Doctoral Thesis Association and dissociation simulations of bio-molecular complex using parallel cascade selection molecular dynamics The University of Tokyo Greduate Shool of Frontier Sciences Department of Computational Biology and Medical Sciences Tran Phuoc Duy Doctoral Thesis 学位論文 Association and dissociation simulations of bio-molecular complex using parallel cascade selection molecular dynamics 並列カスケード選択分子動力学法による生体分子の会合・解離シミュレーション 東京大学大学院新領域創成科学研究科 メディカル情報生命専攻 チャン フ ズイ In memory of my father To my mother and my sister With eternal love and appreciation i Abstract Sampling conformations of protein complexes during association and dissociation processes is a crucial step to estimate the binding free energy and other kinetic properties from association/dissociation pathways. This is a challenging problem for the classical Molecular Dynamics (MD) simulation because the time scale of these processes exceeds the limit of current computation. Therefore, enhanced sampling techniques play an important role to generate sufficient data for the free energy analysis. For example, Steered Molecular Dynamics (SMD) with Umbrella Sampling (US) [Ramirez et al.
(2016)], Replica Exchange Umbrella Sampling (REUS) [Sugita et al. Phys (2000)], Targeted MD (TMD) [Schlitter et al. (1994)], Parallel Cascade Selection Molecular Dynamics (PaCS-MD) [Harada and Kitao, J. (2011)] and other methods not listed here are used for this purpose.
Recently, Yamashita and Fujitani showed that protein structures were distorted when dissociation of lysozyme (enzyme) and HyHEL-10 (inhibitor) was simulated by SMD using a steering force applied to the center of mass (COM) of the protein, which led overestimation of the potential of mean force (PMF) with the following US. This can be considered as the artifact caused by SMD. In contrast to SMD, PaCS-MD performs conformational sampling by cycles of distinct multiple Molecular Dynamics (MD) simulations without applying any bias force to the system. It enhances the sampling by selecting the MD snapshots closest to the destination state and by restarting the MD simulations from the selected snapshots with the velocity re- randomization.
PaCS-MD was shown to be very successful in efficient sampling of protein domain motions. Here in this thesis, we describe unbiased association and dissociation simulations by PaCS-MD. We first show that PaCS-MD dissociated a small ligand, tri-N-acetyl-D- glucosamine (triNAG), from hen egg white lysozyme (LYZ) very efficiently. We performed PaCS-MD trials with 3 different simulation settings: PaCS-MD10,0.1 ns MDs per cycle), PaCS-MD100,0.1 ns MDs) and PaCS-MD10,1 (ten 1.
We found that PaCS-MD is 5 times faster than SMD. In combination with Markov State Model (MSM), we calculated the binding free energy directly from the ii PaCS-MD trajectories. In comparison, binding free energy was also calculated by the analysis of SMD trajectories using the Jarzynski equality [Jarzynski. Although SMD/Jarzynski overestimated the binding free energy, PaCS- MD/MSM yielded the results in good agreement with experimental results.
We also examined the effects of the number of replicas, the length of each MD, the velocity re- randomization, and the selection of snapshots on PaCS-MD sampling. We found that the increase of the number of replicas reduced the number of cycles required for dissociation because the probability of observing rare events is proportional to the number of replicas. The velocity re-randomization enhances the sampling in the bound state as it acts as a perturbation to raise the occurrence of rare events (dissociation). We next applied PaCS-MD to the dissociation of MDM2 protein and trans- activation domain of p53 (TAD-p53).
Binding free energy of MDM2/TAD-p53 calculated by PaCS-MD/MSM was 40.7 kJ/mol , which almost agrees with experimental value 37. Our result is more accurate than the value calculated by the MMGBSA method, 68.2 𝑘𝐽/𝑚𝑜𝑙 [Dastidar et al. We found the calculated binding free energy for each trial is strongly dependent on the dissociation pathway of TAD-p53, which is related to the dissociation of the key residues PHE19 and TRP23 of TAD-p53 involved in π-π stacking interactions between TAD-p53 and MDM2. We also employed PaCS-MD for simulating association and dissociation process of MDM2/TAD-p53, which can be considered as a flexible-body docking simulation.
