Theoretical Study Of Free Energy Calculations With Multiscale Simulations

Free energy calculations can guide the experimental screening techniques for measuring biological interaction energies and offer the potential of a faster and cheaper way to extract thermodynamic information over large chemical space in a variety of molecular contexts.Accurate free energy calculation depends on the accuracy of the Hamiltonian.Quantum mechanical(QM)Hamiltonian is capable of providing a more reliable potential energy surface.However,the cost is formidably expensive,especially for biomacromolecules,for which interesting events take place usually on a wide range of spatial-temporal scales.Reference-potential method can be employed to reduce the computational cost,in which an inexpensive reference Hamiltonian can be utilized for sampling and a one-step correction from the reference Hamiltonian to the target Hamiltonian using thermodynamic perturbation(TP)can be applied to obtain the ensemble averages under the target Hamiltonian.This method often suffers from convergence failure.In addition,criteria for the validation of the calculations are yet to be proposed.In this thesis,I will explore different schemes to improve the accuracy and confidence of free energy calculations via the reference-potential method.When the phase space overlap between the reference and target Hamiltonian is not insufficient,two schemes were proposed to calculate the free energy difference between these two Hamiltonians.For the first one scheme,a SQM Hamiltonian was used to connect MM and QM Hamiltonians(QM/MM-B).The second scheme utilizes nonequilibrium simulation to translate MM Hamiltonian into QM Hamiltonian(QM/MM-NE).We also defined reweighting entropy S which can be used to quantify the reliability of the calculation.In chapter two,the solvation free energies of side chain analogs(SCA)in water and chloroform were studied to test these three approaches.The calculated hydration free energies show that when S below a certain value,the free energy difference between reference Hamiltonian and objective Hamiltonian obtained from a single step TP calculation is not reliable at all.In this case,a semiempirical Hamiltonian can be used to connect the MM and QM Hamiltonian.Alternatively,nonequilibrium simulations can also be employed to apply the QM correction.Both of those two schemes improve the calculated results significantly.Binding constant is one of the most important quantity for drug design.The relationship between binding constant and binding affinity shows that a difference in binding constant of1 order of magnitude translates to a difference of only 6 kJ/mol in binding affinity.Thus,the accuracy of computational method must be very high.In this thesis,the binding affinities were also studied with reference potential methods.In chapter three,nonequilibrium simulations were performed to speed up the convergence of host-guest binding affinities at SQM level.The reference Hamiltonian is MM and the target Hamiltonian is SQM.For the large difference between MM and SQM Hamiltonians,to ensure the sufficient phase space overlap,some study employed several ? to switch the MM Hamiltonian to the SQM Hamiltonian gradually(RPQS).This method facilitates the convergence.However,the computation is very demanding.The rationale for reference-potential method is reduction of the computational cost.Therefore,QM/MM-NE schemes were used to speed up the convergence.With QM/MM-NE scheme,nonequilibrium simulations were performed to calculate the free energy difference between the MM and SQM Hamiltonians.The results show that QM/MM-NE scheme can obtain the same results as RPQS method(within ±1 kJ/mol)with only 50% of simulation time.The calculated relative binding affinities of host-guest at SQM level have been converged,but the deviations between the predicted results and the experimental values are very large with a MAD of 5.0 kJ/mol.To improve the calculated results,reference-potential method were used to calculate the host-guest relative binding free energy difference at DFT level.For the sampling on the potential energy surface at a level of density functional theory(DFT)is extremely expensive,QM/MM-NE scheme is still unaffordable.To ensure the phase space overlap between reference and target Hamiltonians,QM/MM-B and QM/MM-D schemes mentioned in chapter two were employed.The free energy difference between the reference and target potential energy surfaces were calculated with both TP and cumulant expansion to the second order(CA).The results show that the calculations with CA method converge faster than that with TP,and the use of SQM Hamiltonian as an intermediate step between MM and DFT improves the convergence significantly.To check the reliability of the calculations,standard deviation of ?U(?),reweighting entropy(S),effective sampling size(Q)and bias metric(?)were studied.Among these convergence criteria,we made an intensive study of ? and ?.? > 0.5 and ? together with approximately Gaussian simulation(CGS)can be used to check the convergence.However,more accurate method is still desired.