A Study On Enhanced Sampling Method And Electrostatic Polarization Model Of Biological Systems

With the rapid development of theoretical methods and computer technology,the theoretical and computational simulations of biological systems have been applied to show the microstructure and dynamic evolution properties of systems such as pro-teins and enzymes.Molecular simulations played an important role in drug design and screening,and rationalization of the mechanism of drug and protein interactions.However,computational simulation of biological systems still faces some challenges in structural prediction and electrostatic description with specific biological functions.In general,the calculations of biological systems suffer from many difficulties such as thousands of atoms,complex structures,large molecular frameworks with high flexi-bility,high degrees of freedom,rugged potential energy surfaces for molecular confor-mation transitions,and the existence of numerous energy minima and metastable states.Conventional molecular dynamics simulations based on force fields cannot completely track the conformational changes of biomolecules across the entire potential energy surface.Therefore,how to explore the conformation space as much as possible in a limited time scale is an urgent problem.On the other hand,as the computational cost of the force field(which increases squarely with the number of atoms)is much smaller than that of the quantum chemical calculation(which increases with the power of 3to 6),force-field based molecular dynamics simulation is widely used in the simula-tion of biological systems.In the conventional molecular dynamics simulations,the atomic partial charges are predetermined and fixed values,which cannot describe the hydrogen bonding effect and the electrostatic polarization effect of the charged groups in biological systems.How to accurately describe the polarization effect of the sys-tem is also an important issue.In this thesis,we attempted to tackle two problems about how to observe structural changes”faster”and how to”more accurately”de-scribe polarization effects in the system.We developed a series of enhanced sampling methods armed with normal mode analysis(NMA)and principal component analysis(PCA)and polarizable model based on quantum mechanism calculations.We applied these methods to explore the conformational changes of alanine dipeptide,N-terminal Calmodulin(n Ca M),Adenylate Kinase(Ad K)and dynamics process of a drug passing across a membrane.We found that entropy and polarization are the main driving forces for drug molecules to penetrate the membrane,and provide theoretical guidance for protein structure research and drug design.The main research results are outlined as below:1.Proposal of enhanced sampling methods armed with PCA and NMAIn biological systems,function of proteins are highly related to their structures.Inter-conversions between structures generally correspond to dominant motion pat-terns.When a system is composed of N atoms,3N-6 conformational degrees emerge.Conventional molecular dynamics spend a lot of time sampling over some unrelated degrees,thus consume a lot of computational resources.Here,we utilized the normal mode analysis(NMA)and principle component analysis(PCA)to obtain the most im-portant motions which are highly related to the conformational change.These motions are derived by solving the Hessian matrix and covariance matrix.In these low dimen-sional conformational spaces,we picked out the corresponding structure,and then re-assigned the initial velocity according to the Maxwell-Boltzmann distribution,so that the molecule is more prone to cross the energy barrier to another steady state.With these ideas,we have developed two kinds of enhanced sampling methods,namely,DAta-Driven Acceleration(DA2 enhanced sampling method with unknown final state),two-ended DAta-Driven Acceleration(te DA2,the enhanced sampling method with known final state).For alanine dipeptide,within 200 ns,DA2 method can identify 6 functional states.However,given 1200 ns,conventional molecular dynamics simulations could only sampled 4 functional states.By using DA2,transition between the“Open”and“Closed”states of n Ca M together with 2 distinct transition pathways could be observed in the time scale of nanosecond.On the other hand,in the system of Adenylate Kinase(Ad K),the te DA2 method can identify 3 kinds transition pathway between“Closed”state and“Open”state,these results are consistent with the crystal structures reported experimentally and explained the difference between transition pathways observed ex-perimentally.te DA2 is 1 to 2 orders of magnitude faster than conventional MD.To further improve the efficiency of sampling,we attempt to introduce Monte Carlo(MC)simulation strategies to help biomolecular molecules cross over higher en-ergy barriers faster.DA2 series methods are an original research result and expected to become a powerful tool for studying protein structures.2.Implementation of electrostatic polarization methodsThere are a large number of charged amino acids in biological systems.They inter-act with the external environment through hydrogen bonding and electrostatic polariza-tion effects.In the conventional molecular dynamics simulations,the value of atomic charge cannot change with respect to the surrounding medium environment.In order to accurately describe the electrostatic polarization,we introduced the electrostatic pa-rameters such as the charge calculated by quantum mechanism into the force field so as to develop a polarizable force field model.Two models were proposed,namely,explicit polarizable force field and implicit polarizable force field.In the explicit polarizable force field,the charge is calculated by QM with the environment treated as background point charge,and the charge varies when the environment changes;in the implicit po-larizable force field,although the charge is fixed,its derivation is from QM calculation with the environment treated as polarizable continuum model(PCM).Then,we applied them to study the dynamic behavior of a drug molecule 2-aminoethoxydiphenyl borate(2-APB)passing across the bilayer.The partition coefficient derived from our model is consistent with the one measured experimentally.In addition,free energy calculations were performed and revealed that compared with the neutral drug,charged one takes much more energies,?10 kcal/mol,to penetrate across the membrane.In the aqueous phase,the p K_ais found to be 9.6,while in the core of the membrane,it decreased to4,this result shows that deprotonation occurs when protonated drug molecules enter the cell membrane center from the aqueous phase.The entropy of the drug molecules significantly affects the distribution and transport capacity of the molecules in the mem-brane.In addition,we further explored 1211 compounds based on the mother structure2-APB.Armed with PCA,we found delicate balance between entropy and polarity which are two important factors affecting the transferability of the drug.It provides theoretical guidance for high-throughput drug screening and design.