| The fundamental laws of thermodynamics and statistical mechanics, and the deeper understandings of quantum mechanics have been rebuilt in recent years. It is partly because of the increasing power of computing resources nowadays, that allow shedding direct insights into the connections among the thermodynamics laws, statistical nature of our world, and the concepts of quantum mechanics, which have not yet been understood. But mostly, the most important reason, also the ultimate goal, is to understand the mechanisms, statistics and dynamics of biological systems, whose prevailing non-equilibrium processes violate the fundamental laws of thermodynamics, deviate from statistical mechanics, and finally complicate quantum effects.;I believe that investigations of the fundamental laws of non-equilibrium dynamics will be a frontier research for at least several more decades. One of the fundamental laws was first discovered in 1997 by Jarzynski, so-called Jarzynski's Equality. Since then, different proofs, alternative descriptions of Jarzynski's Equality, and its further developments and applications have been quickly accumulated. My understandings, developments and applications of an alternative theory on Jarzynski's Equality form the bulk of this dissertation. The core of my theory is based on stepwise pulling protocols, which provide deeper insight into how fluctuations of reaction coordinates contribute to free-energy changes along a reaction pathway. We find that the most optimal pathways, having the largest contribution to free-energy changes, follow the principle of detailed balance. This is a glimpse of why the principle of detailed balance appears so powerful for sampling the most probable statistics of events. In a further development on Jarzynski's Equality, I have been trying to use it in the formalism of diagonal entropy to propose a way to extract useful thermodynamic quantities such temperature, work and free-energy profiles from far-from-equilibrium ensembles, which can be used to characterize non-equilibrium dynamics.;Furthermore, we have applied the stepwise pulling protocols and Jarzynski's Equality to investigate the ion selectivity of potassium channels via molecular dynamics simulations. The mechanism of the potassium ion selectivity has remained poorly understood for over fifty years, although a Nobel Prize was awarded to the discovery of the molecular structure of a potassium-selective channel in 2003. In one year of performing simulations, we were able to reproduce the major results of ion selectivity accumulated in fifty years. We have been even boldly going further to propose a new model for ion selectivity based on the structural rearrangement of the selectivity filter of potassium-selective KcsA channels. This structural rearrangement has never been shown to play such a pivotal role in selecting and conducting potassium ions, but effectively rejecting sodium ions. Using the stepwise pulling protocols, we are also able to estimate conductance for ion channels, which remains elusive by using other methods. In the light of ion channels, we have also investigated how a synthetic channel of telemeric G-quadruplex conducts different types of ions. These two studies on ion selectivity not only constitute an interesting part of this dissertation, but also will enable us to further explore a new set of ion-selectivity principles.;Beside the focus of my dissertation, I used million-atom molecular dynamics simulations to investigate the mechanical properties of body-centered-cubic (BCCS) and face-centered-cubic (FCCS) supercrystals of DNA-functionalized gold nanoparticles. These properties are valuable for examining whether these supercrystals can be used in gene delivery and gene therapy. The formation of such ordered supercrystals is useful to protect DNAs or RNAs from being attacked and destroyed by enzymes in cells. I also performed all-atom molecular dynamics simulations to study a pure oleic acid (OA) membrane in water that results into a triple-layer structure. The simulations show that the trans-membrane movement of water and OAs is cooperative and correlated, and agrees with experimentally measured absorption rates. The simulation results support the idea that OA flip-flop is more favorable than transport by means of functional proteins. This study might provide further insight into how primitive cell membranes work, and how the interplay and correlation between water and fatty acids may occur. |
