Practical Protein Chemistry - A. Darbre 1989

Prediction of Peptide and Protein Conformation
An Arsenal of Modern Theoretical Methods
The Molecular Dynamics Method

Applying the Born–Oppenheimer approximation makes it possible to calculate the energies of individual Conformations using Quantum Mechanical Methods. The physical essence of this principle lies in the possibility of separating nuclear and electronic motions and isolating the kinetic energy contributions of each particle type. When performing energy calculations for specific conformations, we usually neglect the kinetic energy of nuclear motion. Can this contribution be estimated?

Generally speaking, the quantum mechanical approach also allows us to examine the evolution of molecular systems over time, but in practice, such calculations are extremely difficult to carry out. A practical representation of kinetic energy relies on a further simplification, according to which the system obeys the laws of classical mechanics, and atoms behave as macroscopic objects. Therefore, the nuclear momenta are represented not as p = (—ih/2n) ∙ (d/dq), but as the product of mass and velocity, p = mv. In this case, the Hamilton operator no longer acts on the wave function, but becomes a function whose value is the system's energy. The operator transforms into the classical Hamiltonian. The energy of the system is no longer a discrete quantity, the quantum mechanical uncertainty vanishes, and nuclear motion obeys Newton's law. Of course, nuclear and electronic motions are quantized, but neglecting these motions only affects the vibrations of chemical bonds. Even with a classical description of nuclear motion, it is possible to calculate the potential energy of each conformation using quantum mechanical methods; however, this requires an excessively large amount of computer time. In this instance, quantum mechanics offers no advantages, and the potential energy of each conformation is calculated using empirical potential Functions. Naturally, quantum mechanical approaches are still employed in deriving analytical relations.

An important outcome of Structure/139.html">Molecular Dynamics Calculations using potential functions is The ability to determine the forces acting on each particle. This is easily accomplished by taking the derivative of energy as a function of coordinates. Knowing the nuclear masses and applying Newton's law (force = mass ∙ acceleration), one can calculate the acceleration and subsequently the coordinates, momentum, and kinetic energy of each particle over a short fixed time step. Unlike Traditional Methods FOR searching the most favorable conformations with the lowest energy, the researcher cannot freely scan through conformations in this case. The applied algorithm is based on Newton's law, and the choice of the next conformation is determined accordingly. The simplicity of Newton's law dictates the simplicity of the basic algorithm, though in practice, modified algorithms are used to ensure the required speed and computational accuracy. The most popular of these [2] is noted for its simplicity, speed, and reliability. In addition to specifying the initial conformation and the type of potential functions (for numerically solving the equations), the algorithm requires knowledge of the initial particle velocities and a defined time step interval. Too large an interval saves computation time but fails to ensure smooth variations in potential and kinetic energy. Initial particle velocities must be specified because the average kinetic energy determines the system Temperature. There is little point in performing calculations at absolute zero or at very high temperatures, where most of the starting conformation's energy is converted into the kinetic energy of the system.

Despite neglecting quantum mechanical effects, the molecular dynamics method demands substantial CPU time. Describing a sequence of events over a time interval of 10^-10 s requires several minutes of processor time. The folding process of a real protein globule takes ∼1 s, and simulating such a process could require several hundred years, which is, of5 course, impractical for predictive purposes. Nevertheless, this approach is well-suited for studying vibrational processes in "small" protein molecules [36] and The behavior of simple Peptides in an aqueous environment [68].

Since the preferred structure of a molecule corresponds to its equilibrium state, The history of its preceding transformations is irrelevant for predictive purposes. It is interesting to note, however, that the molecular dynamics method allows for a rigorous estimation of Free energy, which depends on the degree of molecular mobility near the minimum on the potential energy surface (a surface described by a function of conformational parameters). It is still not entirely certain whether the native Cell/13.html">Protein Structure corresponds to the deepest energy minimum or an intermediate minimum accessible within a reasonable biological timeframe. In any case, investigating the kinetic changes of a molecule serves as a useful tool in predicting its native structure.