We used the switching condition between the dissociation and association simulations as follows: if the association simulation does not make any progress for continuous 20 ps, it will switch to the dissociation simulation. When the inter COM distance between MDM2 and TAD-p53 reaches 2.0 nm longer than the last switching point, the association simulation will start. We performed 274 cycles of PaCS-MD and examined whether generated structures of TAD-p53 and MDM2 complex are similar to the crystal complex structure and found that the minimum RMSD was 0. In addition, TAD- p53 could bind to the correct binding interface without the guiding force.
We further examined 4 representative structures selected from all the bound conformations. Although the two key π-π stacking interactions were not formed in these structures, iii residual contacts are in agreement with those in the crystal structure with the binding interface RMSD of 0. To predict the bound conformation without prior- knowledge of the crystal structure, we examined if the conformation similar to the correct bound conformation can be identified as the lowest free energy structure. We built MSM based on the trajectories of distance RMSD (dRMSD) from the initial conformation of MDM2/TAD-p53 in the unbound state and calculated the Potential of Mean Force (PMF).
We found that dRMSD of the lowest PMF position was 4.21 nm, which the corresponding structure was identical to the structure with the lowest interface RMSD from the crystal structure. Therefore, we can select the best structure based on the calculated RMSD. In conclusion, PaCS-MD algorithm was shown to be an efficient unbiased enhanced sampling tool which can be applied to bio-molecular complexes and is highly suitable for distributed computing. Overall, PaCS-MD is faster in computational time than the other biased sampling techniques.
We are currently making an effort to apply PaCS-MD for reducing total simulation time of flexible-body docking simulation. iv List of publications 1) Duy Phuoc Tran, Kazuhiro Takemura, Kazuo Kuwata, Akio Kitao, “Protein- Ligand Dissociation Simulated by Parallel Cascade Selection Molecular Dynamics”, Journal of Chemical Theory and Computation 14, 404 (2018) v List of abbreviations COM: Center of mass MD: Molecular dynamics NPT ensemble: isothermal-isobaric ensemble NVT ensemble: canonical ensemble PaCS-MD: Parallel Cascade Selection Molecular Dynamics PaCS-MDx,y: Parallel Cascade Selection Molecular Dynamics with x replicas and its simulation time for each replica is y ns MSM: Markov State Model SMD: Steered Molecular Dynamics LYZ: Hen-egg white lysozyme triNAG: tri-N-acetyl-D-glucosamine PDB: Protein data bank PMF: Potential of mean force MM/PB-SA: Molecular mechanics/Poisson Boltzmann –Surface Area WHAM: Weighted Histogram Analysis Method RMSD: Root Mean-Squared Deviation dRMSD: distance Root Mean-Squared Deviation MFPT: Mean First Passage Time PMF: Potential of Mean Force vi Table of Contents Abstract ii List of publications v List of abbreviations vi Table of Contents vii Chapter 1. The importance of understanding association and dissociation events of biomolecular complex 2 2. Classification of binding free energy calculation and limitation of current methods 4 3.
Free energy calculation without using any biased force 6 Chapter 2. Simulation methods for binding free energy calculation 8 1. Parallel cascade selection molecular dynamics simulation method 9 2. Markov State Model in combination with PaCS-MD as a state-of-art free energy estimation tool 11 3.
Steered molecular dynamics in combination with Jarzynski equality 13 4. Weighted Histogram Analysis Method with Umbrella Sampling 15 Chapter 3. Dissociation of small ligand from its complex with protein 16 1. Result and discussion 19 3.
Interactions between LYZ and triNAG in the Bound State and the Stability of the Complex 19 3. LYZ-triNAG Dissociation by PaCS-MD 21 3. Effects of Velocity Re-randomization and Selection on triNAG Dissociation during PaCS-MD 23 3. LYZ-triNAG Dissociation by SMD 27 3.
