactions are treated as "springs" with an equilibrium distance equal to the experimental or calculated bond length

Single Molecule Biophysics

In the past decade, new methods have helped scientists visualize microscopic molecules. These new techniques such as atomic force microscopy, optical and magnetic tweeezers, and single-molecule fluorescence spectroscopy allow scientists to visualize molecules on a single molecule scale instead of how large gigantic systems interact and taking averages of large moles.

The single molecule method takes advantage of being able to determine distinct structural states or large biomolecules. Though it cannot reveal as much structural information as can X-ray crystallography it can obtain nanometer-scale information on structural features.

Atomic Force Microscopy

An atomic force microscope (2009).

This tool was first developed for topographically imaging molecules on a flat atomic surface. AFM is generally used on generating static images of biomolecules and can be performed on dry or samples in solution. Due to these factors AFM has been useful for spectroscopy of protein structure.

IBM in Zurich, Switzerland has improved the AMF technique well enough to capture the most detailed and smallest-scale image of a pentacene molecule.

Pentacene in its solid form viewed within optical range.

The main idea behind atomic force microscopes is that an image can be created from a detailed force map of minute atomic scale forces. These are sensed by some sort of probing device; analogous to hands feeling an object in a completely dark room as to gain a sense of it's shape. The atomic probe is thereby creating an image of the surroundings in a see-by-feel manner.

The problem one would expect with this close-up sort of atomic measurement is the attractive force of Van Der Waals. At very close distances, this force is strong enough to potentially pull and subsequently attach the penacene directly to the surface of the probe. Luckily, a phenomena noted as the Pauli exclusion principle prevents this sort of behavior. This priciple states that quantum particles called fermions cannot occupy the same quantum state within a certain range of each-other.

The microscope uses a carbon monoxide "tip" to pan over a penacene molecule (or other desired molecule) which is bound to a silicon surface. The carbon monoxide molecule is bound to the probe directionally, such that the oxygen is aligned along the axis of force measurement. This relatively inactive oxygen is able to measure varying forces along the surface of the penacene molecule. This is accomplished through atomic forces created by the repulsive behaviour described by Pauli's principle. This 2D force map is used to create the corresponding image.

Magnetic Tweezers

This approach is often used for studying the structural properties of DNA and protein-DNA transactions.

Methods/ Techniques

Classical Molecular Dynamics is a computational method for simulating the motion of particles. It involves calculating the spatial derivatives of the energy to get the force acting on each atom according to Newton's Laws of Motion.

Ab-initio methods may also be used to simulate the motion of atoms by solving the Schroedinger equation to obtain results that are more accurate but much more computationally expensive.

Molecular Docking is a method which predicts the preferred orientation of one molecule that binds to another molecule. It is an important tool in structural molecular biology and computer-assisted drug design because it use computers to figure out the shape and properties of a molecule. An example of molecular docking is when a ligand binds to a protein to form a stable complex. Even when a protein and a ligand does not completely complement each other, they would adjust their conformation so there would be an overall "best fit" (also called induced-fit). The goal of molecular docking is to minimize the free energy of the whole system by achieving an optimized conformation for both the protein and ligand.

Challenges In Molecular Modeling

free energies

Thermodynamic free energy is the energy in a physical system that can be converted to do work:
- First law: conservation of energy
- Second Law: the universal principle of entropy, stating that the entropy of an isolated system which is not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium.
- Third Law: deals with entropy and how it is impossible to reach the absolute zero of the temperature.

solvation is the process of attraction and association of molecules of a solvent with molecules or ions of a solute.
simulating reactions is the modeling of natural systems or human systems in order to gain insight into their functioning and how reactions happens.