Moleküler Dinamik Simülasyonlarında Dissipatif Kuvvetin Yaptığı İşin Hesaplanması

Abstract

Although it is quite difficult to model friction on the atomic scale, recent theoretical and experimental techniques have enabled the study of friction at atomic scales, which could not be studied with conventional models until recently. In this thesis, numerical free energy calculation methods that do not require equilibrium state for biomolecular systems will be developed, while the work done by dissipative forces, which are constantly encountered in calculations that do not require equilibrium state, will be calculated with the help of these methods. In literature, it has been shown that the Jarzynski equation, which is a non-equilibrium method, works in simple systems but does not work in complex systems such as biomolecules, and it is concluded that the reason is the work done by the dissipative force during the pulling motion. With the phase space method that emerged in the following years, it was possible to calculate the work done by the dissipative force. Within the scope of this thesis, first of all, the Jarzynski equation and phase space methods were coded to use the outputs of molecular dynamics simulations. In this process, the weighted histogram analysis method approach was used to obtain the probability density distributions required for the use of the phase space method from steered molecular dynamics simulations. In the next step, to test these non-equilibrium methods, a non-physical system in which a single ion is pulled in water was created. In this simple system, the Jarzynski equation and the phase space method have been tested and shown to work. However, due to the lack of comparable experimental data for this system, a Gaussian potential was applied along the pulling coordinate to the system. It was shown that Dissipative work can be calculated in the system up to 10 Å/ns pulling speed. After obtaining the potential applied to the system, these methods were used for the calculations for Gramicidin A ion channel, which is a more complex biomolecular system. Free energy profile of Gramicidin A channel was only obtained consistent with the literature for 1 Å/ns and it was observed as a common behavior that the dissipative force was lower than it should be at higher pulling speeds. It is thought that the reasons for this deviation are insufficient sampling and the margin of error in the approach made to find the probability density functions.

In conclusion, a program has been developed and applied in simple and complex systems to apply the phase space method, and in the literature, in cases where the Jarzynski equation does not work even at very low speeds, the work done by the dissipative force is calculated with the phase space method and free energy surfaces depending on the path are obtained. Hence, the first study, which calculates the work done by the dissipative force in molecular dynamics simulations, and thus enables the calculation of the friction force at nanoscale, has emerged.