Dissociation Pathways in PaCS-MD and SMD 28 3. Dissociation Free Energy 30 3. Disruption of LYZ-triNAG Interactions during the Dissociation Process 34 4. Dissociation Peptide from Its Complex with Protein 40 1.
Result and discussion 44 3. Equilibration of the remodeled system MDM2/TAD-p53 44 3. Free energy difference of dissociation between MDM2/TAD-p53 45 3. Structural changes during dissociation 47 4.
Flexible Docking of Protein/Peptide Complex 50 1. Result and discussion 53 vii 3. Flexibility of TAD-p53 53 3. Generating the bound conformations 54 3.
Predicting the best complex structure via MSM 57 4. Concluding remarks 60 References 62 Acknowledgements 71 viii Chapter 1. The importance of understanding association and dissociation events of biomolecular complex Association and dissociation of bio-molecular complexes play an important role in biological phenomena. For example, G Protein Coupled Receptor (GPCR) family, a seven transmembrane helices receptor, exists to be the communication channel between intra-cellular and extra-cellular environment.
Upon binding of a ligands in the case of Adenosine A2A receptor, GPCRs changes to be in active-intermediate state, and later in a fully active state upon the association of G Proteins1. After being in fully active state, following cascade events will take place that makes the organism to adapt with the external signaling2. Specifically, when drinking coffee, caffeine ligands bind to Adenosine A2A receptor, a subtype of GPCR, and deactivate Adenosine A2A leading to the reduction of stress response3,4. As shown in this example, understanding the association and dissociation of bio-molecular complex is the crucial works for thoroughly understanding the given biological phenomena.
It is obvious that there is a need for determining quantities to describe the strength of the binding in energy unit, e., “binding free energy”. For instance, let’s consider two biomolecules A and B that can bind to each other via a reaction as following: 𝑘;< 𝐴 + 𝐵 ⇄ 𝐴𝐵 (1) 𝑘;>> Here we denote the so-called quantity the association rate constant 𝑘;< to describe the rate of binding of AB, and the dissociation rate constant 𝑘;>> to represent the separation rate of the two molecules A and B from their complex AB with the concentrations [A], [B], [AB] respectively. The reaction in (1) is in equilibrium only if the concentrations [AB] does not change in the vicinity of time as follow: ?[AB] = 𝐴. 𝑘;>> = 0 (2) ?D Here, one can define the equilibrium association constant 𝐾H or equilibrium dissociation constant 𝐾? as the fraction of 𝑘;< and 𝑘;>> .B 𝐾? = = = (3) JK NLO AB From equation (3), one can directly convert the equilibrium constant to the free energy difference via the following equation.
I I ∆𝐺 = − 𝑙𝑛 𝐶 U 𝐾V = − 𝑙𝑛 𝐶 U /𝐾? (4) R R in which 𝛽 is the thermodynamic temperature and 𝐶 U is the standard concentration which is equal to 1 M. Equations (3) and (4) show the relation between the concentrations of subtances in the samples and the binding free energy of the given complex. In experiment, the common method to determine the binding free energy is from the estimation of equilibrium constant such as Isothermal Titration Calorimetry (ITC)5, Surface Plasmon Resonance (SPR)6, flourescene quenching method7, and binding assay8,9. ITC experiment is the only and the most common method directly measuring the binding kinetics of a given bio-molecular complex5.
ITC experiment measures the energy consumption to maintain the temperature in the sample cell and adiabatically identical reference cell while increasing the ligand concentration in sample cell. Although ITC is considered as high pricision method, the amount of sample used is high that limits the applicability of the methods to the protein complexes which is difficult to express massively. Moreover, the experimental methods to determine the binding free energy in general that cannot be done extensively due to the difficulty in experiment setup procedure. Therefore, computational methods for binding free energy computation are generally essential for the initial stage of the research i.
bio-molecular interaction design in general speaking or computational drug design specifically. In addition, computational methods can provide additional information on structural and dynamic properties of the given biomolecular system, which requires enormous efforts in crystallography. Up to now, the extensive development of either computing resource, accuracy of calculation methods or parameters allow in silico experiment to reduce total budget for research in screening and structural optimization.
